Geophys. J. Int. (1995) 123,409-419
Absolute and relative locations of similar events with application to
microearthquakes in southern Iceland
Ragnar Slunga,' Sigurdur Th. Rognvaldsson2* and Reynir Bodvarsson2
'Institutefor Hydroacoustics and Seismology, Foa 26, Stockholm, Sweden
'Dqartment of Geophysics, Uppsala University, Villaviigen 16, S-75236 Uppsala, Sweden
Accepted 1995 May 12. Received 1994 November 8; in original form 1994 June 9
Key words: earthquake swarms, fault-plane solutions, Iceland, relative locations,
similar events.
1 INTRODUCTION
It is well known to seismologists that, in earthquake swarms
and aftershock sequences, a large percentage of the (micro)earthquakes often have extremely similar waveforms (e.g.
Peachman & Thorbjarnardbttir 1990). The similarity is frequently not restricted only to the main phases; even the coda
* Now at: Nordic Volcanological Institute, Geoscience Building,
University of Iceland, IS-101 Reykjavik, Iceland.
0 1995 RAS
may be almost identical between events, except for a scalar
difference. This is, of course, to be expected for earthquakes
located within a quarter of a wavelength of each other and
having the same mechanism and dominant frequency.
Typically, local recordings of microearthquakes have peak
signal-to-noise ratios at around lOHz, i.e. at wavelengths of
approximately 350 m for S waves and 600 m for P waves.
The strong similarity between the signals of different earthquakes recorded at the same station means that signal analysis
can give extremely accurate estimates of the arrival time
409
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SUMMARY
It is well known that similar earthquakes, i.e. earthquakes having almost identical
waveforms, allow extremely accurate relative timing of the seismic arrivals. This has
traditionally been used for achieving accurate relative locations of clusters of similar
earthquakes. The arrival time differences between similar events depend not only on
their relative location but also on the absolute location of the group. Moving a pair
of events 200m while retaining their relative locations can cause a 1 ms change in the
time difference between the first arrivals of the events at a station 6km distant. A
change in time difference of l m s can easily be estimated by cross-correlating the
waveforms of the two earthquakes. We use the accurate relative timings to improve
absolute locations of groups of similar events, as well as to obtain extremely accurate
relative locations. The absolute locations from relative timings are expected to have
errors that are independent of the errors associated with locations based on absolute
arrival time observations.
We analyse data from five earthquake sequences, comprising a total of 96 earthquakes,
recorded by a regional network in southern Iceland. One of the clusters is located
within the on-land spreading ridge in south-western Iceland, and the other four are
within the South Iceland seismic zone, a transform zone between overlapping branches
of the spreading ridge. The events vary in magnitude between M , -0.3 and 2.8. After
determining the absolute and relative locations of each swarm, we estimate the
orientation of a best-fitting plane through the hypocenters. The mean distance of events
from a best-fitting plane varies between 4 and 15m for the five swarms. This is
comparable to the formal error estimates for the relative locations. Together with (nonunique) fault-plane solutions, the relative locations constrain the fault planes and the
type of faulting. Faulting within the nascent transform zone in southern Iceland is
predominantly strike slip on near-vertical N-S striking planes, in agreement with the
orientation of mapped earthquake fractures in the area. The earthquakes within the
spreading zone clearly define a fault plane striking parallel to the ridge and dipping
63". Each group of similar events probably represents repeated slip on the same fault.
410
~
R. Slunga, S. Th. Rognvaldsson and R . Bodvarsson
2 A M E T H O D FOR D E T E R M I N I N G THE
ABSOLUTE LOCATION O F SIMILAR
EVENTS
Due to differences between the earth model used in earthquake
location and the real Earth, one would expect the time residuals
to be much larger than the accuracy of reading the first
arrivals. An error of 0.1 s corresponds to a distance of 650m
for P waves. In most cases the S velocities of the Earth are
even less well-known than the P velocities. The formal estimate
of the single event location accuracy given by the routine
location algorithm of the SIL system is in the range 500-700m
for the horizontal coordinates and about 1OOOm in depth.
