Geophys. J. R.ustr. SOC.(1976) 45, 245-295
Earthquake Swarms and the Semidiurnal Solid Earth Tide*
Fred W. KleinT
Lamont-Doherty Geological Observatory, and Department of Geological Sciences, Columbia
University, Palisades, New York 10964, USA.
(Revised 1975 December 10; in original form 1975 August 8)
Summary
Several correlations between peak earthquake activity during swarms and
the phase and stress orientation of the calculated solid earth tide are
described. The events correlating with the tide are clusters of swarm earthquakes. Swarm clusters from many sequences recorded over several
years are used. Significant tidal correlations (which have less than a
5 per cent chance of being observed if earthquakes were random) are
are found in the Reykjanes Peninsula in Iceland, the central Mid-Atlantic
Ridge, the Imperial Valley and northern Gulf of California, and larger
(mb2 5.0) aftershocks of the 1965 Rat Islands earthquake. In addition,
sets of larger single earthquakes on Atlantic and north-east Pacific fracture
zones are significantly correlated with the calculated solid tide. No tidal
correlation, however, could be found for the Matsushiro Japan swarm of
1965-1967. The earthquake-tide correlations other than the Reykjanes
Peninsula and Mid-Atlantic Ridge can be interpreted as triggering caused
by enhancement of the tectonic stress by tidal stress, i.e. the alignment of
fault and tidal principal stresses. All tidal correlations except in the
Aleutians are associated with oceanic rifts or their landward extensions.
If lithospheric plates are decoupled at active rifts, then tidal stresses
channelled along the lithospheric stress guide may be concentrated at ridge
type plate boundaries. Tidal triggering of earthquakes at rifts may reflect
this possible amplification of tidal strains in the weakened lithosphere at
ridges.
1. Introduction
Tidal triggering of earthquakes has always seemed feasible, since crustal stresses
of the solid earth tide are of the order 0-03bar, or about lo-’ to
of the stress
drop of earthquakes. Nevertheless, most searches for a significant earthquake-tide
correlation have been unsuccessful.
An approach which has failed to demonstrate significant tidal triggering is the use
of large catalogues of earthquakes from a large geographic area. Any tidal correlation
of earthquakes in a small region, in a certain magnitude range, or of a particular
type such as aftershocks may be masked by averaging with a large sample of random
* Lamont-Doherty Geological Observatory Contribution No. 2315.
245
246
F. W. Klein
earthquakes. Clearly, there is a trade-off between using a statistically large sample of
earthquakes and isolating smaller sets of earthquakes from tectonically different
regimes. This paper primarily examines swarms (earthquake sequences localized in
space and time and not dominated by an initial mainshock) from submarine rifts or
their landward extensions. Correlations are made between earthquakes from small
regions believed to be of nearly uniform crustal stress and the semidiurnal tide.
The search for an earthquake-tide correlation is conducted by computing tidal
functions at the time and place of the earthquake events. The events are either
clusters in time of swarm earthquakes, or the larger earthquakes in a given area. These
events must be independent of one another in the sense that they are separated in
time by at least several hours. Thus a cluster of five earthquakes in the same hour is
counted as one event independent from another cluster 13 hr later. A successful
correlation as used in this paper means that earthquake events occur primarily
during a certain part of the tidal cycle. This paper is not a search for periodicity
in earthquake occurrence, but a study of correlations between the phase of the semidiurnal tide and earthquake events.
The patterns of failure and success of other authors suggests that earthquake-tide
correlations can best be found within localized earthquake sequences such as aftershocks or swarms. Though the statistical significances and physical interpretations
of many published correlations can be debated, references are made to show where
correlations have generally been found. No correlation with the semidiurnal tide was
found for large catalogues of southern California earthquakes (Knopoff 1964), central
California earthquakes (Willis et al. 1974), or global earthquakes (Simpson 1967;
Shlien 1972). A correlation of microaftershocks with the tide was noted by Ryall,
Van Wormer & Jones (1968) for the 1966 Truckee California earthquake and by
Hofmann (1961) for microaftershocks of the 1959 Hebgen Lake earthquake. Heaton
(1975) found that tidal stresses acted in the slip direction for a set of shallow dipslip
earthquakes for which the focal mechanisms are known. Moonquakes correlated
well with the lunar fortnightly tide and occur at definite times in the nodical (librational)
month (Lammlein et al. 1974). Tamrazyan (1974) notes a fortnightly tidal correlation
of the 1966 Tashkent earthquakes and its 14 largest aftershocks, which occur at
times of extreme lunar declination. Filson, Simkin & Leu (1973) found that the first
large swarm earthquakes associated with a caldera collapse in the Galapagos Islands
occurred at 6-hr intervals at times of tidal extrema. Mauk & Kienle (1973) demonstrated the tendency of swarm microearthquakes at Alaska’s St Augustine volcano to
occur near either peak solid or ocean tide. Kayano (1973) noted a tidal correlation
of 12 small earthquakes (1 ‘9 G M < 3.3) which occurred during a 10-day period in
Okayama Prefecture, Honshu. In addition Mauk & Johnston (1973) showed that
global volcanic eruptions correlate with the fortnightly tide and tend to occur at the
times of maximum tidal amplitude. Hamilton (1973) obtained similar results. The
close tectonic association of volcanic activity and earthquake swarms suggests that
tidal influences might be seen in swarm occurrences as well. In addition, several
examples of tidal influence on ground water, artesian wells, and geysers have been
cited (George & Romberg 1951; White 1968; Rinehart 1972a, b; Marine 1975;
Wakita 1975), which could in principle influence seismicity through fluctuations in
pore fluid pressure.
If it is ultimately established that swarm earthquakes are frequently triggered by
tides, then constraints will be placed on either the physical mechanism of swarms or on
the special geological conditions where they occur. Based partly on laboratory
microfracturing experiments, Mogi (1963) proposed that earthquake swarms are
associated with inhomogeneous physical properties or non-uniform stress in the
faulting medium, whereas mainshock-aftershock sequences are associated with
uniform properties and stress. The stiffness model of faulting of Nur & Schultz
(1973) explains swarm seismicity when fault friction and stress are non-uniform.
Earthquake swarms
247
Seismicity induced by concentrated sources of stress or fluid pressure, such as reservoirs or disposal wells, is generally of the swarm type.
Sykes (1970b) noted the correlation between earthquake swarms and areas of
submarine rifting or volcanism. The heterogeneous structures and stresses of
volcanic areas could then make swarms possible, and also limit earthquake size
because of short rupture zones and the relatively low strength of fractured or volcanic
areas. By analogy with the swarm accompanying the Fernandina Caldera collapse
in the Galapagos, Francis (1974) proposed that swarms in volcanic rift areas such as
the Mid-Atlantic Ridge may be generated when supporting magma pressure drops
and caldera floors or median valleys collapse.
The simplest tidal function to compute at the Earth's surface is the vertical component of tidal force, expressed as upward acceleration or change in gravity. The
procedure followed here is to compute the phase of the semidiurnal gravity tide at
the times of the earthquakes. Then a correlation is made between the earthquake
events and the phase of the semidiurnal gravity tide, rather than the gravity tide
itself. Since the strain tidal functions have the same period as the gravity tide, any
strain tidal correlation will be revealed by the distribution of earthquakes with respect
to the phase of the gravity tide. If a correlation is found, a triggering mechanism
can be sought by comparing tidal stresses with earthquake faulting mechanisms and
the regional tectonic stress.
Earthquakes are compared here with the semidiurnal tide because it is generally
the largest tidal component. A semidiurnal tidal correlation of earthquakes means
that tides are one of the most important triggering mechanisms on the time scale of
several hours. Fortnightly and longer period tides compete with other triggering
mechanisms on longer time scales, such as possible pore fluid flow into a dilatant
region preceding an earthquake (Scholz, Sykes & Aggarwall973).
Earthquake-tide correlations with a probability of random occurrence of less than
5 per cent occur at the Reykjanes Peninsula in Iceland, the central Mid-Atlantic
Ridge, the Imperial Valley and northern Gulf of California, and north Atlantic and
north-east Pacific fracture zones. Tidal triggering also appears to control larger
aftershocks of the 1965 Rat Islands earthquake. Earthquake swarms in the north-east
Pacifictend to occur at two points in the tidal cycle, possibly reflecting two populations
of faulting mechanisms in the data sample. Correlation of reservoir induced swarms
with the tides is the subject of another paper (Klein 1976). The Matsushiro swarm, one
of the largest ever recorded, apparently displays no semidiurnal tidal correlation.
Thus, earthquakes on several parts of the world rift system are significantly
correlated with the semidiurnal tide. Tidal triggering at rifts may reflect a possible
channelling of tidal stresses along the lithospheric stress guide and a concentration
of stress and strain at the weaker spreading centres.
Unlike most other studies of earthquake-tide correlation, this work attempts to
identify possible mechanisms of tidal triggering. For all areas treated except the
Reykjanes Peninsula and the central Mid-Atlantic Ridge, tidal stress apparently is
oriented to enhance tectonic stress when earthquakes occur. Loading by ocean tides
influences some observed tidal correlations, especially for near-coastal earthquakes
and submarine earthquakes involving uplift or subsidence. Pore fluids can also
alter the time in the tidal cycle at which fault slip would occur.
The plan of this paper is first to explain the methods used to correlate swarm
earthquakes with the tides and to estimate the significances of correlations when found.
The tidal correlations of swarms and other earthquake data are then discussed and
interpreted for each region individually. Finally, a discussion of features and interpretations common to many regions is presented with their implications. The appendices contain an explanation of the calculation of tidal strain functions, tables of the
F. W.Mein
248
5 -loot
II
I
t
20
JULY, 1950
IMPERIAL VALLEY
FIG.1. Seismicity and upward tidal force (gravity tide) as a function of time for an
earthquake swarm in the Imperial Valley. Note the tendency of earthquakes to
cluster together into subswarms, or bursts of activity lasting an hour or two. The
largest events of three out of the four subswarms occur when the semidiurnal
component of the tide is rising.
earthquake swarms used in this paper, and a method for evaluating the significance
of complex distributions of earthquakes in the tidal cycle.
2. Correlating earthquakes with the semidiurnal tide
Earthquake sequences usedfor tidal correlation
Earthquakes in this study are separated into mainshock-aftershock and swarm
categories, and tidal correlations are made separately for each group. Mogi (1963)
classified earthquake sequences into three types: type 1 is a mainshock with aftershocks,
type 2 is a mainshock with foreshocks and aftershocks, and type 3 is a swarm sequence
not dominated by a mainshock. In this work types 1 and 2 are grouped together, and
all remaining sequences are taken to be swarms. Mainshock-aftershock sequences
are here defined as dominated by a single shock at or near the beginning of the
sequence which is at least one half magnitude unit larger than the second largest event.
The criterion for discriminating a swarm from a mainshock sequence depends on the
relative magnitude and placement of the largest shock among the larger earthquakes
of the sequence. Therefore only the larger shocks are needed to determine sequence
type, and classification and tidal correlation are attempted in this study when as few
as the three largest events are reported, provided they occur within about 2 hr of each
other.
Earthquakes within swarms are seldom stationary in time: events frequently
cluster into subswarms as in Fig. 1. Single earthquakes in the subswarms are in some
way dependent on each other, and it is the subswarms which are taken as the independent events used for correlation. The subswarms are typically about 2 hr in length
Esrthquake swarms
249
and are long enough to be a statistically significant event and short enough to resolve
the phase of the semidiurnal tide. The phase of the semidiurnal tide is computed at
the time of the largest earthquake in the subswarm. The distribution of earthquakes
and subswarms with respect to tidal phase is then examined for a possible earthquaketide correlation.
Calcitlation of tidal functions
The tidal functions used for comparison with earthquake sequences are based
on the tidal formulas of Longman (1959) and Pollack (1973). Longman provides
closed form expressions for the zenith angles and distances of the Moon and Sun.
From these expressions one may calculate the vertical component of the tidal gravity
force (expressed as acceleration) caused by the Sun and Moon at any particular
time. The phase angle of the semidiurnal tide is measured from the peak upward
force of the semidiurnal component, which corresponds to maximum ground uplift
and to minimum total gravity. Pollack provides closed form expressions for the
azimuth to the Sun and Moon at any point on the Earth's surface, which are calculated
from the same orbital parameters computed by the Longman formulas. Other tidal
functions, namely the horizontal strain components, may be calculated from the
celestial positions and distances of the Sun and Moon (see Appendix A).
All earthquakes examined in this study are sufficientlyshallow that the free surface
boundary condition may be applied. Thus the vertical tidal stress T~~ vanishes at the
surface and the total vertical stress at shallow depths is the nearly constant lithostatic
stress. Vertical tidal stresses are about lod4bar at a depth of 10 km as compared with
bar. Thus it is sufficient to calculate only
the horizontal tidal stress of about
horizontal tidal stresses.
Correlation with tidal stress
Once a tidal correlation has been found by comparing times of earthquakes in a
particular region with the gravity tide, the correlation can be interpreted in terms of
tidal stress. A rigorous treatment would require the calculation of the tidal stress
history on the fault plane of the earthquake. But focal mechanism solutions are
available for only a few of the earthquakes treated in this paper. We therefore must
compare the tidal stress at the time the correlation occurs with the general type of
faulting expected and the regional tectonic stress.
Table 1 summarizes the variations of tidal strain during the semidiurnal tidal
cycle. The table can be used to determine the approximate time in the tidal cycle at
which tidal stress most enhances slip on a given fault.
An important tidal strain parameter is the direction of greatest extension, or
azimuth of the least compressive horizontal strain. During one semidiurnal tidal
cycle, tidal phase increases at a constant rate from peak solid tide to peak solid tide.
During the same interval, the extensional azimuth in the Northern Hemisphere at
latitudes above 20" sweeps from north through east to south. Since the strain field is
bipolar, it sweeps simultaneously from south through west to north. The extensional
azimuth, however, does not increase at a uniform rate, but sweeps through easterly
azimuths more slowly than northerly. The distribution of extensional azimuths of
random events is peaked toward the east, and the relative size of the peak increases
with decreasing latitude. The distribution of the azimuths of tidal extensional strain
is shown in Fig. 2 for several latitudes.
The extensional azimuth indicates the orientation of the shear component of the
horizontal tidal stress, and can always be used to tell whether tidal shear stress enhances
or retards slip on strike-slip faults. Thus for the tide to enhance slip on an EW
striking right-lateral fault, the tidal extension direction must be in the NE quadrant.
This occurs between 0 and 180" of tidal phase for faults above 20" latitude. For
D
250
F. W. Klein
Table 1
Semidiurnal tidal strains
Tidal
phase
Tidal strain
Lat < 20"
20" < Lat < 50"
50" < Lat
Areal Hor.Shear Ext. Dir. N SS T Ext. Dir. N SS T Ext. Dir. N SS T
0"
90"
180"
270"
Max
Min
Min
Max
N
ENE,ESE*
ENE,ESE*
ENE,ESE*
+
+
++
+
N
ENE
E
ESE
+
+
++
+
N
NE
E
SE
Depends
on
fault
strike
* The extensional direction is nearly constant during most of the semidiurnal cycle, but
alternates between ENE and ESE in successive semidiurnal cycles.
Table 1. Chart showing the variations of tidal strain during the semidiurnal tidal cycle. Areal
strain is greatest at peak tide (0' of tidal phase), and horizontal shear strains are greatest at minimum
tide (180" of phase). The principal extension direction is given for three latitude ranges. For latitudes
above 20", note that the strain field rotates and the extension direction sweeps clockwise through all
azimuths. The table also indicates what types of faulting are most enhanced at different tidal phases.
Below 50" latitude, normal faulting is generally enhanced at peak tide, but strike-slip and thrust
faulting are favoured at minimum tide. Slip on faults above 50" latitude and on strike-slip faults
is most enhanced when tidal and tectonic extension directions are nearly the same. The table applies
to faults in the Northern Hemisphere. For observers in the Southern Hemisphere, south and north
should be interchanged wherever they appear.
latitudes above 50°, the tidal extension direction determines the sense of shear on
dip-slip as well as strike-slip faults. For example, normal faulting is most enhanced
when the linear tidal extension parallel to the tectonic extension is greatest. For
latitudes above 50°, this occurs near the time when the direction of principal tidal
extension coincides with the tectonic extension direction. At latitudes less than 50°,
normal faulting is generally enhanced near peak tide, regardless of fault strike.
I
N
I
I
N20E
AZIMUTHAL DISTRIBUTION
OF PRINCIPAL EXTENSIONAL
TIDAL STRAIN
1
FOR RANDOM EVENTS
N40E
0
1
2
3
4
RADIAL COORDINATE: PROBABILITY DENSITY
1 UNIT = V(9ODEG)
FIG.2. Azimuthal distributions of the principal extensional tidal strain, for
randomly occurring events. The curves are for various latitudes on the Earth at
10" intervals. The curves are symmetrical about the NS and EW directions. For
latitudes far from the poles, the direction of tidal extensional strain is more likely
to be oriented EW than NS.
Earthquake swarms
251
Significance of correlations
One test of significance used here is Schuster’s test (ShIien 1972). It measures the
tendency of a set of events to occur near the same point in the tidal cycle, and requires
no a priori assumptions such as grouping of data. The method vectorially adds the
phases of the events, and if a phase correlation exists many events are at the same
phase and the resultant vector is long. If lCli are the semidiurnal tidal phases of the
events, and A = C COS$~, B = C sin@i, then the resultant vector is of length
R = J ( A 2 + B 2 ) and at phase 4 = tan-’(B/A). The probability that the resultant
length is greater than R is a measure of the significance of the correlation and is
P = e-R2/n,
where n is the number of events and n Z 10. The smaller the value of
P, the better the correlation.