The timing accuracy achieved by cross-correlation techniques can be used not only for relative locations but also for
absolute locations. This is illustrated in Fig. 1. The figure
indicates that an absolute movement, of a group of densely
spaced events, of as little as 200 m is enough to cause systematic
effects on the arrival time differences of 1 ms, for a station at
6 km distance. Since such timing accuracy is possible for arrival
time differences, one would not expect the absolute location
errors to be many times larger than 200m, if the closest station
is at a distance of 6 km. This means that including the accurate
arrival time differences in a joint location algorithm is expected
to improve the absolute location of the group. The absolute
arrival times are affected by the whole ray path. Any deviation
from the velocity model along the path will integrate and
possibly cause significant residuals. This can be partially
overcome by introducing station corrections, which leads to a
common type of JHD.
The main sources of error expected when locating with time
differences of similar events are the uncertainties in the ray
directions in the source volume. The deviations of ray directions from those predicted by the model are partially independent of the integrated traveltime error along the path. This
means that the absolute location errors that arise from the use
of arrival time differences will be nearly independent of the
single event location errors.
Most location algorithms work by minimizing a weighted
square sum of arrival time residuals. When working with
similar events, it is straightforward to extend the method by
including the weighted sum of the residuals of the arrival time
differences. This means that several events must be located
200 m
A’
7
I
&
82
Figure 1. An event pair separated by a distance of 200m is initially
located at A1 and A2. Event 2 at A2 is closer to the station and the
P-wave traveltime is approximately 0.5 ms is shorter than for event 1.
If the absolute location is shifted to B1 and B2, without changing the
relative location, the P-wave traveltime for event 2 will be 0.5 ms
longer than for event 1. If the arrival time difference observations have
an accuracy of l m s or better, an absolute movement of 200111 can
have a significant effect on the arrival time difference. Hence, the
arrival time difference between similar events, observed at several
stations, can affect the absolute location.
0 1995 RAS, GJI 123, 409-419
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difference. This can be done either by cross-correlating the
signals (e.g. Slunga, Norrmann & Glans 1984; Deichmann &
Garcia-Fernandez 1992) or by searching for linear trends in
the spectral phase differences (e.g. Ito 1985). As long as antialiasing filters have been correctly applied, both methods give,
in principle, arbitrarily good accuracy. In theory, the limited
sampling frequency places no restriction on the timing accuracy
of the estimated arrival time difference for truly similar signals.
This is obvious if one bears in mind that a continuous signal
can be reconstructed completely from its digitized counterpart,
provided that the signal contains no energy above the Nyquist
frequency.
The accuracy of the estimate of arrival time differences
between pairs of similar events is normally reported to be of
the order of 0.001 s for microearthquakes recorded by local or
regional seismic networks (e.g. FrCmont & Malone 1987). The
most obvious use of the extreme timing accuracy is for the
relative location of earthquakes. The basic idea is that if such
similar events originate very close to each other, the ray paths
for the events will be practically the same. The only difference
in the traveltimes will then be due to the small location
difference, as seen from the observing station. This has been
utilized in a number of publications. Deichmann & GarciaFernandez ( 1992) studied earthquake swarms in Switzerland,
Console & Di Giovambattista ( 1987) applied the technique to
events in central Italy, Ito (1985) applied it to swarms in
Japan, and Fremont & Malone (1987) used relative location
to study the seismicity beneath Mount St Helens in the USA.
Poupinet, Ellsworth & Frechet (1984) used similar earthquakes
to monitor velocity variations in the Californian crust, and
more recently Moriya, Nagano & Niitsuma (1994) have applied
relative location to study crack behaviour in a geothermal
field in Japan. All these authors use some variation of the
master event method, i.e. the absolute location of one earthquake (the master event) is determined using some standard
single event location algorithm. The locations of other similar
events, relative to the master event, are then determined
through cross-correlation of their waveforms with the master
waveform.
Cross-correlating all possible pairs of events, rather than
correlating each event with a master earthquake, provides
additional constraints on the relative locations. This has been
utilized by Slunga et al. (1984), who applied relative location
to a main event and four aftershocks in Sweden to determine
the fault plane, and by Got, Frechet & Klein (1994) to relocate
more than 250 earthquakes beneath Kilauea, Hawaii. Got
et al. (1994) determined the absolute location of the earthquake
swarm by requiring the barycentre of the hypocentre distribution after relative location to coincide with that of the single
event location distribution.