Some distributions of events with respect to tidal phase may have physical significance, but are not simply biased to a single tidal phase. Such might be the case for a
phase distribution with two independent peaks. A method for calculating the
probability of seeing a particular distribution such as one narrow peak or two peaks
is given in Appendix C.
Another significance test is used for sets of strike-slip earthquakes for which the
focal mechanism is known. Given the probabilityp that one earthquake occurs when
tidal stress enhances fault slip, the method computes the probability P that m or more
out of n earthquakes occur at favourable times. An earthquake-tide correlation will
be seen as a tendency of earthquakes to occur when tidal shear enhances slip, which
yields a large m and a small value of P. The probability that exactly m events occur
at favourable times is given by the binomial distribution. We seek a more realistic
and strict test and sum to obtain the probability that m or more earthquakes occur at
favourable times and get
P=
m‘=m
n!
p”‘(1-py-m’.
rn’!(n-m’)!
The value o f p depends on the strike of the fault and on the earthquake latitude,
and can be obtained from the curves of Fig. 2. Though the binominal distribution is
strictly valid only for sets of earthquakes with the same p values, the p values for the
earthquakes considered are nearly the same and their geometric mean has been used
in the significance test.
3. Analysis of individual regions
Imperial Valley and Northern G u y of California
Tectonics and seismicity. The plate boundary in the Gulf of California and its
northward extension into the Imperial Valley mark the transition between the East
Pacific Rise and the San Andreas Fault to the north. The plate tectonics model
of this transition region (Fig. 3) is a series of en echelon transform faults offset by
miniature spreading centres which are tens of kilometres in size (Lomnitz et al. 1970;
Thatcher & Brune 1971; Elders et al. 1972). The spreading centres are characterized
by geothermal activity, recent volcanism, earthquake swarms, or submarine topographic depressions, and are thus similar to other parts of the world rift system.
Dextral strike-slip faulting generally characterizes the plate boundary from the
southern Imperial Valley near the international border south to the Wagner Basin
and in the mid Gulf region south of the Delfin Basin (Sykes 1968; Thatcher & Brune
1971; Tatham & Savino 1974). The spreading centres are probably characterized by
combinations of normal and strike-slip faulting (Thatcher & Brune 1971; Hill et al.
1975).
252
F. W. Klein
115.
114.
SWARM SEQUENCE
MAINSHOCK-AFTERSHOCK SEQUENCE
/ MAJOR FAULT
0
'
,PROPOSED OR INFERRED SPREADING
CENTER OR FAULT
WAGNER
BASIN
31'
(\-
.J
/'
v\oL GULF O F
\\
\
CALIFORNIA
*
\
\
30'
29'
I
I
I
I
I
Fro. 3. Map of the Imperial Valley-Gulf of California region. The earthquake
sequences shown are those used in the tidal correlation and are listed in
Tables B1 and B2. The Imperial Valley locations are from the Caltech network, and
those in the Gulf are from PDE listings. The scatter in locations results from poor
station coverage. The plate boundary through this region has been interpreted as a
series of transform faults offset by small spreading centres, and is generally
characterized by ESE to SE tensional stresses.
The seismicity near the spreading centres is also a combination of swarm and mainshock-aftershock sequences. Fig. 3 shows the earthquake swarms and mainshocks
used for tide correlation, and which are also listed in Tables B1 and B2. The Imperial
Valley sequences are those detected by the Caltech network, and the location is that of
the largest event in the sequence as reported by Hileman, Allen & Norquist (1973).
Earthquake swarms
253
IMPERIAL VALLEY & NORTHERN GULF
OF CALIFORNIA 1934- 1973
PHASE OF SEMIDIURNAL GRAVITY TIDE
I
t
MAINSHOCKS AND
MS
AFTERSHOCK CLUSTERS
SWARM CLUSTERS
FIG.4. Tide phase diagrams for 43 earthquake swarm clusters (left) and 40 mainshocks and aftershock clusters (right) from the Imperial Valley and northern Gulf of
California. The figures are histograms of earthquake events as a function of
phase of the semidiurnal earth tide. The earthquake events are counted into 20"
sectors of tidal phase. Time and tidal phase increase clockwise. Note the strong
correlation of swarms with a rising solid tide (significant to a probability of
O-O0046), and the lack of tidal correlation of mainshocks. Points in the tidal cycle
are: PS and MS, peak and minimum solid tide; POSD and MOSD, peak and
minimum ocean tide at San Diego; and PONG and MONG, peak and minimum
ocean tide in the northern Gulf.
Only sequences near the southern end of the Salton Sea between the limits of 32.8"
to 33.3"N and 115.4" to 116-4"W have been plotted in Fig. 3 or used for tide
correlation. Sequences in the Gulf are taken from Preliminary Determination
of Epicenters (PDE) and CaItech lists, with PDE locations used if different from
Caltech's.
The scatter of locations is a result of poor station coverage. Location accuracy
does not allow swarms and mainshocks to be separated into different regions or
faults, but swarm sequences are less common outside the Imperial Valley and northern
Gulf regions. Though both swarms and mainshocks occur in the same areas, they
represent locally different physical conditions which respond differently to the tidal
triggering forces.
Tidal correlations. Many of the sequences plotted in Fig. 3 contain tight clusters
of 3 or more earthquakes. Fig. 4 is a histogram of number of swarm clusters (left)
and mainshocks (right) as a function of their semidiurnal tidal phase. Peak tide is at
the top, and time increases clockwise. Fig. 5 is a histogram of the same data as a
function of the azimuth of principal extensional tidal strain, with north at the top.
It is apparent from Fig. 4 that swarm clusters occur primarily between 180" and
360" of phase, i.e. when the solid tide is rising. The probability of seeing this strong a
correlation between swarms and the semidiurnal tide is 0-00046.Note that the phase
distribution of mainshocks and aftershock clusters, however, is not significantly
different from random, implying that only swarms respond to the triggering mechanism. Furthermore, swarms in the Imperial Valley and northern Gulf both
correlate with a rising solid tide. The times of rising solid tide correspond approximately to times of NW-SE directed tidal extensional strain as shown by the high
swarm occurrence in this quadrant in Fig. 5. Clearly there is a strong tidal effect on
swarm occurrence, and both solid tidal strains and ocean tidal loading provide
plausible mechanisms for this effect.
254
F. W. Kleh
IMPERIAL VALLEY & NORTHERN GULF
O F CALIFORNIA 1934-1973
AZIMUTH
OF EXTENSIONAL STRAN
AZIMUTH
DISTRIBUTION
IF EARTHQUAKES
WERERANDOM
IN TIME
SWARM CLUSTERS
MAINSHOCKS AND
AFTERSHOCK CLUSTERS
FIG.5. Histograms of azimuths or principal extensional tidal strain of the same
earthquake data plotted in Fig. 4. The earthquake events are counted into 10"
sectors of azimuth. Note the strong tendency of swarm clusters to occur when the
tidal extension is in the NW-SE quadrant.
Triggering mechanism. One possible triggering mechanism is the enhancement of
tectonic stress by solid tidal stress. If faulting was pure normal, the tidal stress most
favourable to faulting would occur at 0" of tidal phase (Table 1). If faulting was pure
right lateral strike-slip on NW to NNW striking planes, tidal stress enhances slip
between 180" and 270" of tidal phase. Hill et al. (1975) obtained a largely strike-slip
focal solution for a swarm near the south end of the Salton Sea. Thatcher & Brune
(1971) present a focal mechanism for the Wagner Basin with nearly equal normal and
strike-slip components. These two types of faulting (and other faulting which combines
both types) are most enhanced by tidal shear at times following 180" and preceding
0" of tidal phase. These are the times when swarm activity is highest. Note also that
swarms tend to occur when the tidal extensional azimuth is ESE, which is the direction
of tensional axes of focal mechanisms in the area.
Ocean tidal loading. The effect of the ocean tides on the Pacific coast and in the
northern Gulf of California must also be considered. The ocean tides at San Diego
and in the northern Gulf are nearly in phase, and both peak around 280" of solid
tidal phase (Fig. 4). While tidal amplitudes are about a metre at San Diego, the
amplitude increases northward in the Gulf, averaging 4 or 5 m over the earthquake
swarm regions (Roden 1964).
With such high tidal amplitudes in the northern Gulf, the stress from ocean
tidal loading must dominate all other tidal stresses, especially when dip-slip faulting
is involved. Lateral variations in ocean load can introduce additional shear stresses,
but the largest effect of ocean load is an increase in the vertical principal stress. The
vertical stress resulting from ocean loading would be about half a bar in the northern
Gulf, and for submarine earthquakes should enhance normal faulting near high ocean
tide. The solid and ocean tidal triggering mechanisms have their maximum effect
at the same times in the tidal cycle. Thus it is impossible to identify which mechanism
might be operating on submarine faults except to note that ocean loading stress should
be an order of magnitude greater than solid tidal stress for normal faults. Ocean
loading should have a smaller effect on strike-slip faults.
The ocean loading effect is much smaller in the Imperial Valley than the northern
Gulf. No strains caused by ocean loading have been computed here, but Berger &
Loveberg (1970) found that ocean tides accounted for about 20 per cent of observed
Earthquake swarms
255
tidal strain 15 km from the Pacific coast. Since the Imperial Valley is over 100 km
from both Pacific and Gulf coasts, ocean loading strains should be much smaller than
solid tidal strains. The only effect of ocean tides considered here is the direct loading
effect on submarine earthquakes in the northern Gulf.
It is interesting to note the different behaviour of swarms and mainshocks. In the
northern Gulf, swarm clusters and mainshocks both occur during rising solid tide.
In the Imperial Valley, however, the difference is striking. The 28 mainshocks occur
randomly with respect to the semidiurnal tide, so the times at which they occur must
be controlled by some mechanism different from that of swarms. It is an important
constraint on the physical conditions necessary for the occurrence of swarms in the
Imperial Valley that they are susceptible to tidal stress when it is oriented to enhance
the regional tectonic stress.
Mid-Atlantic Ridge
Swarm occurrence. Earthquakes originating on the Mid-Atlantic Ridge often
cluster into earthquake swarms (Sykes 1970b; Francis 1968a; Francis & Porter 1971).
The Mid-Atlantic Ridge sequences are taken from several sources, namely the PDE
listings of the Coast and Geodetic Survey and its successors, Sykes (1970b), and
published bulletins of the Reykjavik seismic station in Iceland, 1944-1967. Times
and magnitudes of additional earthquakes for many sequences were read by the author
by matching events with similar wave strains on seismograms recorded at Palisades,
New York.
The sequences used in this study are listed in Table B3, and their locations are
plotted in Fig. 6. Only sequences with three or more earthquakes are used, and no
single events are considered. The detection of PDE earthquakes is better north of the
equator. The large number of swarms plotted on the Reykjanes Ridge reflect both
this and the inclusion of sequences recorded in Iceland before the PDE earthquake
listing began. The map is not to be taken as an indication of relative seismic activity
but it shows the locations of swarms versus mainshock-aftershock sequences.
Separation of swarm and mainshock-aftershock sequences. Fig. 6 shows that
mainshock-aftershock sequences occur primarily on or near fracture zones. Swarms,
which account for most of the sequences detected, are located primarily on or near
ridge crests and zones of active rifting. Of 16 mainshocks plotted, only two near
the Atlantis F.Z. are not closely related to a major offset of the ridge crest. The
association of swarms with spreading ridge crests is also strong. Sections of the
rift without major transform fault offsets show only swarm activity, such as the
Reykjanes Ridge and the section of ridge just north of the Azores. The three swarms
plotted on the western section of the Azores-Gibraltar plate boundary are consistent
with the dilatational tectonics of that area shown by McKenzie (1972). Two swarms
apparently occur on transform faults far from the ridge crest, namely on the Oceanographer F.Z. and near Jan Mayen Island. It is possible that swarms are associated
with small and unmapped spreading segments which may offset the fracture zone.
The occurrence of swarms primarily on the ridge crest and mainshock-aftershock
sequences primarily on transform faults implies different clustering properties for
earthquakes in these two regions. For many of the smaller mainshock-aftershock
sequences, only the mainshock will be reported. The small swarm, however, is more
likely to be reported as a cluster of events, since the difference in magnitude of the
largest and next largest events is less than for a mainshock sequence. Thus the fraction
of earthquakes occurring in a cluster will be greater for swarms and ridge segments,
than for mainshocks and transform faults. Francis & Porter (1971) have, in fact,
demonstrated that earthquakes from ridge crests cluster in both space and time
proportionally more than earthquakes from transform faults.
256
F. W.K l e h
80'
70'
60'
40'
20
0'
20
40
60
FIG.6. Locations of the 85 earthquake sequences on the Mid-Atlantic Ridge listed
in Tables B3 and B5. An earthquake sequence must contain at least three events
grouped very closely in space and time. No single earthquakes are plotted.
Swarm sequencesare shown as solid circles and occur primarily on or near sections
of ridge crest. Mainshock-aftershock sequences are plotted as open circles, and
occur primarily on or near transform faults. Numbers indicate more than one
sequence in the same location.
257
Earthquake swarms
From the separation of swarm and mainshock sequences into ridge crests and
transform faults one can infer an approximate correlation between sequence type and
faulting mechanism. Most of the swarms are associated with the normal faulting
characteristic of the ridge crest (Sykes 1967, 1970a), and most mainshocks with strikeslip faulting on transform faults. There are exceptions to this rule, however. Examples
of strike-slip faulting during swarms are given by Klein, Einarsson & Wyss (1973)
and Tatham & Savino (1974). Sykes (1967) demonstrated normal faulting for a
Mid-Atlantic Ridge mainshock. These three examples, however, all occurred near
ridge crest-transform fault intersections. Thus, the occurrence of earthquakes in
swarms is not implied by a normal faulting mechanism. Swarm occurrence seems
instead related to physical conditions typical of the ridge crest, such as presence of a
thin Iithosphere, heterogeneous structures, caldera collapse (Francis 1974), or high
magma or fluid pressures. These conditions may be present on some transform
faults, usually near their intersection with the ridge axis where the lithosphere is very
thin.
Swarm statistics. Studies of the statistics of earthquakes on the Mid-Atlantic
Ridge suggest different physical conditions on ridge crests and transform faults.
Francis (1968a, b) has shown that the slope of the cumulative frequency versus magnitude distribution, or b value, is systematically greater for earthquakes on ridge crests
than for those on transform faults. A high b value, i.e. high percentage of small earthquakes, is found for events occurring under conditions of low stress. This has been
demonstrated for rock microfracturing in the laboratory (Scholz 1968), and for earthquakes (Wyss 1973). The dominance of swarm type sequences, absence of large
( M > 6) earthquakes, high b values, and the inferred low stress in the rift zones,
suggest a shallower brittle-ductile transition on ridge crests than on transform faults.
Variations in ductility along the ridge may account for variations in seismic energy
MID-ATLANTIC RIDGE SWARMS
7'- 50' N
IPS
SEMIDIURNAL
GRAVITY TIDE
pHAsEoFQ
54O- 62O N
1ps
0
AZIMUTH OF
EXTENSIONAL
STRAIN
FIG.7. Histograms of earthquake swarm clusters from the Mid-Atlantic Ridge are
plotted as a function of semidiurnal tidal phase (top) and azimuth of principal
extensional strain (bottom). The data include 14 swarm clusters from the central
portion of the ridge between the Z and Charlie-GibbsFracture Zones (left) and 13
swarm clusters from the Reykjanes Ridge (right). Peak solid tide (0' of phase) is
shown by PS. Swarms from the central Mid-AtlanticRidge correlate with minimum
solid tide to a probability of 4.3 per cent. Swarms from the Reykjanes Ridge occur
randomly with respect to the semidiurnal tide,
258
F. W. Klein
release as noted by Francis (1973) along the Reykjanes Ridge. The relatively high
seismicity of the ridge in the Atlantis F.Z. region may be caused by a deeper brittle
zone there. This would promote not only more earthquakes but higher stress levels,
which could be associated with the two mainshock-aftershock sequences on the ridge
axis. Thus for the Mid-Atlantic Ridge, swarms are usually associated with the ridge
crest, the absence of large earthquakes, high b values, probable low stress, and a
possible shallow transition from brittle to ductile conditions.
Tidal correlation of Mid-Atlantic Ridge swarms. Swarms and clusters of earthquakes from the Mid-Atlantic Ridge are listed in Table B3, and their tidal phases
and extensional azimuths are plotted in Fig. 7. Two portions of the Mid-Atlantic
Ridge offer a sufficient number of swarms in a region of fairly uniform spreading to
attempt a tidal correlation. These are the Reykjanes Ridge and the central MidAtlantic Ridge between the Charlie-Gibbs and Z Fracture Zones. Swarms from the
Reykjanes Ridge show no tidal correlation. On the central portion of the Ridge,
however, swarms significantlytend to occur near minimum solid tide with a probability
of 0.027. Since most of these swarms presumably involve normal faulting, it is surprising that the correlation is not with peak solid tide when normal faulting would be
most enhanced at these latitudes (Table 1). Notice, however, that the correlation of
swarms with minimum solid tide corresponds to times when the direction of principal
tidal extension is ESE, or nearly parallel with the spreading direction on this portion
of the ridge.
The direct effect of ocean tidal loading on vertical stress could also act as a trigger
for normal faulting. For ocean tides of 50-cm amplitude, the vertical stress due to
loading is comparable to the amplitude of the horizontal stresses of the solid tide.
The amplitude and phase lag of the ocean tide are poorly known in the open ocean and
vary in phase and amplitude along the ridge. Thus the effect of the ocean tides on
stresses cannot adequately be considered here.