In this paper, we point out that the extremely high arrival
time difference accuracy, obtainable for similar events, allows
improvements in absolute locations. We apply a method for
joint hypocentre determination (JHD) to similar events
recorded by the South Iceland Lowland (SIL) network, giving
both accurate relative locations and improved absolute
locations. In combination with fault-plane solutions, the relative locations give fairly well-constrained estimates of the fault
plane for earthquakes recorded at three or more stations. For
the SIL network, this corresponds to earthquakes with magnitudes less than zero.
Absolute and relative locations of similar events
simultaneously, since the observed arrival time differences
depend on locations and origin times of two events.
For arrival time residuals, we have
%(i,j
k)=tzbs(i, j , k ) - T(i,j , k ) ,
(1)
and For arrival time difference residuals we have
ed(lJ, k,, k2)=tgbs(i,j,k,, k2)-T(i,j, k2)+T(i,j,k l ) ,
(2)
nobs=mn(n-1 )
m
2
n
(4)
(3)
where every pair has been used. These observations are,
however, not independent. The number of independent observations is 2m(n - 1). Each event has four unknowns: latitude,
longitude, depth and origin time. Thus we have a total of 4n
unknowns. This means that even for small networks the relative
timing will give an overdetermined location problem. Note
that in our formulation of the problem as an absolute location
problem, we also have 2nm absolute arrival times if all stations
report both P and S arrivals. The residuals of these are not
independent since the major source of error is the deviation
between the real Earth and the velocity model used for
calculating the theoretical traveltimes.
Our algorithm is thus as follows.
(1) The arrival time differences are estimated at each station
and for each phase ( P and S) for all pairs of similar events.
0 1995 RAS, GJI 123,409-419
This estimate is made by direct correlation of bandpass-filtered
signals, using a fast Fourier transform (FFT). When determining the time lag we resample the cross-correlation function at
1000Hz and after that interpolate with a second-order polynomial around the maximum.
(2) Since the number of observed arrival time differences
for each station and phase is much larger than the number of
unknowns, the internal consistency of the data can be checked
before starting the location procedure. The consistency check
for each phase at each station consists of a least-squares
estimate of the arrival times of the phase from each event, i.e.
finding n unknowns, where n is the number of events. However,
since only arrival time differences are used, one arrival time is
fixed. This is similar to the consistency check described by
Deichmann & Garcia-Fernandez (1992). In the least-squares
solution for the rest of the arrival times, we weight the observed
differences by their correlation coefficients from the crosscorrelation. With a bandpass filter of 3 to 12 Hz, the correlation
is often above 0.99 for a window length of 64 samples. No
observations having correlation coefficients of less than 0.8 are
used. In this check, we successively eliminate outliers until the
largest residual is less than 0.003s. In most cases, all observations are accepted for the closer stations. Typically the rms
value of the arrival time differences for each station and phase
is in the range 0.3-1.3ms. The rms values for P and S waves
are similar, but usually a larger number of S phases can be
correlated successfully.
(3) All timing data are compiled, i.e. the absolute arrival
time observations, the differences in absolute arrival times, all
consistent relative arrival time difference observations, and the
differences in the arrivals of P and S waves between similar
events. We then minimize the total weighted square sum of
residuals, Q, by iteratively solving the linearized problem. Q is
defined as
where w,, wG,wd and wps denote the weights of absolute arrival
times, difference in absolute arrival times, relative arrival time
differences and differences in P to S interval, respectively. The
sum in i is over the number of stations, j refers to the type of
phase ( P or S) and k to the number of events. The variables
kl and k2 refer to events forming a pair used for determining
arrival time differences. Retaining only the first term in the
sum corresponds to standard single event location. Including
the second term is equivalent to a simple JHD with constant
station corrections. The second term eliminates the need for
explicit station corrections in the location procedure. The last
two terms include arrival time differences determined by crosscorrelation and give the relative locations for a group of
similar events.
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where ea is the arrival time residual, ed is the residual of the
arrival time differences, t:bs the observed arrival time, tgbs the
observed time difference, and T is the theoretical arrival time.