Since fault plane solutions are not available for these earthquakes, it cannot be
determined whether shear stress on the fault plane enhances (strike-slip mechanisms)
or retards (normal mechanisms) faulting at minimum solid tide. Although triggering
by ocean loading cannot be ruled out, swarms on the central Mid-Atlantic Ridge tend
to occur when the tidal extensionalazimuth is directed parallel to the tectonic extension
direction.
Mainshocksfrom Mid-Atlantic fracture zones
Since most mainshocks are located on fracture zones and are strike-slip, it makes
physical sense to seek a correlation with the horizontal stresses resolved on the fracture
zone. This has been done for the 16 earthquakes in Table B4. The table also lists their
' stress angles ', i.e. the angle between the direction of greatest tidal extension at the
time of the earthquake and the azimuth of the fracture zone. These stress angles are
pIotted in Fig. 8. The set of earthquakes used is taken from north Atlantic events
of known strike-slip focal mechanism and from larger mainshocks inferred as strikeslip from their location on fracture zones far from ridge crests. For earthquakes with
no focal solution, the fault azimuths are taken from Minster et al. (1974).
For 14 of the 16 fracture zone earthquakes the sense of tidal shear matches the
observed displacement, i.e. the stress angles are less than 90". The curves of Fig. 2
and the fracture zone azimuths may be used to calculate for each epicentre the probability that its stress angle is less than 90". Since the mean Probability is 0.532, earthquakes are slightly more likely to occur with a stress angle less than go", but the
probability of 14 out of 16 doing so is only 0.0044. The only earthquake in this set
not between ridge crests is the Tjornes event of 1963 March 28. Sykes (1967) has
shown that its right-lateral shear displacement is in the same sense expected for
earthquakes to the east between the ridge crests. It is interesting to note that this is
Earthquake swarms
259
ANGLE OF
TIDAL EXTENSION
FROM FRACTURE
ZONE AZIMUTH
MID-ATLANTIC KDGE 7 O N - 7 5 O N
FRACTURE ZONEEARTHQUAKES
FIG.8. Stress angles of the 16 earthquakes from Mid-Atlantic fracture zones listed
in Table B4. The stress angle is the angle between the least compressive tidal stress
and the fracture zone azimuth. For 14 of the 16 earthquakes, the tidal shear on the
strike-slip fault is in the same direction as the fault displacement. The long marks
represent earthquakes of known strike-slip focal mechanism, and the short marks
are mainshocks on fracture zones distant from ridge crests with an inferred strikeslip mechanism.
one of the two events whose displacement is opposite to the tidal stress. The tectonic
stress near this earthquake is surely complicated by proximity to Iceland and by its
position west of both spreading centres. The correlation between tidal and tectonic
stress for the remaining events, however, is remarkable.
Reykjanes Peninsula, Iceland
Tectonics. The Reykjanes Peninsula forms the landward extension of the MidAtlantic Ridge and is the south-westernmost part of the neo-volcanic zone of Iceland.
The surface geology is characterized by glacial and post-glacial lavas, extensional
features such as normal faults and open fissures, and active geothermal areas. Klein
et al. (1973) demonstrated that focal mechanisms of microearthquakes can be of
both normal and strike-slip type. They interpreted the tectonics of the Peninsula as
transitional between a spreading ridge cpest and transform fault. Earthquake swarms
dominate the seismicity, and swarm earthquakes may be of either normal or strike-slip
mechanism. Although faulting may be of different types, the tensional axes of the
focal mechanism solutions are uniformly NW and horizontal. Thus the earthquakes
respond to similar tectonic stress orientation regardless of location or fault type.
Swarms and tidal correlation. The earthquake swarm data examined here are
from four sources: (1) bulletins of the Reykjavik seismic station 1954-63, (2) an
unpublished list of earthquakes of the September 1967 swarm (Tryggvason 1973,
and personal communication), (3) data from the September 1972 swarm (Klein et al.
1973), and (4)unpublished data from the University of Iceland seismic array, 1971-73,
made available through the generosity of Sveinbjorn Bjornsson. The list of swarms
and earthquake clusters identified appears in Table B6. The tidal phases are plotted
in Fig. 9 for the Reykjanes earthquake clusters with at least three earthquakes of
magnitude two or larger. Seismicity as a function of time is shown in detail for the
best-recorded swarm, that of September 1972, in Fig. 10.
Swarm clusters during the September 1972 swarm appear to be tidally correlated.
A sharp peak of activity occurs at about 20" of tidal phase (Fig. 9(a)). Note also that
three of the four largest subswarmsoccur at this time. The correlation is significant to a
level of 4 per cent by Schuster's test, and the probability of six or more of the 15 swarm
clusters occurring in one sector is even less (0.0011 as calculated by the method of
Appendix C). All swarm clusters for the period 1954-1973 do not appear to be tidally
correlated (Fig. 9(b)), although three peaks appear prominent on the phase diagram.
260
P. W. Uein
REYKJANES PEN1NSULA
ICELAND
MO \
!
\
6
1973
PO
PO
MS
FIG. 9. Semidiurnal tidal phases for earthquake swarms on the Reykjanes
Peninsula, Iceland. All swarm clusters are listed in Table B6, and have at least
three events of A4 2 2. Four points in thesemidiurnal tidal cycle are PS: peak solid
tide, PO: peak ocean tide, MS: minimum solid tide, and MO: minimum ocean
tide. (a) Earthquake clusters during the September 1972 swarm recorded by a
temporary network. The four major swarm clusters are shown as solid black.
Note the peak of activity, especially of the larger swarm clusters, near 20" of
tidal phase. (b) A histogram of all swarm clusters recorded in Reykjavik 1954-67,
by the Reykjanes seismic network 1971-73, and the swarm clusters of September
1972.
Possible triggering mechanisms. The effect of ocean loading on tidal strain on the
Reykjanes Peninsula must be considered since it is comparable to the solid earth
tidal strain. Ocean loading can introduce appreciable horizontal shear strains when
Ioading is not uniform laterally, as at a coast. Some earthquake epicentres are less
than 5 km from the coast, and ocean tidal amplitude averages about 2 m peak to peak.
The ocean load strain was calculated for the M 2 tidal component by the method
summarized by Beavan (1974). Tidal amplitude and phase for the 400 km of ocean
surrounding the Reykjanes Peninsula are taken from an unpublished chart compiled
by John Kuo and from Icelandic tide tables. The strain Green's function for a
Gutenburg-Bullen earth with an oceanic mantle is from Farrell (1972).
The calculated solid tidal strain field is essentially a dipole of two compressional
lobes rotating from north to east (Fig. 11). Although the magnitude of the compression varies during the cycle, the magnitude of shear strains (difference between
principal linear strains) is approximately constant. The ocean load strain, however,
is nearly constant in orientation but it oscillates in amplitude and has a large shear
component since the areal strain is nearly zero. The total strain field (Fig. 11, third
row) consists of a compressional lobe alternating between NE and NW orientations.
Although the tidal strain field at this latitude always has a net compressional areal
strain, only the oscillatory component of the strain field can influence earthquake
occurrence.
Using the tidal strain field of Fig. 11, and making some reasonable assumptions
of some elastic constants, the applied stresses on any fault plane may be calculated.
Slip will be enhanced on any fault by some combination of (1) maximum shear stress
in the slip direction, (2) minimum normal stress, and (3) maximum pore fluid pressure.
Although the failure criterion is not known, the approach taken here is to identify
which of these possible triggering mechanisms enhance or retard seismic slip at the
time in the tidal cycle when swarm earthquakes occur. Knowing which triggering
mechanism is operative may indicate the point on the Mohr failure envelope at which
failure occurs.
Y C
3
3 2
V
=3
-I
c
z
c3
a
'r4
w
n
5
0
50
I
II
It
SEPTEMBER
,
t
1972
t
t I
I
t
I
I
I
FIG.10. Seismicity and the solid earth tide as functions of time for the September 1972 swarm on the Reykjanes Peninsula. Note the tendency of earthquakes to
cluster together in time. The swarm clusters marked here are those listed in Table B6 and whose tidal phases are plotted in Fig. 9. Those clusters which form the
prominent correlation near peak solid tide are marked with arrows. M refers to a mainshock-aftershock sequence.
3
-7
I
m
W
ar
'
O
120.
1lMEe
w
'..
%MINIMUM
- - F)Q
214
sou) TIDE
c
240.
270.
w
330.
--- COMPRESSION
Fxci. 11. Maps of the calculated horizontat strain field on the Reylcjanes peainsula during one tidal cycle. The curves represent the calculated
strain in any
partiah direction,with north at the top. The ban are 0.01 micmtmm
' l
o-. The top row is the strain caused by the solid earth ti& it is essentdly two compressional lobes rotating clockwise. The middle row is the elastic strain resulting from loading by the ocean tide; it is essentially a sheat field fixed in orientation but
oscillating in magnitude. The bottom row is the total horizontal strain. Solid lines show extension (positive strain), and dashed lines represent Compnssion.
W
90.
G
E
A
K S OLrlDE (c200.9 SEPT 1972)
263
Earthquake swarms
REYKJANES PENINSULA
MINIMUM
N-W LINEAR
STRAIN
I
.
TIMES OF
EARTHQUAKE
M IN1MUM
VOLUME TR I C
STRAIN
MS
I
MAXIMUM
SHEAR STRESS
(E-W STRIKE SLIP
& NE-SW
NORMAL FAULTS)
FIG.12. The semidiurnaltidal cycle for the Reykjanes Peninsula, Iceland. The time
of prominent clusters of swarm earthquakes and the time of greatest effect for three
possible triggering mechanisms are shown. The calculated effects of shear stress,
normal stress and volumetric strain on the fault planes would all act to enhance
faulting near minimum solid tide. Minimum strain means greatest compression.
Faulting on the Reykjanes Peninsula ranges between normal slip on north-east
striking planes and left-lateral strike-slip on east-west striking planes (Klein et al.
1973). Normal faulting predominates during the September 1972 swarm, but nearly
all focal solutions have a common north-west trending horizontal Taxis.
The times during the tidal cycle when various strains most enhance slip are shown
in Fig. 12 together with times of earthquake swarm occurrence. The total shear
stress on both normal and strike-slip faults most enhances slip at minimum solid tide.
If we seek a triggering mechanism for the prominent peak at 20" phase from the
September 1972 swarm, Fig. 9(a), the shear stress acts in the wrong sense and cannot
act as a trigger. Normal stress on the dip-slip faults is most compressive near peak
solid tide, which should also inhibit faulting at that time.
The remaining triggering mechanism, pore pressure fluctuation, is the most
difficult to calculate. The presence of extensive geothermal systems in recent volcanics
makes the existence of saturated pores and joints a reasonable assumption in the
hypocentral area. The tidal variation of pore pressure depends very much on the
orientation of fluid filled cracks, on crack shape, and on the porosity. If the cracks are
randomly oriented, pore pressure is greatest near minimum solid tide when volumetric
strain is a minimum, i.e. when the rock is most compressed. Preferred crack orientation would make pore pressure strongly dependent on linear strain perpendicular
to the plane of cracks. If cracks are dominantly perpendicular to the least compressive
total stress, they would be vertical and trend north-east, parallel to extensional faults
and fissures at the surface. The greatest compressive stress (minimum strain) perpendicular to cracks and hence the maximum pore pressure would then occur near peak
solid tide. This time approximately coincides with the peak in swarm activity. If
increasing pore pressure by tidal stress is to act as an earthquake trigger, the pore
pressure increase must be greater than the applied stress increase in order to lower
264
F. W. Klein
effective stress. On a regional average, pore pressure fluctuation cannot exceed the
applied stress fluctuation although it may do so locally in a structurally heterogeneous
area. Thus earthquake triggering by peak pore pressure cannot be ruled out, and
might occur if cracks have a preferred NE orientation. The dependence of such a
model on pore geometry and local structural heterogeneity makes the sharpness of the
peak in swarm occurrence a bit surprising. Pore pressure, however, may in some
form be responsible for the tidal correlation of the September 1972 swarm.
Stress delay and the eflect of pore fluidflow. A further interpretational diificulty
is introduced if pore fluids flow significantly during a tidal period. The flow of pore
fluids under the applied tidal stress can retard the phase of the responding effective
stress. The Reykjanes Peninsula is a major geothermal area, with high temperature
circulation systems extending through fractured permeable volcanics to depths of
several kilometres. It is likely that significant fluid flow can occur on a tidal time scale
in some areas. To find the magnitude of the phase shift of effective stress, we may
examine a simple flow model using the hydraulic diffusion equation (Lambe 8c
Whitman 1969). If c is the hydraulic diffusivity,P the pore pressure, and u the applied
tidal stress, then
Here B may be 1/3 times the trace of the applied stress tensor or any principal stress.
We seek the effective stress cE = a+P, and substituting get
We assume that both stress functions are approximately sinusoidal with semidiurnal
periods. In addition, we must postulate a spatial inhomogeneity in B, or no flow at all
takes place. If the characteristic length of spatial inhomogeneities is L = 2n/k, and
we take the simplest one-dimensional case, then
= eior
Then the solution is
-_- c1
BE
where
U =
,-ikx
,-ikx
1 __- 1
ck2 -__
ck2+ io
1+ iwz
J(1+ w27')
exp [ -i arctan (wz)J
where we let z = lick2. Note that the effective stress always lags the applied stress,
but by no more than 90". Also note that if wz = wL214x2c 4 1, B, 4 B with a small
phase lag (perfect fluid flow). If wz 9 1, oE is vanishingly small with a 90" phase
lag (no fluid flow). If we take arctan (07) = 30", as suggested by the September 1972
swarm, and c = 6 x lo4 cm2 s-' (Scholz et al. 1973), then L 1 km, which is roughly
the source size of a magnitude two earthquake. This simple model thus suggests that
fluid flow can occur on the scale of a microearthquake source dimension in a tidal
period. Unfortunately some combination of crack orientation and pore fluid pressure
and flow can be invoked to explain nearly any observed tidal correlation.
Interpretation of the tidal correlation observed for the Reykjanes Peninsula
swarms of September 1972 is not easy. Other swarm clusters in the area do not
occur at the same time in the tidal cycle as the September 1972 sequence. The
predominant occurrence of swarm clusters in the September 1972 swarm near peak
solid tide is significant to a level of 4 per cent. Unfortunately, at this time in the tidal
cycle the calculated shear stress, normal stress, and pore pressure all act to inhibit
-
265
Earthquake swarms
130'
125'
I
52
50
48
46
44
42
FIG.13. Earthquake sequelices in the north-east Pacific. Major ridges and fracture
zones are shown by selected isobaths in fathoms. Swarms and mainshockaftershock sequences do not separate onto ridges and transform faults as in the
Atlantic, perhaps because rifts and transform faults are shorter or because the
area may have more ductile and inhomogeneous material properties.
fault slip. A variety of factors, including saturated cracks that are preferentially
aligned and significant pore fluid flow under tidal stress, can act to shift the time in
the tidal cycle when pore pressure might act as an earthquake trigger.
North-east Pacific Ocean
Tectonics. Another part of the world rift system with good seismic coverage is
the north-east Pacific region from the Mendocino Fracture Zone north to the Queen
Charlotte Fault (Fig. 13). The Juan de Fuca and Gorda Ridges have been identified
as actively spreading ridges offset by the Blanco Fracture Zone from their nearly
symmetrical magnetic anomaly pattern (Raff & Mason 1961; Menard 1964). Earthquake focal mechanisms have confirmed the alternating ridge-transform tectonics
(Tobin & Sykes 1968; Bolt, Lomnitz & McEvilly 1968; Chandra 1974). Earthquakes
on the Queen Charlotte Fault and Blanco Fracture Zone are generally strike-slip, and
those on the Gorda Ridge are normal. The Juan de Fuca Ridge is nearly aseismic:
hence no focal mechanism solutions from that ridge are available.
E
266
F. W. Klein
NORTHEAST PACIFIC SWARMS
PO
4
PS
AZIMUTH
DlSTRlBUT
FOR RAND
EVENTS
SEMIDIURNAL PHASE
EXTENSIONAL AZIMUTH
FIG.14. Twenty earthquake swarm clusters from the north-east Pacific are plotted
as a function of semidiurnal tidal phase (left) and azimuth of principal extensional
strain (right). Data are from the swarms listed in Table B7. Swarm clusters which
occur between 170"and 250" of tidal phase are shown by solid black. The peak of
swarm activity near 230" of tidal phase thus corresponds to times when the
extensional strain is directed ESE. The labelled tidal phases are PS and MS, peak
and minimum solid tide; PO and MO, peak and minimum ocean tide.
There are two main compIicationsin the simple ridge-transform picture, however.
The seismicity in the Gorda Basin east of the ridge is relatively high for a supposedly
stable area (Chandra 1974). Bolt et al. (1968) and McEvilly (1968) obtained strike-slip
focal mechanisms in the Gorda Basin, and interpret these as dextral shear on NW
striking faults, caused by the San Andreas Fault's attempt to extend northward and
join with the Blanco transform fault. In addition, magnetic lineations show the
southern end of the Queen Charlotte Fault is displaced from the Sovanco Fracture
Zone by the Explorer rift (Raff & Mason 1961; Atwater 1970). The Explorer rift
and Sovanco Fracture Zone, though not apparent on maps of general seismicity,
appear to be outlined by earthquake swarms in Fig. 13. The fault plane solutions of
Tobin & Sykes (1968) and Chandra (1974) in this region, however, reflect dextral
shear on fault planes striking nearly north, though the transform faults have a northwesterly strike. Thus the seismicity and tectonics are complex, as might be expected
in an area of short en echelon fault segments.
Swarm occurrences. Earthquake swarms occur frequently in the north-east
Pacific as noted by Sykes (1970b), Wetmiller (1971), and Tatham & Savino (1974).