The subscript 'i' denotes station, 'j' denotes phase, and k, kl,
and k, denote events. Note that the tgbs values are estimated
directly from the correlation of similar signals, independent of
the arrival time observation t,obs.
The expected variance of e, (i, j , k) will include effects due to
the difference between the real Earth and the model used for
calculating T Experience shows that this variance will rarely
be much less than 0 . 0 1 ~for
~ events recorded by the SIL
network, corresponding to a standard deviation of 0.1 s. This
contrasts with the expected variance of ed(i,j, kl, k2), in which
the earth model errors will almost cancel and the variance will
be of the order 1 x 10-6s2, corresponding to a standard
deviation of 0.001 s.
In this paper we retain the absolute formulation of the
problem, because the high accuracy of the relative timing has
a potential not only for achieving extremely accurate relative
locations but also for improving the absolute location. This
will happen if the absolute location significantly affects the
theoretical arrival time differences. In general, this effect is
reduced with increasing distance between events and station.
In our formulation, we do not have to put any restrictions on
the absolute locations. If the geometry is such that the arrival
time differences favour a particular absolute location, the
group may move there.
In our applications in this paper we work with groups
consisting of between eight and 36 similar events. These are
recorded at only three to eight stations. With n events for
which P- and S-wave recordings are available at m stations,
the number of arrival time difference observations nabs will be
411
412
R . Slunga, S . Th. Rognvaldsson and R . Bodvarsson
3
T H E SIL N E T W O R K A N D D A T A
The data used in this study were recorded by the South Iceland
Lowland (SIL) network during 1991 and 1992. The tectonics
of southern Iceland are dominated by two overlapping spreading centres, the Eastern Volcanic Zone (EVZ) and the Western
Volcanic Zone (WVZ). The spreading centres are connected
by a nascent transform fault, the South Iceland Seismic Zone
(SISZ). The network covers an area of approximately
70 x 70 km2 between the volcanic zones, with a station spacing
of 20-30km (Fig. 2). At the time of data collection, the array
consisted of eight short-period, three-component digital seis-
mic stations, connected to a central processor by an X.25
communication link. The SIL network uses 1 Hz geophones,
has a digitization rate of 100 samples-' and a total dynamic
range of 136dB (Steftinsson et al. 1993).
Many older networks have analogue transmission on permanent lines to a central digitizer. In such cases the timing of all
stations will have the same clock error, and in a relative
location algorithm the error will only affect the origin times
of the recorded events. This follows because for each station
the transmission delay will be constant and the same for all
events, and will thus cancel in the estimation of arrival time
differences. For a more detailed discussion of possible causes
of network timing errors and remedies to these, see Poupinet
et at. (1984).
An arrival time difference accuracy of 0.001 s, achievable by
cross-correlation and necessary for relative location, is much
better than the timing accuracy used in classical seismology.
The experience gained from work with the relative location of
microearthquakes in Sweden (Slunga et al. 1984) prompted
the designers of the SIL network to require an absolute timing
accuracy of better than 1 ms for the network clocks (Stefansson
et al. 1986). The installation of the SIL system included the
design and construction of clocks meeting these requirements.
The prototype clocks, in use during 1991 and 1992, have an
absolute timing accuracy of f 3 m s , i.e. they lock onto the
omega pulse train with this accuracy. However, the accuracy
is better than & 1ms, as long as the clock stays locked to the
omega carrier signal, i.e. during periods of uninterrupted
operation of the seismic station. We selected five clusters where
each cluster spans less than a 48 h interval, during which all
the stations operated normally and without interruptions to
the clocks. The prototype clocks were replaced in 1993 July
with upgraded versions.
The location of the earthquake clusters is shown in Fig. 2.
b
Y
64' 30'
A
/
64' 00'
A
e
63' 30'
0
I
-23"
-
-
-22"
-
-
-21 *
-
-
-20"
-
-
-
-19"
Figure 2. The study area in south-western Iceland. Stations of the SIL network are denoted by triangles, and the locations of the earthquake
swarms discussed in the text are shown by ellipses. The Western Volcanic Zone (WVZ) is outlined with thin lines.