The earthquake swarms and mainshock-aftershock sequences used in this study were
compiled from Sykes (1970b), from PDE earthquake listings, and from additional
small events in swarms noted on Palisades, Port Hardy and Corvallis seismograms.
These sequences are listed in Table B7 and are shown in Fig. 13. Most of the sequences
on the Sovanco and Blanco Fracture Zones are swarms, which suggests lower stress
and greater ductility conditions than on Mid-Atlantic fracture zones. The occurrence
of swarms on fracture zones supports the contention that swarm earthquakes can be
strike-slip (Tatham & Savino 1974). Swarms and mainshocks in the north-east
Pacific do not seem to separate into ridges and transform faults as in the Atlantic
but appear to assume a more complicated pattern.
Tidal correlations. A histogram of swarm clusters in the north-east Pacific is
plotted as a function of tidal phase in Fig. 14. There is little tendency for swarms to
occur near a single tidal phase, and the tendency to correlate has a probability of 0.38.
Two peaks of swarm clusters are apparent on the phase diagram, however, and tend
267
Earthquake swarms
to cancel each other in the significance test. The significance of the peak near 230"
of phase can be estimated by noting that the probability of seeing eight or more swarm
clusters in any two adjacent 20" sectors (as observed) is 1.5 per cent. Thus it is possible
that the peak near 230" has some physical significance which is masked in Schuster's
test by another peak at 0" of tidal phase.
The types of faulting and the tectonic stress orientation in the north-east Pacific
is similar to that in the Imperial Valley region. Therefore the times of tidally enhanced
faulting are the same: tidal stress enhances normal faults near peak solid tide and
strike-slip faults between 180"and 270"of tidal phase. It is possible that the two peaks
in the tide phase distribution reflect tidal triggering of two populations of focal
mechanisms in this region. If this is true, however, the lack of events between 250" and
350" of tidal phase (corresponding to enhancement of faulting combining strike-slip
and normal slip) is surprising.
Since all earthquakes in this set are submarine, the loading effect of the ocean
tide must be considered. Normal faulting is most enhanced by ocean loading near
peak ocean tide. Since peak ocean tide occurs near 350" of solid tidal phase, ocean
and solid tides enhance normal faulting near the same part of the semidiurnal cycle.
As with the northern Gulf of California, only the direct ocean load effect on normal
faults can be reasonably considered.
Thus the peak of swarm activity near 230" of tidal phase may be significant, and
corresponds to solid tidal enhancement of shear on strike-slip faults. This is the time
in the tidal cycle when tidal and tectonic extensional azimuths are in the same direction.
The smaller group of swarms near peak solid tide occurs at the time when solid and
ocean tides both enhance normal faulting. A definite interpretation of triggering
by tidal enhancement of shear on faults cannot be made, however, without focal
mechanisms for all events.
North-east Pacific earthquakes of known focal mechanism
Other earthquakes which are correlated here with the tides are those for which a
focal mechanism has been determined by Tobin & Sykes (1968), Bolt et al. (1968),
or Chandra (1974). Only strike-slip mechanisms are included, and earthquakes for
which two published focal solutions differ by more than 20" in fault plane orientation
are excluded. In addition, normal faulting mechanisms from the Gorda Ridge
have been excluded because of possible influence of ocean tides, and because of the
wide variation in the azimuths of T axes. The earthquakes are listed in Table B8,
5
MENDOCINO GORDA
BASIN
F. 2.
BLANCO
F.Z.
SOUTHERN
QUEEN
CHARLOTTE
FAULT
TIDAL EXTENSIONAL AZIMUTHS FOR
NORTH- EAST PACIFIC EARTHQUAKES
FIG.15. The azimuths of tidal extensional strain for north-east Pacific earthquakes
of known focal mechanism listed in Table B8. Arrows indicate the average
directions of tensional axes of observed focal mechanisms, and the range of
observed Taxes is also indicated. Shear symbols show corresponding fault planes.
Ten of the 12 earthquakes in the Gorda Basin or on the Blanco or Mendocino
Fracture Zone occurred at times when tidal stress enhanced the tectonic stress.
Tidal stresses for the Queen Charlotte earthquakes, however, are less consistent.
268
F. W. Kleln
MATSUSHIRO SWARM
OCT 1965-DEC 1966
,
\
\
\
\
\
\
\
-__-
1 EARTHQUAKES.
/
'
FIG.16. Outer section: histogram of numbers of earthquakes versus semidiurnal
tidal phase for the National Research Center for Disaster Prevention's catalogue of
Matsushiro earthquakes. Shown also are the mean level (thin solid line) and two
standard deviation levels (dashed lines) expected for the counts in each sector if the
earthquakes were random in time. For randomly occurring events, an average of
4.5 per cent of sectors should exceed the two standard deviation levels. Inner
section: a histogram of number of swarm clusters versus semidiurnal tidal phase,
with mean and two standard deviation levels. Peak solid tide is at the top. Note
that fluctuations between sectors are exaggerated since the centre of the diagram
does not correspond to zero events. These earthquake counts are not significantly
different from random.
and the azimuths of their principal extensional tidal strain are plotted in Fig. 15.
Also shown in Fig. 15 are the average of the azimuths of the Taxes of the focal solutions (arrows), observed range of T axes, and corresponding strike of the shear
dislocation. Fig. 15 shows that of the 11 earthquakes in the Gorda Basin or on the
Blanco or Mendocino Fracture Zones, ten have tidal stress fields in orientations
enhancing fault slip. Since the probability of a random earthquake in this group
occurring at a time of favourable tidal stress is 0.609, the probability of 10 out of 11
earthquakes occurring at favourable times is 0,034. The four earthquakes from the
southern Queen Charlotte Fault do not fit this pattern, perhaps because of the tectonic
complexity mentioned earlier. This correlation suggests triggering by the addition
of tidal and tectonic stress, and enhanced shear on fault planes.
Matsushiro, Japan
A major earthquake swarm occurred in Matsushiro, Japan in 1965-67. It is
fundamentally different in scale from the swarms along rift zones examined earlier
in this paper, since it lasts several months rather than several days. The total seismic
energy release of the Matsushiro swarm is equivalent to a single event of magnitude
6.3 (Kisslinger 1968). By comparison ridge-type swarms generally have a single
event equivalent of magnitude 5 1/2 or less. The swarm itself is variously interpreted
as being related to dilatancy and fluid diffusion (Nur 1974; Kisslinger 1975) and an
igneous intrusion (Stuart & Johnson 1975).
The seismicity of the Matsushiro swarm was examined for semidiurnal tidal
correlation in several different ways, but no correIation was found. Fig. 16 shows
269
Earthquake swarms
'
.--__--,,
AUG-DEC 1966 ,
;
'
~
\
FIG.17. Histograms of Matsushiro earthquakes as a function of semidiurnal tidal
phase. The events of theNationa1 Research Center for Disaster Prevention catalogue
are divided into the four periods shown in the central plot of seismicity as a function
of time. The mean and two standard deviation levels are included. Peak solid tide is
at the top. Note that fluctuations between sectors are exaggerated since the centre
of the diagram does not correspond to zero events. N o consistent tidal correlation
is apparent.
semidiurnal tidal phases for the 6678 earthquakes catalogued by Tokyo's National
Research Center for Disaster Prevention (1969). Neither this catalogue nor the 216
swarm clusters identified from it show any significant semidiurnal tidal correlation.
Also shown in Fig. 16 is the mean level and the two standard deviation limits for the
same number of random events. If the earthquakes were random in time one would
expect 4.5 per cent of the sectors to exceed the two standard deviation limits, or
roughly one sector in each histogram of 18 sectors. Neither the number of sectors
exceeding these limits nor the tendency of events to occur near one tidal phase are
significantly different from random.
To test the possibility that the semidiurnal tide may influence seismicity during
only a part of the swarm, the earthquakes were separated into four periods as shown
in Fig. 17. The activity during each one of these periods is not significantly different
from random in tidal correlation. Tidal phases of the larger events of the Matusuhiro
swarm compiled by the Japan MeteorologicalAgency (1968) are plotted in Fig. 18 and
similarly show no significant correlation. Earthquakes tend to occur near 240" of
tidal phase, but the correlation is not significant since there is an 8 1 per cent chance
of doing so from random events.
The geological setting and crustal stress at Matsushiro differ from the spreading
ridges examined so far in this paper which may account for the lack of tidal correlation.
Crustal stress is dominated by a horizontal and east-west principal compression, as
evidenced by other focal mechanisms in central Japan, regional folding with NNE
trending fold axes, and the uniform east-west compression direction of the Matsushiro
strike-slip focal mechanism (Morimoto et a!. 1966; Ichikawa 1967). The regional
-
270
F. W.Klein
MATSUSHIRO SWARM
LARGEST EVENTS
- -.- \
I-
I
I
I
I
\
\
FIG.18. Histogram of semidiurnal tidal phases for larger earthquakes at Matsushiro
(from the catalogue of the Japan Meteorological Agency). Shown also are the
mean and two standard deviation levels. Peak solid tide is at the top. These
earthquake counts are not signscantly different from random.
compression and the continental crustal thickness may provide a regime less suitable
to triggering than the oceanic crust and regional extension characteristic of submarine
rifts.
Aftershocks of 1964 Alaska and 1965 Rat Islands Earthquakes
1964 Alaska earthquake. Sequences of aftershocks, like swarms, are closely related
in time, space, and faulting mechanism. Aftershock sequences are therefore one place
to look for tidal triggering. In fact, tidal correlations of aftershocks have been noted
for the Truckee earthquake (Ryall et al. 1968) and for the 1964 Alaska earthquake
(Berg 1966). Although an extensive examination of aftershock sequences is beyond
the scope of this paper, an effort has been made to interpret two Alaskan aftershock
sequences in terms of tidal strain.
Berg (1966) examined the larger aftershocks of ntb > 5.5 of the 1964 Alaska
earthquake. He considered events which occurred between 24 hr after the mainshock
and 1964 August 30. Berg noted that of these 29 shocks, 21 were under the continental
shelf, and all but two of these occurred during the lower half ocean tide or at half
ebb tide. Since tidal ranges on the shelf area are 4-5 m, ocean unloading significantly
enhances thrust faulting and uplift.
The semidiurnal tidal phases and extensional strain azimuths are plotted for the
ntb Z 5.5 events in Fig. 19 and are listed in Table B9. In the Gulf of Alaska solid
and ocean tides are in phase, so the low tide events including the mainshock plot
near minimum solid tide. The peak of events near minimum tide may be related to
both enhanced shear and reduced normal stresses at that time on the low angle
thrust planes. Both effects follow from ocean tidal unloading. Note that of the nine
events near minimum solid tide, six are submarine and may be triggered by ocean
unloading, while two are at least 50 km inland and would experience a much reduced
loading effect. Therefore, this peak cannot be solely attributed to ocean unloading.
There is also a peak of nine events at half ebb tide, or 90" of tidal phase. By the
methods of Appendix C, the probability of there being two or more such peaks of nine
or more events is 0.17. The tendency of these earthquakes to occur near half ebb or
Earthquake swarms
271
ALASKA AFTERSHOCKS M25.5
IN TIME
MAiNSHOCK
ON CONTINENTAL SHELF
INLAND, ON KODIAK, OR OFF SHELF
0
FIG. 19. Tidal phases and extensional azimuths of the 1964 Alaska mainshock
and 28 larger aftershocks examined by Berg (1966) and listed in Table B9. Peak
solid (PS) and peak ocean (PO) tides occur at the same time in the cycle. Berg
separated aftershocks with epicentres on the continental shelf (black squares),
and noted that many were at minimum tide when ocean unloading would enhance
thrust faulting. In fact there is another peak (events are labelled by a white circ1e)at
90" of phase, which corresponds to NE horizontal tension and SE horizontal
compression. Thus the peak at 90" may be explained by tidal compressive stress
acting in the known direction of thrust faulting.
minimum tide has a probability of 0.28 for all 29 events, and 0.066 for the 21 shelf
earthquakes. Thus these two peaks are not statistically significant, although they may
be influenced by two tidal triggeringmechanisms.
The events at 90" of tidal phase are those for which the tidal extensional strain is
directed NE (see right side of Fig. 19), and thus for which the compressive strain is
oriented SE. Since the dominant faulting mechanism is a shallow thrust dipping NW
(Stauder 8c Bollinger 1966), tidal stress enhances tectonic stress for these events.
An attempt was made to correlate smaller aftershocks in the Gulf of Alaska with
the tides. Fig. 20 maps the PDE aftershocks together with those larger than magnitude
5.5. Region 1 is the zone of linear thrust faulting with compressional axes of focal
mechanisms trending uniformly NW (Stauder 8c Bollinger 1966). Faulting in region
2 is more variable as the rupture zone curves around Prince William Sound; compressional axes range from NNW to NE. The tidal phases of aftershocks from these two
regions are plotted separately in Fig. 21, and their extensional azimuths appear in
Fig. 22. The events do not fall at the same tidal phases as the larger aftershocks, and
are not significantly different from random events.
If tidal triggering in the Gulf of Alaska is real, it is a weak or nonuniform effect.
Page (1968) examined the Fourier spectrum of Alaska microaftershocks near the
northern part of region 1, and found no diurnal or semidiurnal periodicity. Ocean
unloading and NW compressive stress are possible triggering mechanisms for some
larger aftershocks but do not appear to be so for smaller events.
1965 Rat Islands earthquake. Since the larger 1964 aftershocks may suggest triggering by the addition of tidal and tectonic stresses, the greater number of m b5 5 5
aftershocks in the Rat Islands sequence should give a statistically more reliable
evaluation of triggering at the Aleutian trench.
Stauder (1968) reports two types of faulting mechanisms for the Rat Islands
aftershocks: thrust faulting with NW compression north of the trench, and normal
faulting with NE extension for aftershocks under the trench. The larger aftershocks
are divided accordingly into two geographic regions as shown in Fig. 23.
-
272
F. W. Klein
60'
59'
57 '
56'
,.
,-----
154"
I
152"
I
150"
I
I
1
148"
146"
I
I
144"
FIG.20. Map of PDE aftershocks of the 1964 Alaska earthquake, with the larger
aftershocks of Berg (1966) shown as dots. (1) is the region of uniform NW thrust
faulting, (2) that of non-uniform thrusting, and (3) outside the main aftershockzone
(Stauder & Bollinger 1966). Shelf and trench are denoted by 100- and 2503-fm
contours, respectively.
Semidiurnal tidal phases were computed for the largest shocks of mb larger than
5.0, and they are plotted in Fig. 24 for both geographicregions. The larger aftershocks
in region 2 are not uniformly distributed with tidal phase, and concentrate primarily
into two peaks near 140" and 340" of phase. The aftershocks from both regions taken
together tend to occur near 100"of tidal phase with a probability of 0.024 by Schuster's
test. The two peaks of earthquakes occur at nearly opposite phases, however, and tend
to cancel each other in this test. The importance of the peak near 140"can be estimated
by noting that the probability of 32 or more of the 69 aftershocks larger than magnitude 5 . 5 falling into any four adjacent 20" sectors (as observed) is only 0.00014. Thus
the peak near 140" of tidal phase is significant by either test, and the smaller peak
near 340" may have physical significance.
A triggering mechanism for the large peak of Rat Islands aftershocks is suggested
by the distribution of azimuths of principal tidal extension in Fig. 25. The peak of
activity at 140" of tidal phase corresponds to NE trending tidal extension, and hence
SE trending tidal compression. Since the dominant trend o f P axes of focal mechanisms
in region 2 is S30"E (Stauder 1968), the larger aftershock peak can be explained by
triggering resulting from addition of tidal and tectonic stresses. The small number
of m,,2 5 . 5 aftershocks in region 1 corresponds very closely with the peaks of region
2, indicating a similar triggering mechanism in both regions, even though focal
mechanisms differ. The horizontal tectonic stress orientation is nearly the same in
Earthquake swarms
273
ALASKA
AFTERSHOCKS
FIG.21. Tidal phase histograms of 1964 Alaska aftershocks in regions (1) and (2)
of Fig. 20. Aftershocks in the 24 hr following the mainshock are excluded. Points
in the semidiurnal cycle are PS,PO, MS, MO; peak and minimum solid and ocean
tide. Mean and two standard deviation limits for equivalent random events are
indicated by error bars.
FIG. 22. Azimuths of principal extensional tidal strain for the aftershocks of
Figs 20 and 21. Arrows show the horizontal stresses associated with the thrusting of
region (l), with P denoting the dominant P axis trend of focal mechanism
solutions.
regions 1 and 2, since the Taxes of focal mechanisms in region 1 are nearly perpendicular to P axes of those in region 2. The similarities in the two regions of tectonic
stress and tidal correlations in Figs 24 and 25 suggest that the enhancement of tectonic
by tidal stress is also the triggering mechanism in region 1.
The second largest peak of earthquake activity in both regions occurs near minimum
ocean tide. As with the 1964 aftershock sequence, enhancement of thrust faulting by
ocean unloading can explain triggering at minimum ocean tide. The tide range at
Attu Island is about 0 . 5 m and is much smaller than in the Gulf of Alaska. Nevertheless, it can exert stresses comparable to the solid earth tides. If the ocean unloading
mechanism of triggering is involved, it is noteworthy that it forms a distinct peak
274
F. W. Klein
,
I
II .
I
I
I
I
I
i
I
I
R A T ISLANDS
AFTERSHOCKS
F E B 1 9 6 5 - D E C 1966
...
n...
-
. ... .%. . . ..
n
54.
530
m b 2 5.0
m b Z 5.5
I.
52"
510.
500
FIG.23. Map of the larger aftershock epicentres of the I965 Rat Islands Aleutian
earthquake. Region (I) over the trench is characterized by normal faulting with
NE tension and region (2) by thrust faulting with NW compression (Stauder 1968).
RAT ISLANDS AFTERSHOCKS
FEB 1965
1966
PS
MO
-
- DEC
ff
REGION
MOQ
\ \
c
in
-1
4 PS
fl
I
I
FIG.24. Semidiurnal tidal phases of the Rat Islands aftershocks of the two regions
of Fig. 23. Aftershocks in the 24 hr following the mainshock are excluded. Points in
the semidiurnal cycle are PS, PO, MS, MO; peak and minimum solid and ocean
tide. Note the peak in aftershock activity near 140"of tidal phase in both regions
and both magnitude ranges.
nearIy at the phase opposite the largest peak of activity. This means that triggering
by ocean unloading might act independently of and in fact override the effect of solid
earth tidal strains.
Thus we see that larger aftershocks of both 1964 Alaska and 1965 Rat Islands
earthquakes tend to occur either at minimum ocean tide or when the direction of
Earthquake swarms
275
RAT ISLANDS AFTERSHOCKS FEB'65- DEC' 66
REGION
REGION
FIG.25. Azimuths of principal tidal extensional strain of the Rat Islands aftershocks
shown in Figs 23 and 24. Arrows show the horizontal stresses associated with the
normal faulting of region (1) and thrust faulting of region (2). P and T denote the
dominant trends of P axes in region (2) and Taxes in region (l), respectively. The
central curve is the expected azimuthal distribution for random events.
tidal compression matches the tectonic compression. The triggering effect is much
more significant in the Rat Islands sequence, however, and unlike the 1964 sequence
is also present for smaller magnitude events. The Rat Islands sequence i s different
in other respects. Although the surface wave magnitude of the mainshock is about
314 of a unit smaller, its rupture length slightly less, and its seismic moment 1/5
as large (Kanamori 1970; Wu & Kanamori 1973) as the 1964 Alaska earthquake, the
Rat Islands earthquake has a significantlygreater number of large aftershocks. There
are 69 Rat Islands aftershocks of m b 3 5 5 compared with 34 for the Alaska sequence.
Jordan, Lander & Black (1965) note a greater number of large Rat Islands aftershocks,
all above the detection thresholds, in the first 45 days of both sequences. Since the
Rat Islands sequence released a proportionally greater energy in aftershocks than the
1964 Alaska sequence, slip during the mainshock was probably less complete. This
may mean that after the mainshock, more of the aftershock zone was closer to the
critical stress conditions required for aftershock slip, and that the small tidal stresses
could more easily trigger the critically stressed parts of the aftershock zone.
-
4. Discussion and conclusions
Significant correlations. The various tidal correlations discussed in this paper have
been evaluated by the methods of Section 2. These include Schuster's test for a simple
biasing toward a single time in the tidal cycle and a calculation of the probability that
tidal stress enhances faulting in the observed number of cases. The more complex
methods of Appendix C are used to estimate significances in some special cases. The
regions examined in this paper, number of earthquakes in each set, and probability
of seeing the observed correlation from random events are summarized in Table 2.
The most significantcorrelations and possible triggering mechanisms are also identified.
276
F. W.Klein
Table 2
Significance of correlations
n
R
4 m
p
Imperial Valley & N. Gulf
Swarms
43 18.2 255
Mainshocks
40 4.2 31
Mid-Atlantic Ridge
Swarms 7"-50" N
Swarms 54O-62" N
Fracture Zones
14
13
16
0.00046
15
37
6-9 11
9.2 21
North-east Pacific
Swarms
Fracture Zones
20
11
4-4 252
*
0.64
7.1 191
1.3 345
Reykjanes Peninsula,
Iceland
Swarms,Sept. 1972
Swarms, 1954-1973
P
Possible triggering mechanisms
Shear
Ocean Pore press
Notesenhancement load
effect
0.027
0.87
+
*
14 0.532 0.0044
*
0.043
0.10
*
10 0-609
+
0.38 (2)
0.034 *
Matsushiro Swarm
J.M.A. Catalogue
NRCDPCatalogue
Swarm Clusters
347 29.5 236
6678 101.8 346
216 12.1 289
0.081
0.21
0.51
Alaska Aftershocks
M 2 5.5
A42 5.5,shelfonly
M 2 5.0
All PDE events
29 6 - 0 152
21 7 . 5 135
135 10.4 208
673 30.1 276
0-28
0.066
0.45
0.26
Rat Island Aftershocks
M 2 5.5
A42 5.0
65 11.2 120
274 32.0 103
0.15 (2)
0.024 *(2)
+
?
?
?
?
?
+
?
+
* significant correlation.
(2) two peaks in tide phase distribution.
probable mechanism.
? possible mechanism.
+
Table 2. Table summarizing the significance of correlations and possible triggering mechanisms
for the regions and data sets examined in this paper. n is the number of events or earthquakes in the
data set, and P is the probability of seeing the observed correlation if the events were random. For
Schuster's test P measures the tendency of events to occur near a single semidiurnal tidal phase.
In two cases P is also the probability that m out of n events occur when tidal stress is favourable to
faulting. Schuster's test also yields the phase angle 4 near which earthquakes tend to occur. R, m and
p are defined in Section 2.
Significant tidal correlations with less than a 0.5 per cent chance of random
occurrence are seen for swarm clusters in the Imperial Valley and for strike-slip
earthquakes on Mid-Atlantic fracture zones. Additional significant correlations with
random probabilities less than 5 per cent are seen for swarms on the central MidAtlantic Ridge and Reykjanes Peninsula, for aftershocks of the Rat Islands earthquake
and for earthquakes on north-east Pacific fracture zones. In addition, there are
secondary peaks in the phase distributions or north-east Pacific swarms and Rat
Islands aftershocks. These peaks may have physical significance even though their
statistical significance is difficult to evaluate objectively.
Earthquake swarms
277
Triggering mechanisms. The apparent mechanism which can account for most
of the observed correlations is a tidally enhanced shear on fault planes. This mechanism
is consistent with the dominant correlations in every region examined except the
central Mid-Atlantic Ridge and the Reykjanes Peninsula in Iceland. The implication,
at least for these regions, is that fault rupture responds primarily to applied shear
stresses.
Other observations of tidal triggering appear to be consistent with the mechanism
of tidal enhancement of tectonic stress. Although some may debate the statistical
significance of many of these observations, the purpose of this discussion is to indicate
possible triggering mechanisms if the tidal correlations are real. Sympathetic tidal
shear appears to have been present for a group of shallow dip-slip earthquakes for
which the focal mechanism is known (Heaton 1975). Hofmann (1961) noted a correlation of microaftershocks of the 1959 Hebgen Lake earthquake with peak solid tide, a
time when the normal faulting observed for that earthquake is most enhanced.
Kayano (1973) reported a sequence of earthquakes in Okayama Prefecture in southern
Honshu, all of which occurred near 90" of solid tidal phase. The principal tidal
compressional axis is directed NW-SE at this time. This is the direction of P axes
of regional focal mechanisms and of plate convergence normal to the Nankai Trough
(Kayano 1973; Katsumata & Sykes 1969). Triggering mechanisms are uncertain for
other observed semidiurnal correlations (Ryall et al. 1968; Filson et al. 1973; Mauk &
Kienle 1973), but focal mechanisms are also uncertain.
Direst loading effects of the ocean tide may trigger submarine earthquakes if
dip-slip faulting is involved (Berg 1966). Secondary peaks in the tide phase distribution
occur for north-east Pacific swarms and for aftershocks of the 1964 Alaska and 1965
Rat Islands earthquakes. These peaks occur at the tidal phase when ocean loading
(or unloading) would most enhance slip. When another larger peak is present in
the tide phase distribution, the statistical significance of these secondary peaks is
difficult to estimate. If the secondary peaks are real, it is surprising that earthquakes
separate into two peaks and respond to two effects independently instead of depending
on the tensor sum of the two stresses combined. The two peaks in the tide phase
distribution of north-east Pacific swarms may result from triggering of two populations
of focal mechanisms at two different times.
Apparently, all three conceivable triggering mechanisms of maximum shear stress,
least compressive normal stress and maximum pore pressure operate at the tidal phase
opposite to that of the 1972 Reykjanes Peninsula swarm. If fluid filled cracks are
assumed to be preferentially oriented (NE in this case), then pore pressure would
depend on a linear rather than volumetric strain. Peak pore pressure would then occur
in the same part of the tidal cycle as the earthquakes. In addition, it is generally
true that if significant pore fluid flow can take place on the time scale of a tidal period,
then the effective stress can be delayed and attenuated. Thus the tidal phase at which
earthquakes are triggered will be shifted.
Implications of tidal triggering for earthquake swarms. Tidal correlation of
earthquake swarms should place constraints either on the physical mechanism of
swarms, or on the special geological conditions where they occur. Earthquake swarms
on the Mid-Atlantic Ridge generally occur on sections of actively spreading ridge
crest and occasionally on 'transform faults near intersections with the ridge crest.
Mainshock-aftershock sequences, on the other hand, are generally limited to fracture
zones. Mid-Atlantic Ridge swarms are generally associated with normal faulting
(Sykes 1967; 1970a,11970b), the absence of large earthquakes, high b values (Francis
1968a, b) low stress accumulation, and a possible shallow transition from brittle
to ductile conditions. Swarms generally are associated with areas of volcanism
or rifting (Mogi 1963; Sykes 1970b).
278
F. W. Klein
Models of the swarm mechanism generally involve inhomogeneous or concentrated
sources of stress or pore pressure, heterogeneous material properties, or spatially
variable fault friction (Mogi 1963; Kasahara & Teisseyre 1966; Nur & Schultz
1973). During an earthquake swarm this means that many parts of the seismic zone
will be near the critical stress required for rupture. This is because inhomogeneities
prevent any single rupture from propagating through the entirezone in one earthquake.
Instead, each swarm earthquake stops where stress cannot overcome dynamic friction
and loads several adjacent regions, bringing many nearer their critical stresses.
Rupture of adjacent regions may be delayed by effects such as pore fluid flow (Nur
& Booker 1972; Nur & Schultz 1973) and these delays result in seismic energy release
more extended in time than from a mainshock. Kisslinger (1975) proposed that
during a swarm (specifically Matsushiro) pores open during dilatancy and are kept
saturated by rapid fluid flow, so that dilatancy hardening does not occur, and stresses
do not build up but are gradually released in a swarm rather than a mainshock.
In the Imperial Valley and northern Gulf of California, where swarms and mainshocks occur in the same region, the data of Fig. 4 show the strong tidal correlation
of swarm clusters and failure of mainshocks to correlate with the tide. This may imply
that at 1east:portions of swarm earthquake zones spend more time nearer their critical
stresses and are more susceptible to tidal triggering than mainshocks in the same
area. Thus the fault inhomogeneities associated with swarms may provide many
places where rupture can be initiated by the small perturbing tidal stresses.
The data from the Imperial Valley suggest that tidal triggering of swarms is more
common than tidal triggering of mainshocks. Two hypotheses might account for this
apparent difference. First, physical conditions on the fault are different for swarms
and this might make slip more susceptible to tidal triggering. Alternatively, tidal
influences may be a regional effect and may be stronger in the tectonic regions in
which swarms generally occur. The swarms examined here that show tidal correlations
are all from submarine rifts or their landward extensions, and the Matsushiro swarm
in a continental regime shows no tidal correlation. Observation of tidal triggering
of mainshocks on north-east Pacific and north Atlantic fracture zones may also reflect
a tidal influence on the world rift system as a whole. Thus tidal triggering may be
related to tectonic regimes such as rift zones.
Tidal triggering of earthquakes on the world rift system could result from a
concentration of tidal stress and an amplification of tidal strain on the ridge system.
Observations of submarine volcanism, high heat flow, anomalous low velocity upper
mantle and low Bouguer anomalies at ridge crests (see for example Talwani, Windish &
Langseth 1971) and of high attenuation of S, waves travelling in the upper mantle
across spreading ridges (Molnar & Oliver 1969) suggest a low rigidity and perhaps
partial melt zone under ridge crests. If so, lithospheric plates would be partially
decoupled from each other at ridges. Also the long wavelength tidal stresses would
be channelled along the rigid lithospheric stress guide (Elsasser 1969) and concentrated
at ridges. Dissipation of tidal energy may be higher at ridges and may contribute
to heat flow (Shaw 1970). Thus, tidal strains might be greater at ridges than elsewhere,
and tidal stresses would be more effective as an earthquake trigger. Although there
is no direct evidence for tidal amplification at ridges, the hypothesis might be tested
by siting long-baseline strainmeters in rift zones. Tidal stresses in the Aleutian
subduction zone may act as an earthquake trigger by a similar decoupling of lithospheric plates at island arcs (Molnar & Oliver 1969).
Limitations. The tidal correlations found here are based on comparison of
earthquakes with essentially one tidal function at one constituent period. The success
at correlating swarms with semidiurnal tidal phase (or with orientation of tidal strain)
suggests that other earthquake data, other strain tidal functions and other constituent
periods might also yield correlations.
Earthquake swarms
279
Most correlations in this paper have been made with tidal phase and interpreted
with the general tidal stress given by Table 1. This method compares tidal and
tectonic stresses in a general way: a rigorous treatment requires calculation of tidal
stresses resolved on the fault plane of the earthquake. Focal mechanisms for most
earthquakes treated here are known only crudely so that tidal stresses are evaluated
only for general types of faulting. In addition, we use only the times in the tidal cycle
when tidal stress most enhances faulting and do not use stress amplitudes to directly
correlate earthquakes with total stress. Limited data and lack of focal mechanisms
make these approximations necessary. The method is adequate, however, to determine
whether tidal stress enhances or retards faulting at the time of the earthquake.
A systematic study could be made of earthquake correlation with longer period
tides. The diurnal tide can introduce a modulation which should generally make
every second semidiurnal tidal peak higher, as in Fig. 1. If earthquake data sampled
from this study are plotted as a function of diurnal tidal phase, however, the diurnal
correlation is not as good as the semidiurnal correlation, i.e. triggering occurs twice
in the diurnal cycle. For areas where swarms are recorded over several years, correlation could be attempted with the fortnightly tide, whose principal effect is an amplitude
modulation of the shorter period tides. However, other triggering effects may become
important on the 14-day time scale, such as pore fluid flow into a dilatant region
before an earthquake. Other tidal correlations should be attempted and may in
some cases prove to be a useful predictive tool.
Acknowledgments
I wish to thank Pill Einarsson, Eysteinn Tryggvason, Sveinbjorn Bjornsson and
Bob Tatham who made available unpublished lists of swarm earthquakes, and John
Kuo for an unpublished tidal chart of the north Atlantic. Thanks also to Lynn
Sykes, Paul Richards, Chris Scholz, Roger Bilham, and John Kuo for useful discussions and for critically reading the manuscript. This work was supported by National
Science Foundation grants GA29405 and GA43382.
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Earthquake swarms
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Note added in proof
This paper notes the tidal correlation of earthquake swarms before 1974 in the
Imperial Valley, California. Sauck (1975) found that a later swarm in January 1975,
in the same area, also correlates with the tide. Both correlations are with the same
part of the semidiurnal tidal cycle, namely, when the solid tide is rising or when total
gravity is falling. Thus the 1975 swarm supports the conclusions of this paper and may
be triggered by the same mechanisms.
Appendix A
Calculation of tidal functions
The symbols used in the appendix are:
Azimuth of principal extensional strain, due to the Sun and Moon, el
Azimuth of principal extensional strain due to the Moon, eK.
Azimuth of principal extensional strain due to the Sun, e&.
Distance between centres of Earth and Moon.
Distance between centres of Earth and Sun.
Principal strains due to the Sun and Moon.
Principal strains due to the Moon.
Principal strains due to the Sun.
Strain in arbitrary azimuth 8.
Total gravity at the Earth's surface.
Upward component of tidal acceleration due to the Moon.
Upward component of tidal acceleration due to the Sun.
Upward component of tidal acceleration due to the Moon and Sun.
Love's number, taken as 0.618 (Alsop & Kuo 1964).
Shida's number, taken as 0-084 (Alsop & KUQ 1964).
Mass of the Moon.
Earth radius at observation point.
284
F. W. Kleh
S
Mass of the Sun.
W2M, W2' Second order tidal potentials due to the Moon and Sun.
0
Zenith angle of the Moon.
4
Zenith angle of the Sun.
Phase angle of the semidiurnal tide, reckoned from the peak (maximum
upward acceleration).
fl
Universal gravitational constant.
*
Longman (1959), and Pollack (1973) provide closed form expressions for the celestial positions and distances of the Sun and Moon, without reference to harmonic
development or use of tables. The expressions for the vertical component (directed
upward) of acceleration due to the Sun and Moon respectively are (Longman 1959,
equations (1) and (3)),
PSr (3 cos2 9- 1).
g, = 7
The phase angle $ of the semidiurnal tide at time to is computed as follows.
Since the diurnal tidal components vanish at the equator, and meridians are lines
of constant tidal phase, the tide is computed at the equator for the same time and
longitude as the earthquake. The tide is nearly a harmonic function of 12.42-hr
period and slowly varying amplitude and mean, and is locally well represented by
g' = gM+gs
%
a+b cos (2n(t-to)/12.42+$),
(-43)
t in hours. If go is evaluated at t = to, and g + and g - at t = toIf: (12*42/2n)6, a and b
can be eliminated and the semidiurnal phase angle at to is
$ =tan-'
where the umerator a d denomination are proportional to sin) I and cos $ respectively, and determine the quadrant of @. 6 is arbitrary, but can conveniently be
chosen as nJ4.
The procedure followed in computing the solid tidal strains is to compute the
principal strains eee and eAAfor both the Sun and Moon, take the strain in some particular direction, and then add the solar and lunar strains directly together. Retaining
only the most significant terms, the tide raising potentials are given by (Garland 1971,
equations 14.1.4, 14.1.5)
r2
w2'
= t p s -$(cos 24
+3).