0 1995 RAS, GJI 123,409-419
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In principle the weights used should be the inverse of the
variance of the residuals of the observed variables in each term
in Q. Since the errors of our observations are not independent,
we reduce the weights in the following manner, to avoid
underestimating the uncertainties. The arrival time weight
wa(i,j, k) is reduced by a factor of l/na(i, j ) if na> 1, w,(i,j) by
a factor (n- l)/nc(i,j) if n,(i, j ) 2 1, wd(i,j , kl, k 2 ) by a factor
of ( n - l ) / n d ( i , j ) if
and wps(i, k , , k 2 ) by a factor of
(n- l)/nps(i).Here n a ( i , j ) is the number of phase arrival time
observations of type j (i.e. P or S) at station i, nc(i,j) is the
number of absolute arrival time differences for phase j and
station i, nd(i,j) is the number of relative arrival time difference
observations for phase j at station i, and nps(i,j ) is the number
of P-S interval observations for phase j at station i. In the
iterative solution, we successively truncate outliers, i.e. events
for which the relative location is poorly constrained. The
theoretical traveltimes are computed for an earth model consisting of horizontal layers with constant velocity gradients.
The velocity model is based on interpretation of refraction
profiles in the area (Bjarnason et al. 1993).
Absolute and relative locations of similar events
4 EXAMPLES
4.1 Vordufell
joint hypocentre determination and relative location. The
epicentres are located within an area of 400 x 600 m2. Fig. 3( b)
shows a view along the strike of the best-fitting plane through
the hypocentres. The strike of this plane is 20" and it dips 78"
to the east, in good agreement with observed fault orientations
in the area. The average distance of events from the best-fitting
plane is 12 m. The earthquakes are distributed in depth between
2.3 and 3.0 km.
Fig. 3(c) shows the range of planes through the hypocentres,
where the average distance of events from the plane is required
to be less than 25 m. The figure is an equal-area projection of
the lower hemisphere, and each plane is represented by its
down-pointing normal. Clearly the acceptable (i.e. with mean
distance less than 25m) planes strike 10"-30" and dip steeply
to the east. Fault-plane solutions were obtained for all 18
earthquakes, using the P-wave polarities and absolute spectral
amplitudes of the direct P and S waves. The fault-plane
solutions are obtained by systematically searching over the
entire parameter space for strike, dip and rake, and comparing
predicted polarities and amplitudes with observations. The
output is a range of acceptable solutions, as well as a single
best-fitting mechanism (Slunga 1981; Rognvaldsson & Slunga
1993). To compare focal mechanisms of all the events with the
results of the relative location, we construct the set of common
(4
i " "at
0.8
I o.6
0.4
F
Y
)I
0.2
0.0 0.2 0.4
2.6
.
c
Y
Q
0
0
0
0.0 0.2 0.4
Misfit
Figure 3. The Vordufell swarm. (a) An epicentral map after joint hypocentral determination and relative location; Y is north, X east. (b) A view
along the strike of the best-fitting plane through the hypocentres. The X-axis is at right angles to the strike, i.e. N11O"E. (c) A lower hemisphere,
equal-area projection of the normals of acceptable planes through the hypocentres. The shading indicates the mean distance of events from each
plane; only planes with a mean distance less than 25 m are included in the figure. The contouring is at 5 m intervals. (d) The acceptable fault-plane
solutions, as determined from polarities and spectral amplitudes. The shading indicates the misfit between theoretical and observed amplitudes;
only solutions with misfits of less than a factor of 2.75 are included.
0 1995 RAS, GJI 123, 409-419
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An earthquake sequence of 21 events (magnitude 0.1-2.8)
located near Vordufell just north of the SISZ, was recorded by
the SIL network on 1991 December 16. Vordufell is a hyaloclastite mountain in the Pleistocene rock north of the SISZ.
The area around Vordufell is heavily fractured, and subparallel,
northerly trending (20"-30") faults abound. Where observable,
the dip of these faults is approximately 80" to the east (Agust
Gudmundsson 1994, personal communication).
We determined the relative locations of 18 earthquakes of
the swarm. The correlation of these events showed them to be
very similar, with correlation coefficients for both P and S
phases often greater than 0.99. The signal windows were 0.64 s
long and bandpass-filtered between 4 and 12 Hz. The internal
consistencies were in the range 0.2-1.8 ms. The final residuals
for the arrival time differences had an rms value of about
2-4ms. The residuals for P were slightly smaller than for S at
most of the stations used. The relative location uncertainties
are estimated to be 5-20m for longitude and latitude and
7-30m for depth.
Fig. 3(a) shows a map view of the epicentres after combined
413
414
R . Slunga, S. Th. Rognvaldsson and R . Bodvarsson
4.1 .I
Comparing different location methods
,
The Vordufell cluster had the best station geometry of the data
sets analysed. This made it suitable for testing the effect of
2.2
2.4
Y
2.6
T
I
4.2 Ingolfsfjall
I
?
3.0
relative timing from cross-correlations on absolute locations.
To compare the different approaches to earthquake location,
we made three computations. The first was a conventional
JHD, which means that we put the weights wd and wps in eq.
(4) to zero. In the second application, we make no use of
absolute arrival times, i.e. we put w, and w, to zero, and in
the third all the observations are used with appropriate
weighting. In Fig. 5 we compare the resulting epicentres of
single event locations and these three cases. Even if the JHD
reduces the scatter of the events (Fig. 5b), the scatter is still
too large to allow determination of the fault plane from the
relative locations. When the cross-correlation timings are used
(Figs 5c and d), the events cluster very tightly and line up
along a steeply dipping plane (see Fig. 3b). Comparing Figs
5(b) and (d), the movement of the group when accurate time
difference observations are included is approximately 1200m
in longitude and 500m in latitude. The formal absolute error
estimates (with our approximate handling of the weighting)
are about 400m in epicentre and 300m in depth for the last
case, while the JHD has about a 600 m uncertainty in epicentral
locations and 1.7km in depth. The differences in epicentral
locations are slightly greater than expected from the formal
uncertainties. This indicates that our assumptions about either
the absolute arrival time residuals or the relative arrival times
(or possibly both) given by the cross-correlation are slightly
optimistic. The relative location errors for longitude are estimated to be 7-22m and the mean deviation from a plane is
12m. There is therefore no obvious reason to think that the
error estimates from the relative locations are biased.
Note that the absolute locations in Fig. 5(c) are obtained
without any use of absolute timing observations. This demonstrates that fairly good absolute location estimates can be
found from high-accuracy arrival time difference data alone.
The true locations of these small events are of course unknown.
However, the great improvement in relative locations motivates
the inclusion of accurate relative timing in the multi-event
absolute location procedure.
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fault-planes from the ranges of acceptable fault planes for each
event (Rognvaldsson & Slunga 1994). This gives the range of
fault-plane orientations that satisfy the available polarities and
amplitude data for all earthquakes of the swarm. The results
are shown in Fig. 3(d), where the normal vectors of the
acceptable fault planes are plotted on an equal-area projection.
Comparing Figs 3(c) and (d), it can be seen that the set of
fault planes common to all the events partially overlaps with
the set of best-fitting planes through the hypocentres after
' relative location. The two independent means of estimating
the fault plane therefore give consistent results.
Having determined the most likely fault plane, the slip
direction for each earthquake on that plane can be found from
the range of acceptable fault-plane solutions. The slip direction,
or rake, of the source is defined as the direction of movement
of the hanging wall relative to the footwall (Aki & Richards
1980, p.106). We take the slip direction that minimizes the
summed amplitude errors of all events of the swarm and
satisfies all polarity observations to define a mean slip direction
for the swarm. This gives a rake of -176" for the Vordufell
swarm, i.e. nearly pure right-lateral strike-slip. The arrows in
Fig. 4 show the slip directions viewed from the hanging wall,
i.e. looking nearly due west. The circles show the estimated
area that has moved in each earthquake. The radii are estimated from the seismic moment and corner frequency. The
lengths of the arrows are set equal to the radius of the
associated slip area but are not proportional to the amount of
slip in each event. The slip varies between 0.01 and 2.30mm.
1
0.2
0.4
0.6
0.8
Figure 4. The best-fitting slip directions (arrows) and slipped areas
(circles) for the Mrdufell swarm, looking from the hanging wall. The
arrows show the direction of the hanging wall relative to the footwall.