285
Earthquake swarms
The principal strains due to the moon are given by (Kuo 1969, equation (l)),
1
eyA = - [ ~ w , M +
rg
with the same equations for e&, and e:" substituting C#J for 8. e g is always the greatest
is always perpendicular.
extensional strain and is at the azimuth of the moon, and
The total strain at an arbitrary azimuth B is then
ez
es = eg cos2((B-AM)+eyA
sin2(j?-&J+e&
cos2(j-As)+&
sin2(/3-As).
(A7)
The tensor of plane strain at a surface earthquake focus is often summarized in
this paper by the azimuth of principal extensional tidal strain. If the Sun exerted no
tidal force, the direction of principal extension would always be just the azimuth of
the Moon. But in effect, the solar and lunar strain tensors must be added and the
result diagonalized. This can be done in closed form as follows. Strain at an arbitrary
azimuth B may be also expressed by
es = el cos2(A-j?)+ez sin'(A-B)
(A81
where A is the azimuth of principal extensional strain.
Since equations (A7) and (A8) are equal and since j? is arbitrary, we may generate
as many equations involving the unknown A as desired. Subtracting the two equations obtained by setting (B equal to 0 and n/2 in the expression (A7) = (A8) yields
(el -ez) cos 2A = (eg -ez) cos 2 A M -t (d+
-4")cos 2As.
(AS)
Subtracting the two equations obtained by setting /3 equal to n/4 and -z/4 in the
expression (A7) = (A8) yields
(el -e2) sin 2A = (e; - eyA)sin 2AM -t(40
-4")
sin 2As.
(AW
Taking the ratio (AlO)/(A9) gives an expression for tan 2A, and the signs of equations
(A9) and (A10) will determine the quadrant of 2A. Subtracting AM from all the
angles yields the computationally convenient expression
Expressions for the azimuths AM, As are given by Pollack (1973, equations 7, 8).
286
F. W.&in
Appendix B
Swarms, swarm clusters and tidal functions
HEADING ABBREVIATIONS
L U C = G E O G R A P H I C L O C A T I O N , S T = SEQUENCE T Y P E 9 S = D A T A S O U R C E * MAG = M A G N I T U D E
C T = E A R T H Q U A K E C L U S T E R T Y P E , NO = NUMBER OF E V E N T S I N C L U S T E R
T O T = T O T A L NUMBER OF E A R T H O U A K E S I N SEOUENCE
I N D I C A T E S LARGEST EVENT I N CLUSTER (PLOTTED I N F I G U R E S )
P H S = P H A S E OF S E M I D I U R N A L S O L I D T I C E ( F R O M P E A K )
E A L = A Z I M U T H OF P R I N C I P A L E X T E N S I O N A L T I D A L S T R A I N
ARSTR = A R E A L S T R A I N 1 X 10**8 1
D S T X = D E V I A T O R I C S T R A I N ( D I F F E R E N C E OF P R I N C I P A L H O R I Z O N T A L S T R A I N S X 10**8 t
**
F O R SEQUENCES W I T H NO C L U S T E R S O F E A R T H Q U A K E S * L A R G E S T E V E N T
T I D A L DATA
IS
L I S T E D W I T H NO
****+***9*9088*******+******+*******0************************4****************~******
SEQUENCE T Y P E A B B R E V I A T I O N S
S = SWARM, M = M A I N S H O C K - A F T E R S H O C K
F M = FORESHOCK-NAINSHCICK-AFTERSHOCK
SEQUENCE*
SEOUENCE
2M = TWO M A I N S H O C K S
**4*14***+***0+2+*****0+*******9***+*+9**E****~***~*******************E*********
D A T A SOURCE A B B R E V I A T I O N S
A = B O B TATHEM, P E R S O N A L C O M Y U Q I C A T I O N
C = C A L - T E C H S E I S M I C NETWORK
I = S V E I N H J O R N BJORNSSON, P E R S O N A L C O M M U N I C A T I O N ( F R O M U N I V . OF I C E L A N D NETWORK)
K = AUTHORS D E T E R M I N A T I O N O F T i M E A N D M A G N I T U D E FROM P A L I S A O E S I A K U R E Y R I v
PORT H A R D Y * P O I Q T ARENA, OR L O C A L R E Y K J A N E S P E N I N S U L A S E I S M O G R A M S
P = C G S AND NOAA P D E L I S T I N G S
R = REYKJAVIK STATION BULLETINS,
1944-1967
S = S Y K E S , 19708
T = E Y S T E I N N TRYGGVASON
PERSONAL COMMUNICATION
t+~4**++4+*8********************************************************************
IMPERIAL VALLEY
TABLE 61
D A M O YR HRMN N - L A T
26 2 32
9 10 32
2 3 34
8 9 35
1 1 10 35
20 12 35
20 12 35
2 1 36
24 01 36
7 4 36
7 5 36
16 9 36
19 10 36
1 5 12 37
12 4 38
29 6 38
19 9 38
19 5 40
1 6 40
13 7 40
26 2 41
23 05 42
21 10 42
29 10 42
27 4 43
226
2251
2130
1703
1406
23
745
354
1749
2253
1147
1440
306
0958
1446
1040
1307
436
2359
1639
1309
1547
1622
1556
328
32.5
32.7
33.1
32.9
32.9
33.1
33.1
33.1
33.3
32.9
33.1
32.934.0
33.1
32.9
33.4
33.3
32.7
32.7
33.1
33.3
32.0
32.9
32.9
32.9
W-LON
115.6
115.5
116.0
115.2
115.1
115.5
115.5
115.5
116.3
115.2
116.1
115.7
116.1
116.0
115.6
115.6
116.3
115.4
115.4
116.0
115.5
116.0
116.0
116.0
116.0
LOC S T S MAG
I V
S C 3.5
IV
S C 4.5
I V S C 4.5
IV
M C 5.0
I V M C 5.0
I V 2 M C 3.5
I V ZM C 5.0
I V 2M C 4.0
IV
S C 3.0
I V S C 4.5
I V
S C 4.5
1 V S C 4.5
IV
S C 3.0
I V S C 4.0
I V S C 3.5
I V S C 4.0
IV
S C 3.5
I V M C 7.1
I V M C 4.5
IV
S C 4.0
I V M C 3.5
I V M C 5.0
I V M C 6.5
I V M C 4.5
1 V M t 4.0
C f
S
NO T O T
4
20
**
PHS E A Z A R S T R D S T R
1.42
81
0.31 0.75
1-08 0.96
2.57 0.06
50
50
20
168
97 -2.28
255
105
80
4
F
M
A
**
**
**
17
3
3
7
4
S
**
15
S
**
8
M
**
**
12
4
A
28
58
4
8
3
31
3
3
15
6
4
42
176
90
70
9? -2.02
1.66
82
2 4 8 104 -0.66
1.39 60
316 149 0.71
199 106 -1.64
1.27 51
1.56 90
304 134 1.74
163 104 -0.79
47 102 2.45
0.91
1.26
4
3
M
A
A
**
**
**
8
5
3
3
67
43
70
0 . 5 8 39
281
Earthquake swarms
3
17
2
5
04
11
27
15
2A
4
30
4
6
4
10
14
2
27
28
28
29
24
13
5
5
09
14
4
19
20
15
26
17
17
14
15
20
25
26
16
21
23
12
16
17
4
1
13
13
23
23
77
5
29
11
17
27
26
26
17
29
3
3
11
5
11
3
06
8
04
6
8
7
11
12
08
10
6
7
7
7
7
1
2
R
12
C4
6
1
3
3
06
8
12
12
2
2
5
4
5
10
4
8
9
9
9
3
7
1
1
5
5
10
10
11
04
6
7
8
8
1
7
43
43
43
44
44
45
45
45
46
46
46
48
40
48
49
49
50
50
50
50
50
51
51
51
51
52
53
54
54
54
55
55
55
55
56
56
56
57
57
59
60
61
61
61
61
62
62
63
63
63
63
63
64
64
65
65
6s
65
65
67
67
728 33.8
4 0 '32.7
1 6 4 7 32.9
1 3 4 7 34.0
1 5 1 9 33.0
1 33.9
2322 33.0
1756 33.2
1 7 3 1 33.9
1 2 0 5 33.9
1116 33.2
1844 32.9
2047 32.9
2 3 4 3 33.9
0 9 3 7 33.A
29 33.1
2128 33.5
1129 33.1
325 33.1
1 7 5 0 33.1
1436 33.1
717 32.9
1716 37.9
A33 33.2
1 5 5 3 33.1
1274 34.0
417 37.9
1 8 5 0 33.2
9 5 4 33.2
4 1 9 33.2
1 7 3 5 33.1
5 2 3 33.0
6 0 7 33.0
1905 33.0
1 8 3 3 31.5
120 31.5
839 33.1
2157 33.2
1 5 5 9 33.2
1 7 5 9 33.0
2339 32.7
1 0 0 33.0
1918 3 2 . 5
1 9 4 9 32.8
2 1 3 32.8
2039 33.1
1 7 1 1 33.0
239 33.0
2045 33.0
636 33.0
1 5 5 3 33.0
1 4 5 8 32.8
124 33.0
1425 33.0
0046 33.0
730 33.0
1404 33.2
514 33.2
1338 33.2
2310 31.7
859
32.9
116.2
115.4
116.0
116.4
116.0
116.2
116.0
116.3
115.7
115.7
115.7
116.0
115.6
116.3
115.9
116.3
116.9
115.5
115.5
115.5
115.5
115.7
115.5
116.0
115.4
115.8
115.7
116.1
116.1
116.1
115.4
116.0
115.5
115.5
115.5
115.5
115.5
115.9
116.0
115.6
115.7
116.2
115.4
116.1
116.1
115.7
115.8
116.2
116.2
115.6
115.6
115.8
115.8
116.0
115.6
115.6
116.0
116.0
116.0
114.7
115.4
1V
IV
IV
IV
IV
1V
IV
IV
I V
IV
I V
IV
IV
IV
IV
IV
IV
IV
IV
I V
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
1V
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
I V
1v
1v
I V
IV
IV
IV
IV
IV
IV
IV
IV
M C 3.5
M C 4.5
s c 4.5
S C 4.0
s c 3.8
S C 3.2
S C 3.2
M C 5.7
s c 4.4
M C 4.8
M C 4.6
k' C 3.8
s c 3.5
M C 6.5
s c 3.4
M C 4.1
s c 3.7
s c 4.8
s c 4.7
s c 5.4
$ c 5.5
M C 5.6
S C 4.2
M C 3.2
M C 4.5
5 c 3.9
C C 5.5
5 c 3.9
M C 6.2
M C 4.9
S C 4.0
c c 4.3
s c 5.4
s c 4.3
2M C 6.3
2M C 6.4
M C 3.6
C C 5.2
$1 C 5.0
s c 3.9
S C 4.2
5 c 4.7
F1 C 4.8
FM C 4.4
M C 3.3
s c 3.5
s c 3.4
M C 4.2
P G 3.9
s c 4.3
s c 4.8
s c 4.4
s c 4.4
S C 4.2
S C 4.1
s c 4.3
s c 4.3
S C 3.2
s c 4.5
5 C 3.R
s c 3.3
s **
10
M
**
5
M
**
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M
3
3
3
M
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5
M
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3
s
s
s
s
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s
fi
S
M
W
M
s
M
A
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M +*
s
s
M
M
**
**
**
**
6
8
14
11
4
3
3
3
3
3
12
3
4
4
3
6
5
16
3
3
3
26
4
3
3
51
7
3
3
4
4
7 12
3
5
3 3 108
5
5
3
3
25 34
4
4 41
5
**
**
**
**
5
18
4
3
s **
5
23
5
4
5
5
8
4
6
20
M
M
M
5
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M **
A **
s **
M **
A **
s **
s **
s **
5 **
S **
s **
s **
S **
s **
M
5
4
5
3
5
3
3
9
13
4
3
8
5
4
6
14
19
4
10
5
18
8
15
5
3
1 8 5 1 1 0 -1.78
1.63 .83
147
1.06
94
0.27
80
1.83 0.68 3 9
48 46
1 3 7 8 5.5R 0.10
9
2 8 3 1 4 0 -1.56 0.94 7 0
4 5 25 -1.28 1.10 6 3
11 -1.50
0.47
62
144 59 -2.92
2 4 5 1 2 9 -2.82
3 0 0 107 4.54
1 9 5 76 -2.29
4.58
3 2 3 12'
1 3 6 59 - l i e 0
3 4 5 1 7 1 1.19
6 4 9 5 0.77
2.12
2.07
0.37
1-90
0.27
0.69
0.80
0.39
89
79
25
73
22
87
45
49
2 1 ' 1 1 8 -2.51
337 1 6 8 -0.52
6 5 4 8 1.15
246 1 1 4 -1.24
1.78
1.56
1-01
1.55
89
58
47
65
-1.34
0.70
1.75 0.80
-1.06 1 . 2 1
0.34 1 - 0 4
1.58
-0.80
-1.62 1.30
-0.80 1 - 4 0
2.89 0.48
-1.95 1.75
65
43.
63
51
64
67
69
32
77
26
86
272
289
278
119
109
133
300
234
47
94
141
121
72
60
81
108
119
2 2 1 1 1 7 -2.66
1.92 8 4
311 1 3 7 1.81 0.79 4 1
1.32 72
234 116 -0.92
58 4 1 -0.80 0.57 5 9
52 3 4 0.45 1.47 5 1
1 4 9 67 -2.16
321 1 5 5 -0.06
3 2 5 1 5 9 0.19
234 88 -0.37
317 1 1 9 2.79
184 9 1 -2.98
278 26 0.03
1.74
0.75
1.44
1.68
0.63
2.03
1.27
86
52
54
57
30
89
49
76
42
77
1.26
2.02
1-63
2.31
65
68
59
A3
300
204
293
177
-1.18
-1.76
-0.64
-3.22
57
F. W.mein
288
14
26
9 6 7 519
9 6 7 2013
9 4 69
22 8 68
28 10 6 8
17 12 68
10 0 2 6 9
5 6 69
1 8 6Y
7 12 69
2 7 6 70
21 8 70
3 0 9 71
R 1 1 71
6 4 72
30 6 72
2 8 10 72
21 6 73
228
1935
1151
2253
1507
1119
848
1513
1009
306
2246
1947
111
950
1322
1311
33.2
32.1
33.1
32.9
33.1
33.0
23.8
33.1
32.8
32.9
32.8
32.9
33.0
32.R
33.5
33.1
32.3
33.0
IV
IV
IV
IV
IV
IV
IV
1V
IV
I V
I V
IV
I V
IV
IV
IV
IV
IV
115.7
114.7
116.1
115.8
116.0
115.8
115.4
115.R
115.8
115.5
115.5
115.5
115.8
115.5
115.7
115.6
115.3
115.5
M C 3.1
s c
M C
s c
S C
M
c
s c
S C
5 C
s c
S C
s c
M C
s c
S
C
s c
S C
M C
M
4.0 s
6.4 M
3.3
3.2
4.7 M
3.7
3.5 S
3.0 S
3.1 5
3.2 S
2.7 s
5.1 M
3.5
3.6
2.8 s
4.0 S
4.0 M
**
**
**
**
**
**
**
**
**
**
**
**
**
3
20
4
7
90
4
7
357
6 -0.28 0.90
1.11
21c 121 -0.88
270 106 1 - 6 0 1.05
5
10
139
5
4
6
10
14
4
6
3
3
7
10
4
4
8
58 -3.19
2.24
87
340 173 -0.53
324 153 1.32
266 135 -2.12
213 81 -1.36
144 75 -2.58
164 9 7 -2.41
0.67
0.71
1.92
1.15
1.48
1.65
54
43
71
74
80
77
355
0
16 100
60 4 6
0.89 50
0.57 21
0.98 55
6
9
3
6
4
3
7
5
0.43
3.25
0.25
TARLE R 2
N O R T H k R N G C L F OF C A L I F O R N I A
D A MO YR H R M N N - L A 1
31 5
27 1
4 10
I& 11
23 1 1
3 2
16 4
15 5
2 1 02
R 7
30 12
26 01
03 04
lc! 05
31 05
16 02
14 0 4
0 7 09
21 09
5 12
10 2
20 3
21 3
12 10
20 02
3 9
10 10
61
62
63
63
63
64
64
64
65
65
65
66
66
66
66
67
67
67
67
67
69
69
69
70
72
72
73
1417
2307
1749
1438
832
943
620
1940
G746
2313
1630
0928
1944
0732
1021
1941
1556
0159
0001
1109
815
817
456
2005
0608
1953
1720
30.0
30.8
30.2
29.9
29.9
31.5
31.1
31.5
28.5
29.7
33.2
31.2
30.7
25.0
25.9
31.6
25.3
31.3
31.2
30.8
30.4
31.1
31.1
30.6
29.9
29.9
29.7
M I 0 ATLANTIC RIDGE
W-LON
114.0
114.6
114.3
113.6
113.6
114.2
113.8
113.7
112.1
113.9
116.2
114.3
113.7
109.1
109.1
116.2
109.6
114.4
115.9
114.1
113.0
114.2
114.2
113.7
113.5
113.2
113.5
L C C S T S MAG
F;G
S C 5.5
N G M C 5.3
S C 4.5
NI;
NG
M P 5.7
F!G
M P 5.3
N G S P 4.6
NG
S C 4.8
?4 C 5 . 0
NG
NG
M P 5.3
NG
S P 4.5
NG
5 P 4.9
N G S P 4.3
NG
+! P 4.5
N G H P 5.3
NG
S P 4.2
NG
5 P 4.6
NG
S P 4.2
NC; S P 4.5
NG M P 5.1
NG
S P 5.0
NG
S P 4.6
S C 5.7
NG
NG
S C 5.8
h(G
S P 5.2
h G S A 5.4
NG
S P 4.5
NG S P 4.7
54
83
4.6
NO T O T
CT
5
**
**
**
**
**
**
**
**
X
**
K
S
M
A
S
S
F!
7
4
4
4
4
5
3
3
15
10
4
14
DHS E A Z A R S T H USSR
9
5
3
331
283
184
244
288
248
272
68 1.21 0.26
127 0.33 1.38
1.72
110 -2.28
84 1.10 1.05
I15 1.26 0.91
123 -1.89 1.77
84 2.26 0.9R
4
191 1 1 1 -1.48
33
52
R1
45
45
74
36
1.56
84
2.85
0.81
37
9
15
78
31 94 4.45
196 114 -0.55
346 166 2.04
234 114 -1.68
0.38
1.50
0.72
1.68
14
70
40
76
29
3
27
7
S
**
**
**
**
18
S
**
6
212 109 -0.96
1.75
83
S
**
5
32
7
4
11
326 150
0.72
38
S
S
S
4
3
6
2.44
TARLE R3
LOCATION ARRREVIATIONS
NM = N O R T H E R N M I D - A T L A N T I C R I C G E , JF! = J A N M A Y E N F R A C T U R E Z O N t r
S F = SPAR F R A C T U R E ZONE, RR = R E Y K J A N E S R I D G E , GF = C H A R L I E - G I B E S F R A C T U R E
C M = C E N T R A L M I O - A T L A N T I C R I C G E , A Z = A Z O R E S 7 K f = ROMANCHE F R A C T U R E Z C N E
S M = SOUTH M I D - A T L A N T I C R I G G E
ZONE,
Earthquake Swarms
0 4 1\10 YR HRMN N - L A T
19
21
23
20
21
17
3
18
2a
7
11
04
02
29
18
3
6
I0
6
16
21
4
17
29
22
02
05
16
25
29
03
16
17
11
78
01
05
13
5
19
31
18
27
18
Y
12
09
28
10
20
27
07
20
70
25
06
10
31
01
2 44 1136
2 44 1526
2 4 4 1104
8 54
8 54
10 57
1 58
06 58
07 58
8 59
09 59
10 59
05 6 0
10 6 0
05 61
1 1 61
3 62
05 6 2
10 62
U 1 63
2 64
3 64
08 6 4
08 6 4
05 65
06 65
07 65
0 8 65
9 65
09 65
1 1 65
1 1 65
12 6 5
3 66
03 66
0 4 66
05 66
06 66
7 66
07 66
08 66
1 1 66
1 1 60
02 67
3 67
06 67
07 67
10 67
1 1 67
1 6E
01 68
03 68
04 68
0 4 68
06 68
08 6 8
08 6 8
08 6 8
09 6 8
2029
27
1437
715
0120
1554
1132
1620
1830
0842
1154
0939
2242
2028
1040
332
1232
1715
258
1515
0520
1609
2340
0832
U436
2010
2320
0753
1524
617
2336
1208
0333
1552
1319
509
0020
AH15
1943
2013
0031
2059
0005
2131
1842
0440
822
0048
0727
1018
1950
0646
0012
0456
0754
0448
63.9
63.9
63.9
70.5
70.5
46.5
31.4
68.9
55.6
63.0
71.3
83.5
-3.2
47.7
73.0
61.4
62.2
49.2
40.5
54.2
38.7
43.3
72.1
71.6
-14.1
16.0
52.8
35.3
54.2
45.2
58.2
31.0
8.6
28.4
-55.5
-53.5
61.5
73.4
37.6
55.5
71.6
24.1
78.5
26.9
56.0
16.6
19.2
24.9
45.1
41.3
29.9
71.6
38.3
-19.9
-0.7
26.7
76.7
-1.0
-1.0
W-LON
23.8
23.8
23.8
15.0
15.0
027.4
41.0
16.6
035.1
24.5
013.4
-115.
012.3
027.7
-05.h
27.5
26.6
028.5
?3.6
035.1
28.5
29.0
-01.5
003.7
013.8
046.7
034.2
035.6
35.2
028.2
032.1
041.5
39.5
43.9
001.5
003.1
027.4
-07.8
24.6
035.4
002.3
046.2
-c5.e
043.4
34.5
046.6
046.0
045.9
028.1
29.3
042.8
003.5
026.6
011.8
015.9
044.6
-10.5
024.5
024.5
L O C S T S MAG C T
RR
HR
RR
JM
JM
cn
CK
SF
RR
RR
NP
AR
SM
CM
NA
RR
RH
CK
A2
RR
A2
A2
NU
NM
SM
CM
GF
CH
nu
CM
RR
CM
CM
CM
SM
SM
HK
h(M
A2
HK
NU
CM
NM
CY
HR
CM
CM
CM
CM
A2
Cn
ivt4
CM
SM
RF
CM
NM
RF
RF
S
S
S
S
S
s
S
t4
S
S
**
S **
S **
S **
S **
s **
S **
H **
5 **
S **
S **
R 6.0 S
R 5.7
R 4.8
R 5.0
H 5.5
K 4.7
S 5.6
S 5.1
K 4.6
H 4.0
S S 4.6
S S 5.7
S K 5.0
S P
M K 4.9
S R 3.8
M
S
5 R 4.5 S
S K 5.0 S
S S 5.2
S K 4.9
S S 4.1
S 5 4.3 S
s P 5.4
S P 4.7
S P 5.5
F H S 5.6 M
F P S 5.5
M
5 K 4.9
s s 4.8
S P 5.3 S
S P 4.8 S
M P 6.0 K
s s 4.7
s s 4.5 s
S P 5.3
S P 5.7 S
5 P 4.9 S
s P 4.7 s
S 5 4.6 S
s P 4.5
S P 5.0
M P 4.8 M
s P 5.5
S K 5.2
S 5 4.4 S
S P 5.1
S P 4.6 S
S P 5.1
S
5 f’ 4.8 S
5 K 4.5 S
S P 5.0 S
S P 4.9
S P 5.1
s P 4.9 5
S P 4.9 S
S P 4.7
S P 4.7 S
5 P 4.5 S
S P 5.2 S
**
**
**
**
289
NO TOT
6 203
PHS E A Z A R S T R D S T R
36
17 -3.11 1.28
7
17
14
2.04
2.34
0.9Y
0.81
3
30
5
3
14
6
7
97 46 -3.19
287 145 -3.28
83 34 -3.15
191 82 -2.24
159 95 -2.21
183 109 -2.24
354 1 7 7 -2.88
244 116 -1.65
269 13Y -3.12
3C 1 5 -2.53
1.66
1.21
1.85
3
3
3
9
7
12
237 110 -1.06
340 172 -1.03
187 90 -3.32
1 1 2 56 -1.44
0.91
2.33
1.02
295 134 -0.50
0.94
5
189 1 1 5 -2.42
26 28 -0.60
2.07
0.69
3
4
3
4
4
6
6
3
3
206
269
165
221
161
80 -1.61
-0.14
-2.02
-0.48
-0.52
1.09
0.89
1.17
1.57
1.46
180 101 -1.42
44 3 3
1.29
159 84 -1.7C
61 3 1 -1.49
1.62
1.05
61
11
3
7
4
7
4
4
7
6
3
1.12
1.87
1.Y7
1.12
18
4
**
7
4
7
6
3
+*
**
+*
**
**
**
**
**
*p
**
2
2
2
4
2
4
3
3
3
4
3
13
4
3
6
120
103
103
100
1.12
1.46
4
5
*+
**
**
f*
**
**
**
**
**
**
**
**
2
6
4
3
3
9
3
3
3
3
3
5
6
3
4
21
3
9
3
3
27
3
3
3
3
4
3
3
20
351
2 2 -0.21
0.30
210
96 -1.88
1.65
1 5 C 107 -1.59
203 102 -2.37
20z! 90 -C.lC
98 7 1 -0.40
341 102 5.65
1.81
1.42
1.17
0.92
0.19
326 145 0.79
180 6 3 -2.64
0.06
1.83
137
7
227
1.90
0.30
1.44
65 -2.80
7 9 2.22
62 -0.37
290
01
02
21
08
20
24
07
24
01
18
19
28
03
05
27
09
01
01
08
9
09
11
04
c9
09
09
09
01
01
I
3 1 05
10
05
06
13
00
29
6
08
01
05
06
08
04 C 1
14 01
68
69
69
69
69
69
69
70
70
70
70
70
71
71
71
71
71
71
72
72
72
72
73
73
P. W.K l e h
0819
0105
0805
1108
107
1803
1245
,0123
1526
0206
2057
2357
1735
0504
2045
0346
1902
0158
0542
1640
0525
2205
0803
0857
-1.0
30.5
28.7
-47.7
58.3
15.2
-3.0
55.7
-1.7
71.2
71.2
57.2
-55.5
-59.5
76.7
72.2
59.3
-0.9
55.3
45.0
32.9
OA.5
71.1
14.8
024.5
041.9
043.6
015.8
32.2
045.8
012.0
035.0
012.8
007.7
007.7
033.5
002.6
018.0
-6.8
-01.2
30.4
022.1
035.2
028.2
039.9
033.5
007.7
045.1
RF
CM
CM
SC
RR
CM
SM
RK
RF
JM
JM
RR
SM
SM
NM
NF!
RR
RF
RR
CP
CW
CM
NV
CP
S P 5.0
s
M
M
S
M
s
s
S
t4
V
s
M
5
S
M
S
M
S
S
Ir
s
s
s
P
K
P
K
P
P
P
P
P
P
P
P
P
K
P
K
P
P
P
K
P
**
**
**
**
**
**
**
**
**
M **
A **
i+**
s **
M **
S **
M **
S **
S **
M **
s **
S
4.9 s
5.6 C
5.9 M
4.2 S
5.8 C
5.2 s
5.4 s
5.0 S
5.1
4.5
4.9
6.4
4.7
4.6
5.5
4.6
6.3
4.6
5.0
6.0
4.9
P 5.1
P 5.0
s
**
4
3
4
3
7
320
64
3 3 3 102
88 84
1 5 171
104 45
1 1 1 84
50 79
295 149
6 9 102
6
4
177 80
3
4
4
2
11
5
3
4
6
7
3
-3
4
3
3
3
4
3
3
3
2
3
3
3
3
3
12
4
9
4
3
3
3
3
10
3
10
270
2.07
4.90
1.42
-2.15
-2.33
-0.25
3.97
0.39
0.13
0.87
1.14
1.20
1.47
0.44
-2.71
1.90
2.68
-0.85
-2.40
0.63
1.47
1.18
5 -1.17
7 1 -0.88
0.72
0.44
320 164 -2.53
116 7 8 0.33
4 5 46 3.55
360 168 0.24
77 67 2.95
213 88 -1.72
125 7 2 -0.84
0.62
0.51
0.92
1.24
1.23
281 129
1.19
0.21
0.70
1-18
+*tf+*******t**f************$******$****f****~******$***************************
0
M I D A T L A N T I C R t C G f FRACTURE ZONES
-
STRkKE S L I P FAULTING
TIDAL
DA PO YH HRHN N-LAT
18 6 58 0120
17 3 62 2047
28 3 63 0015
19 5 6 3 2 1 3 5
3 8 6 3 1021
17 1 1 63 0047
17 5 b4 1926
3 7 65 0832
18 11 66 1943
1 4 69 0407
5 5 69 2 147
24 9 69 1803
19 6 7 0 1425
18 9 7 0 0206
7 3 3 71 0926
31 5 7 1 0346
60.5
10.8
66.1
23.9
7.5
7.0
35.3
52.8
24.1
66.4
66.3
15.2
15.4
71.2
70.9
72.2
W-LON
L@CATION
SPAR
VEMA
TJORNES
KANE
16.6
43.3
20.1
46.0
35.8 z
37.4 z
36.1 CCEANOC.
34.2 C H A R - G I B E S
46.2 KANE
17.7 TJOHNES
17.3 T J C R N E S
45.8
45.9
7.7 J A N K A Y E h
7.0 J A N HAYEN
-1.2
SLIP
L
R
R
R
R
R
L
R
R
R
R
R
R
L
L
L
EAZ
TABLE 8 4
FAULT
STRESS
AZIMUTH
ANGLE R E F E R E N C E
115
175
83
136
115
69
67
168
28
90
106
1C3
1CO
98
86
96
96
22
112
112
59
104
84
38
4
167
164
91
98
115
120
115
60
7
150
168
31
31
82
78
74
53
8
7
60
69
47
49
SYKES
SYKES
SYKES
SYKES
SYKES
SYKES
SYKES
I1967
11967
(1967
(1967
(1967
I1967
1197061
CONANT
11971)
W E I D N E R 11973)
CONANT 11971)
******+**+**f*+**O********************************$$******~*********************
NGRTHERN I C E L A N C
DA
27
29
6
6
12
28
1
2
PO
2
LO
12
12
12
03
4
4
YR HHF’N N - L I T
55
56
58
56
58
63
69
69
747
1621
1113
1534
0
0015
407
1600
66.1
66.7
66.4
66.4
66.4
66.1
66.4
66.4
TABLE 85
W-LON
16.3
17.5
18.5
13.5
18.5
020.1
22.8
22.8
LCC S T S PAG
FII
S 9 4.3
NI
S R 4.8
S i?4.8
NI
NI
5 ii 4.7
Nl
S R 3.9
NI
M P 5.6
NI
M K 4.5
FII
M K 2.9
CT
S
S
S
S
S
C
M
A
**
**
+*
**
**
**
**
**
NO T O T
9
7
14
4
4
4
5
11
5
24
3
3
PHS EAZ ARSTR DSTR
1 1 2 5 2 -3.27
181 89 -3.21
40 10 -2.95
166 77 -3.22
3 C 1 142 0.68
277 136 -3.01
1 C 2 54 -2.30
74 42 -1.61
1.38
1.55
1.44
1.40
1.23
1.97
1.81
1.74
29 1
Earthquake swarms
3
3
5
6
8
9
26
24
21
27
78
4 69 1652
5 69 2327
5 69 2147
5 69 2 3 5 6
5 69 332
5 69 330
8 69 1715
8 69 2247
8 69 314
8 69 1212
10 73 1131
66.4
66.3
66.3
66.3
66.3
66.3
66.3
66.3
66.3
66.3
66.9
RtYKJANES PENINSULA,
22.9
17.3
17.3
17.3
17.3
17.3
17.7
17.7
17.7
17.7
019.2
N I M K 3.8
NJ FK K 2.6
N I FM P 5.2
N I FM K 3.8
N I F H K 3.2
N I FM K 3.0
NI
S K 3.5
NI
S K 4.7
NI
S K 3.5
N1 S K 4.0
NI
S P 5.0
A
F
M
A
A
A
S
S
S
S
S
**
**
**
**
**
**
**
**
**
**
**
3
5
31
2
4
5
3
5 119
33
28
9
9
12
85
277
.181
209
262
219
132
295
66
328
282
4a
143
104
118
141
119
74
149
32
161
143
-1.22
-3.09
-1.39
-2.14
-3.12
-3.07
-1.65
-3.17
-3.13
-0.27
-2.62
ICELAND
C A Pi0 YR HRMN FJ-LA1 W-LON LOG S T S MAG
21 5 5 4 2 5 6 63.8
s K 2.8
22.4 R P
27 5 5 4 8 3 7 63.8
22.4 RP 5 R 3.7
1 5 9 5 4 9 0 7 63.8
22.5 R P S R 3.4
15 9 5 4 1 3 3 6 63.8
22.5 HP S R 4.2
15 1 55 1 2 1 7 64.0
22.3 R P S R 3.8
15 1 5 5 1 6 4 3 64.0
S R 5.0
22.3 K P
16 1 5 5
72.3 RP s n 3.5
1 4 2 64.0
1 4 5 6 1 0 4 6 63.9
22.1 KP C R 4.7
24 3 5 7 1 9 3 2 63.8
22.1 R P N R 4.0
22.6 R P S R 3.4
20 8 6 0 1R50 63.R
21 8 60 2336
22.6 nP s a 3.8
63.8
5 9 6 3 1 6 5 1 63.8
S R 3.9
22.A R P
28 9 6 7 2 2 2 3 63.8
22.6 RP S T 5.1
29 9 6 7
22.6 R P s T 4.7
5 3 8 63.H
29 9 6 7 1 0 5 9 63.8
22.6 ItP S T 4.8
30 9 6 7
236
22.6 R P S T 5.2
63.8
08 I 0 7 1 2147
63.8
0 2 2 . 6 HP > I
12 10 7 1 1 6 0 3 63.8
022.6 R P S I
0 9 11 7 1 1 1 4 8 63.8
922.6 U P S I
19 11 7 1 0 1 1 6 63.8
022.6 RP s 1
03 01 7 2 1 9 2 2 63.H
0 2 2 . 6 RP S I
18 0 7 72 2 0 16 63.8
022.6 RP S I
22.6 R P
K 2.6
3 9 7 2 1 1 3 6 63.8
7 9 72
8 5 63.8
22.6 R P
S K 2.9
S K 4.1
7 9 7 2 2 0 9 63.8
22.6 K P
8 9 72 1 3 4 4 63.8
72.6 R P S K 2.8
R
9 7 2 2 3 1 4 b3.8
72.6 R P 5 K 2.4
Y 9 72 0 5 5 63.8
22.6 R P S K 2.5
22.6 K P
S K 3.7
9 9 7 2 1 2 4 0 63.8
Y 9 72 1 4 4 9 63.8
22.6 R P S K 4.2
10 9 72
S K 2.8
22.6 R P
3 2 0 63.8
10 9 7 2 1 5 2 2 63.8
S K 4.2
22.6 R P
1 1 9 7 2 3 4 9 63.R
22.6 n P
S K 2.7
22.6 R P
S K 3.3
1 1 9 72
6 1 6 63.8
12 9 72 1110 63.8
22.6 R P S K 3.1
12 9 7 2 1 6 5 4 63.9
22.6 U P S K 4.4
13 9 7 2 2 3 9 63.8
22.6 R P S K 3.2
13 9 72 14 4
22.6 X Q
5 K 3.1
63.P
1 3 9 7 2 1 7 4 3 63.8
22.6 H P S K 2.7
022.6 R P
25 0 9 7 2 1R43 63.8
s 1
072.6 HP
S I
26 10 72 0 2 1 2 63.8
022.5 R P M I 5.0
15 0 9 7 3 0 1 4 h 63.8
1.66
2.11
1.37
1.15
0.98
0.89
1.87
2.24
2.24
1.51
1.74
T A B L E R6
CT
5
S
S
5
S
S
s
M
M
S
s
S
S
5
5
S
s
S
S
5
s
s
S
S
M
S
S
S
M
S
S
S
S
S
S
S
S
S
S
s
5
M
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
N O TOT
9
18
5
22
72
38
10 9 6
55
7
17 22
3
8
5
12
5
18 33
63 470
83
06
106
10
6
6
15+
7
7
5 361
3
2
5
5
3
10
63
4
12
6
11
24
30
6
4
4
5
5
30+
PHS E A Z A R S T R DSTR
164
330
189
321
180
309
198
112
283
184
309
65
359
210
8
100
167
192
140
34a
121
24
19
205
202
358
280
329
314
16
26
19
27
80
165
98
158
81
156
105
60
122
98
154
36
5
94
1
51
70
107
YO
-3.20
-0.92
-2.72
-2.56
-2.70
-1.13
-0.98
-1.37
-0.35
-2.33
-2.37
-1.55
-2.67
-0.72
0.73
-2.39
-2.40
-2.60
-1.83
2.04
-2.61
-2.36
0.95
-2.61
-2.82
-1.14
-1.72
-1.05
-1.66
-1.56
172
56
3
13
100
101
179
136
162
154
8
1 6 -0.SC
9 -1.R6
1 6 -0.11
99
5 7 -0.85
16 -1.80
227
35
14 -2.32
3 2 5 6 0 0.00
1 1 2 7 0 -0.22
1 5 -2.49
41
1 1 6 5 5 -3.34
1.3Y
316 46
335 65 - C . 3 0
1.21
0.84
2.10
1.89
0.55
0.19
0.87
0.94
0.55
1.70
1.77
1.64
1.16
1.24
0.54
1.69
1.23
0.82
0.55
0.75