The slip is mostly right-lateral strike-slip, with a small component of
normal faulting.
Repeated swarms occur close to a surface fracture just south
of Ingdfsfjall, a mountain at the western end of the SISZ.
Rognvaldsson & Slunga (1994) discussed in detail the focal
mechanisms of 12 events of a swarm that occurred there in
1991 October. They concluded that all 12 events could have
been located on a single fault with a strike fitting that of the
nearby surface fracture. Another small cluster of earthquakes
took place in the area five months later, on 1992 March 10,
and a third one occurred on 1992 August 27. These will be
referred to as clusters 1, 2 and 3, respectively.
The correlation of these events showed that events occurring
within the same day gave very high correlation coefficients,
above 0.99 for most stations. Correlating events from different
swarms rarely gave such high correlation coefficients, and then
only at one station. This indicates differences in location,
source mechanism and/or temporal variations somewhere
along the ray paths. Because of the reduced similarity between
the three clusters, we analysed each group separately. The
resulting arrival time difference residuals were in this case quite
small, 0.5-2 ms, but only four stations had more than n (number
of events, n=8-19; see Table 1) arrival time differences. The
small number of stations used resulted in a less favourable
geometry, which means that hardly any reduction of the estimated absolute location errors was achieved for these three
0 1995 RAS, GJI 123, 409-419
Absolute and relative locations of similar events
2
t-----t
2 ;
I
I
I
I
n
415
II
0
E
25'
1 -
>
0
0
0
1
3
2
0
x [kml
1
I
2
3
x [kml
3
2
x [kml
0
1
2
3
x [kml
Figure 5. Comparison of single event locations (a), joint hypocentral determinations without relative timing (b), relative locations without absolute
timing (c) and simultaneous J H D and relative location (d). See text for discussion.
Table 1. Results of the relative location for the three swarms near
Ingblfsfjall.
Date
Strike
Dip
Mean dist.
from plane
Nr. of
events, n
Magnitude
range
1991/0ct/22
1992/Mar/10
1992/Aug/27
21"
354"
356"
84"
76"
10m
4m
llm
15
8
19
-0.3-1.2
0.3-1.5
0.0-1.9
90"
groups. The estimated relative location accuracies were 10-25 m
for latitude and longitude, and 15-30m for depth.
Table 1 and Figs 6 and 7 summarize the results of analysing
data from the three swarms near Ing6lfsfjall. The top row in
Fig. 6 shows a view along the strike of the best-fitting plane
through each cluster. The y-axis of the coordinate system is
depth, but x is at right angles to the strike direction in each
case, i.e. nearly due east. The stereonets show the range of
planes where the mean distance to the earthquakes of each
swarm is 25m or less, and the range of fault-plane solutions
acceptable for all events of each swarm.
For the Ingolfsfjall clusters, the station configuration is less
favourable and the events are smaller than in the swarm near
Vordufell. Comparing the depth views (Figs 6, top row) with
the same figure for Vordufell (Fig. 3b), it is clear that the events
are much more closely spaced for the Ingolfsfjall clusters.
Consequently, the orientations of best-fitting planes through
the hypocentres are poorly constrained compared to that for
the Vordufell cluster. However, the optimal solutions are in all
cases northerly striking, steeply dipping planes. The results of
the relative location are consistent with the plane orientations
obtained from fault-plane solutions. The relative locations
resolve the ambiguity of the fault-plane solutions, where a
0 1995 RAS, GJI 123,409-419
distinction cannot be made between the fault plane and the
auxiliary plane. Comparing rows 2 and 3 in Fig. 6, the relative
locations clearly exclude the E-W striking planes as conceivable fault planes. Requiring that the results of the focal
mechanism estimates agree with the relative locations also
reduces the range of possible N-S fault planes. Taking the
best-fitting plane through the hypocentres of each cluster to
be the fault plane in each cluster, the optimal slip is rightlateral strike-slip but with a considerable dip-slip component
(Fig. 7). Since a westward dip cannot be ruled out, this
component could be related to either reverse or normal
faulting.