1.73
0.65
0.59
1.92
1.94
1.57
1.59
1.44
1.61
1.56
1.22
1.47
1.00
1.25
1.35
1.12
0.43
0.87
0.89
1.98
0.66
1.33
292
F. W.I(leln
NORTH EASTERN P A C I F I C
T A B L E 87
LOCATION ABBREVIATIONS
QC = Q U E E N C H A R L O T T E F A U L T
QE = Q U E E N C H A R L O T T E F A U L T
EXPLORER R I F T
GB = GORDA B A S I N
GR = GORDA R I D G E
R F = RLANCO FRACTURE ZONE
J R = J U A N DE F U C A R I D G E
M f = M E N O O C f N O F R A C T U R E ZOFIE
-
DA
KO
Y8
H R M N N - L A T W-LON
43.9
128.5
44.3
179.3
51.8
131.2
40.6
127.5
49.9
129.7
50.3
129.6
50.5
129.4
50.5
129.4
50.5
129.4
50.5
129.4
47.7
128.3
42.5
126.7
43.5
127.5
44.6
129.7
42.9
126.1
50.2
129.7
48.4
128.4
41 - 7 1Z6.1
41.7
126.1
51 .2
130.0
51.2
130.0
49.2
129.5
44.0
128.3
50.3
129.7
50.3
129.7
44.5
129.7
44.5
129.7
49.2
129.1
40.1
124.3
44.6
129.4
50.1
129.9
51.7
131.0
51.7
131.0
50.6
129.9
50.6
179.9
42.3
126.3
49.6
129.4
42.7
126.3
50.1
129.2
50.1
129.2
50.1
129.2
44.4
129.3
03 02 55 1241
25 1 1 57 1855
0 4 07 6 0 0428
29 4 61 919
2 6 62 1 2 3 5
1 2 7 6 3 1403
1 9 6 3 701
1 9 63 1 5 2 3
2 9 6 3 346
2 9 63 1330
2 7 64 1703
1 3 7 6 4 1154
24 09 6 4 1359
14 06 65 0940
20 6 65 1R04
1 2 0 8 65 0904
2 9 65 1542
22
1 66 1733
24 1 66 504
7 2 66 848
7 2 66 1403
9 9 66 1 R 3 3
09 01 67 1139
27 8 6 7 1 3 3 5
28 8 67 1526
26 1 2 67 929
28 1 2 67 626
30 2 6 8 314
26 4 b8 142
1 3 7 68 633
18 3 69 2031
24 6 70 730
24 6 70 1309
1 3 3 71 2 3 5 1
15
3 7 1 518
20 5 7 1 801
5 12 7 1 550
O H 0 4 72 0624
2 3 7 72 1052
23 7 72 1439
23 7 72 1913
17 09 73 2333
L n c ST
BF
BF
CC
WF
CC
CE
OE
QE
CE
CE
JR
GR
8F
BF
BF
QE
s
S
S
K
K
M K
M K
S K
HAG CT
5.2 S
5.2 S
5.5 M
5.2
5.3
4.9
3.2
4.0
3.9
4.4
S S
S K
S K
S K
S K
S K 5.2
S P 5.6
S P 6.1
M P 5.4
M P 5.6
S P 4.9
S S 4.5
S S 4.5
S S 4.4
C C 2 M K 4.5
JR
GR
GR
CC 2 C K 4.2
S K 4.8
OC
S P 4.5
RF
CE
S K 5.0
S K 5.1
OE
B F 2 M K 5.2
B F 2 M K 6.0
QC
5 P 5.1
M
S
S
S
S
S
S
M
S
S
M
M
S
S
M
M
V,F F N K 5.2
BF
S P 4.6
M
S
CC
CC
CC
CC
CC
GR
QC
GR
CC
QC
OC
H
BF
M K
S K
S K
M K
IL K
S P
5.1
5.4
5.4
5.5
4.6
5.0
S K 6.0
S P 5.6
S K 5.0
S
S
S
K 3.5
K 6.2
P 5.1
S
S
M
A
S
S
S
S
S
**
**
**
**
**
**
**
**
**
**
NO T O T
3
5
3
-3
5
67
6
8
48
5
5
5
4
3
6
**
3
**
**
**
3
8
**
8
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
4
4
5
4
4
4
9
17
16
8
21
7
5
3
5
88
15
PHS € A 2 A R S T R D S T R
188 111
237 124
344 167
47 30
118 5 5
3 5 28
3 5 5 179
240 102
240 124
168 76
-2.32
-2.49
-1.68
0.17
-3.03
-0.89.
-1.77
-0.33
-2.93
-2.78
1.77
1.42
1-13
1.25
2.09
1.02
1.55
1.36
1.96
2.02
7 1 -0.82
1.25
250 130 -2.45
216
87 -1.09
3 2 1 148 2.21
1 1 5 7 1 -0.95
40 8 8 2.15
1.80
1.43
1.00
1.68
0.36
19 6 1 1.39
24 80 1.81
136 89 -0.32
355 172 4.68
0.36
0.42
1.42
0.05
156
4
9
5
3
3
6
11
3
6
6
10
6
3
39
0
0
50
16
4
50
4
36
3
160
229
342
206
9
69
215
105 -1.30
222
87 -0.43
1.39
114 49 -2.48
224 88 -0.22
357 172 3.57
353 169 -1.61
1.65
1.18
0.21
0.97
120 -2.79
168 0.87
109 -3.09
1 1 -1.36
45 0.13
110 -2.15
1.56
1-66
1.21
1.35
1-05
1.15
1.69
**f9*4+*+*f*~~*ff**************+*********************************~********~***f***
NORTH EASTERN P A C I F I C
-
EARTHQUAKES W I T H FOCAL SOLUTIONS
TABLE 88
293
Earthquake swarms
DA MO
6 7
14 07
23 8
4 9
22 A
31
3
7
13
24
7
7
9
4
6
6
9
12
18
14
2C
16
10
8
S
26 1 1
13 3
5 12
8 4
23 7
5
*
YR
34
62
62
62
63
64
64
64
64
65
65
65
65
67
68
70
71
71
72
72
HRMN N-LAT
2248 41.4
1943 40.3
1929 41.9
1717 41.0
0927 42.0
090 1 50.8
1344 43.4
1154 42.5
1359 43.5
0633 41.5
0940 44.6
1804 42.9
0410 40.4
1206 40.5
1217 43.6
0311 43.0
2351 50.6
0550 49.6
0624 42.6
1913 50.1
W-LON
125.4
124.5
124.3
124.4
126.2
130.2
127.2
126.7
127.5
177.2
129.5
126.1
125.8
124.7
127.9
127.4
129.9
129.5
126.3
129.3
F A U L T 1-AXIS TIDAL
LOC T Y P E AZIMUTH EAZ R E F E R E N C E
GB
S
100
105 24 BOLT E T A L (19701
MF
S
5 3 22 BOLT E T A L (19701
59
G0
S
91 20 B O L T E T A L (19701
71
GB
S
90
96 19 BOLT E T A L (19701
168 24 CHANORA(1974lr 5-100IN+SKS.
100*
G0
S
9 CHANDRAf1974)r b-lOBIN+SKS.
128*
156
ec s
8F
S
72*
79 20 CHANORA(19741, l-TOBIN+SKS.
GR
N+S
13 23 CHANORA(1974l
163
66
74 19 CHANORA(19741
8F
S
76*
131 26 B O L T ~ l 9 7 0 1 ~ 4 - T C B I N + S Y K E S ' 6 8
GH
N
13 32 B O L T E T A L (1970:
BF
S
73
71
2 TOAIN + SYKES (19681
GR N + S
151
KF
69 23 B O L T ( l 9 7 0 1 ~ 3 - T O A I N + S Y K € S ' 6 8
S
62*
09 18 BOLT ET A L (19701
GB
S
87
8F
94 30 B O L T ( 1 9 7 0 1 ~ 1 7 - C H A N O R A ~ 1 9 7 4 l
S
71*
00 16 CHANDRA (19741
BF
S
61
77 10 CHANDRA (19741
S
129
CC
CC
S
120
87 12 C H A N D R A (19741
GR N+S
93 22 CHANDRA (1974)
1
CC
S
110
72 1 1 CHANDRA (19741
S T R I K E - S L I P , N = NORMAL, N + S 0 OBLIQUE
I N D I C A T E S F A U L T AZIMUTH T A K E N AS A V f R A G E FROM 2 FOCAL SOLUTIONS.
+f+0+**0***9++**~0*********************~~******************4*********4***4******
AFT€RSHOCKS
DA N O YR
28 3 64
29 3 64
29 3 64
30 3 64
30 3 64
30 3 64
3 4 64
3 4 64
4 4 64
4 4 64
4 4 64
4 4 64
5 4 64
7 4 64
10 4 64
10 4 64
12 4 64
13 4 64
1 3 4 64
15 4 64
16 4 64
20 4 64
29 5 64
30 5 64
2R 6 64
29 6 64
2 8 64
6 8 64
24 8 64
-
1964 A L A S K A EARTHQUAKE
(
M
H R M N N - L A T W-LON L O C S T S M A G C T
336 61.1
147.6 A3 M P 8.4
604 56.1
154.3 A 1 M P 5.5
1640 59.7
147.0 A2 M P 5.5
218 5 6 . 6
152.9 A 1 M P 5.7
709 59.9
145.7 A2 E P 5.5
1609 56.6
152.1 A 1 M P 5.5
846 57.9
150.5 A 1 M P 5.5
2233 61.6
147.6 A 3 M P 5.6
454 60.1
146.7 A2 Fc P 5.5
910 S6.9
152.7 A 1 M P 5.8
1746 56.3
154.4 A 1 M P 5.6
1759 56.4
154.5 A 1 N P 5.5
1928 60.2
146.7 A2 M P 5.7
1928 55.7
151.9 A3 H P 5.5
108 58.4
150.6 A 1 M P 5.5
2144 60.1
153.7 A 3 Fc P 5.5
124 56.6
152.2 A 1 M P 5.5
1405 57.6
151.2 A 1 F1 P 5.5
2125 57.5
153.9 A 1 M P 5 . 5
1530 56.5
154.4 A 1 M P 5.5
1926 56.4
152.9 A 1 M P 5.5
1156 61.4
147.3 A3 M P 5.6
1017 60.2
146.3 A2 M P 5.5
318 59.5
148-5 A2 ff P 5.5
1909 58.3
150.2 A 1 M P 5.5
0721 62.7
152.0 A3 M P 5.5
0304 56.1
156.1 A 3 M P 9 . 5
1824 56.9
152.1 A 1 M P 5.5
2156 58.4
150.3 A I n P 5.7
5.5
A N D ABOVE 1
NO
PHS
166
211
180
90
246
141
218
266
83
185
63
70
67
359
134
10
105
98
307
94
184
174
330
103
210
199
289
263
329
T A B L E 89
EAZ A R S T R
04 -2.81
105 -2.67
07 -2.69
54 -0.80
123 -2.41
68 -2.65
117 -1.65
95 -0.44
82 0.30
112 -1.30
30 -2.40
32 -2.37
36 -2.07
5 -1.77
68 -2.46
6 -0.99
58 -1.75
50 -2.91
145 0.59
44 -3.18
76 -2.10
99 -2.64
166 -2.5Z,
73 0.42
89 -1.01
110 -2.30
141 -2.25
115 0.80
159 0 . 5 1
DSTR
1.94
1.86
1.81
1.32
1-71
1.67
0.90
0.41
0.42
0.75
0.67
0.68
0.80
1.07
1.92
1.64
1.94
2.12
1.36
1.80
1.42
0.94
1.56
0.81
1.26
1.29
1.17
1.35
1.09
*t+f+8*4**0*84*f*4*4+**$8*+84+4*4~***********~*4**************4********~~4*********~
294
F. W.Klein
Appendix C
Significance of correlations
We wish to be able to evaluate earthquake-tide correlations more complicated
than the tendency of earthquakes to occur in just one part of the tidal cycle. The
significance of any grouping of swarm activity into one or more peaks during the tidal
cycle can be judged by calculating the probability that such a grouping would be
seen if the seismic events occurred randomly with respect to tidal phase. The approach
taken here is to divide the tidal cycle into sectors, and count the number of swarm
clusters or earthquakes in each sector. These counts can be compared with the
expected number of random events which would occur in a sector, and the probability
of seeing the observed or greater number of events can be calculated.
The term sector will here refer to a particular range of tidal phase. The tidal
cycle will be divided into j equal sectors. The term region will refer to a group of k
adjacent sectors. Thus if k is 1 the regions are the same as sectors and there are j
regions. If k is larger than 1 the regions overlap their neighbours, and there are still
j regions.
If the number of events to be distributed in the tidal cycle is n, and the probability
that one event occurs in a particular sector is p, then the probability of m of the n
events occurring in that sector is given by the binomial distribution
P(m) =
n!
p"(1 -p>n-.
m !(n-m)!
If the circle representing the range of tidal phases is divided into j equal sectors, and
the region being considered consists of k (adjacent) sectors, then p = k/j. Then the
probability that a given region of k sectors has rn events is
Now P,,(m) is the probability of seeing m events in a particular one of the j
regions. If we take a collection of s different regions, the expected number of regions
with m events in the collection is just sPklj(m). Since each of the j regions in the tidal
cycle is identical, Pk/j(m) is independent of the region considered, and the expected
number of regions in the tidal cycle which contain m events is jP,,,(m). Of more
physical interest is the number of regions which contain m or more events, given by
Let F&(m) represent an observation of the number of regions in the tidal cycle
which contain m or more events. Then we seek to compare the F&(m) with the
jP,*,(m). If one large peak of m, events occurs in some region of tidal phases, then
F&(mo) = 1, and the peak is significant if jP,*,(m,) 4 1 . For a large number of
random data sets the observed values of FGj(m) will be distributed around their
expectation value jP&(m). We wish to calculate this distribution as a function of h,
the number of regions containing m or more events. If there are two different peaks
of events in the tidal cycle, then setting h = 2 will yield the probability of seeing two
regions each of which has m or more events. P&(m) is the probability of ' success ',
meaning that a region has m or more events. We seek the probability of h ' successes '
and j-h ' failures '. This is given by another binomial distribution
Earthquake swarms
295
which is the probability of seeing h regions each of which has m or more events.
Note that the probability of seeing one region with m or more events is approximately
the expected number of regions with m or more events:
B(1) x jP&(m)
when P&(m) 4 1.
Of the most physical interest is the probability of there being h or more regions
containing m or more events
Note that B*(h) 2 B(h), and that B*(h) represents a more meaningful and severe
test of an observed correlation.
If the number of seismic events is large, one would expect the number of events
in each sector to be Gaussian distributed about the mean number of events Ei = np
with standard deviation CT = J(np(1 -p)), where the probability of getting one event
in a sector is p = I/j. If the events occur randomly, the event counts in 32 per cent
of the phase regions should exceed EL-a, and 4.5 per cent will be outside Ei420.
As a test of the significance of m events in k adjacent sectors when n is large, we can
approximate Pk,j(m)and P&(m) developed earlier by using Stirling's approximation.
If
m
!b(t) =
J f#4x)dx = -!2 (1 +($))
t
then
and