4.3 The Western Volcanic Zone
On 1992 July 30 and 31, a swarm of 40 events located at
64.5"N, 20.77"W in the rift zone in south-western Iceland (the
Western Volcanic Zone) was registered by the SIL network.
The earthquakes range in magnitude between 0.4 and 1.9 and
were recorded at four to eight stations of the network. Again,
very high correlation coefficients were found for some of the
event pairs. In this case the data were of high quality, in the
sense that seven stations had overdetermined observations of
arrival time differences both for P and S waves. However, the
cluster was situated outside the network, which reduced the
possibility of achieving accurate absolute locations. The final
residuals were of the order of 3-5ms, which means that the
absolute location of the group has not improved by much.
The estimated relative location errors are also larger than for
the clusters within the network, 60-100 m in latitude, 20-30m
in longitude and 100-150m in depth. The large final residuals
Downloaded from http://gji.oxfordjournals.org/ at Pennsylvania State University on September 18, 2016
0
I
1
416
R. Slunga, S. Th. Rognvaldsson and R. Bodvarsson
Swarm 1
.
E
Swarm 3
Swarm 2
4.5
-
5.3
4.6
-
5.5
-
5.7
- 5.8
4.8
0.6
5.6 Y
5.4
4.7
0.0 0.1
0.7
0.0
0.2
0.1
.
c
-
+
Q
a,
0
0.2
25
20
15
10
5
0
Mi
2.75
2.50
2.25
2.00
Figure 6. The three clusters near Ing6lfsfjall. The top row is a view along the best-fitting plane through each group. The second row shows the
range of acceptable planes through the hypocentres after relative location, and the third row shows the range of fault planes that satisfy all polarity
and amplitude observations.
-E
5.2
x
u
5 5.4
Q
a>
n 5.6
Swarm 1
Swarm 2
Swarm 3
t
-I
1.0
1.2
5.6
5.8
0.4
0.6
0.8
0.6
0.8
Figure 7. The slip directions and slipped areas for each event of the three clusters near Ingolfsfjall (the conventions are as in Fig. 4). The dip of
the fault plane in each swarm is poorly constrained (see Fig. 6 ) and can be either to the east or to the west. Hence, the vertical component of slip
can be related to either normal or reverse faulting.
may be due to the fairly large distances between the events.
The final locations are spread over a (fault) plane with a
diameter of 1.5 km. This is more than one wavelength and
means that the ray paths may be significantly different, and
thus that the basic assumptions for the high-accuracy relative
location have been violated. The apparent success of the
relative location may then be due to the good overdetermination given by the seven stations.
0 1995 RAS, GJI 123,409-419
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istance
Absolute and relative locations of similar events
I
I
I
,
I
,
I
ment with geological observations in the area (Gudmundsson
1992).
5
D I S C U S S I O N A N D CONCLUSIONS
We have demonstrated the application of a joint hypocentre
location algorithm which makes use of the high accuracy of
relative arrival times that can be achieved for similar earthquakes. In favourable cases (good station coverage and some
close stations), not only the relative locations but also the
absolute location of the group can be improved by the use of
similar events. For the cases studied here, the relocated similar
events turned out to define planes. These planes fit not only
the independent fault-plane solutions but also the fault directions and fault dips visible at the surface. Altogether, this is a
,
-
3.6
- 1.8
0
3.8
0
-
0 0
-
0
OO
0
-
- 1.4
0
0
-
0
0
- 0 0 0
-
-
O
0
1.2
0
0
0
-
1.0
oo
OOQ)
0
-
0
0
0
-
-
0
0
0
1.6
0.8
4.0
.
E
.
>
4.2
4.4
Y
E
.
c
Y
.I-r
4.6 Q
a,
4.8
0
- 0.6
8
I
n
5.0
-
- 0.4
5.2
I
'
I
'
I
~
I
'
0.2
0.4 0.6 0.8 1.0 1.2
Distance
[ml 25
20
15
10
5
0
Figure 8. The earthquake swarm in the WVZ. (a) An epicentral map. (b) View along strike of the best-fitting plane. (c) The range of acceptable
planes through the hypocentres. (d) The range of fault planes satisfying polarity and amplitude observations. The fault plane solutions are poorly
constrained, due to the unfavourable station geometry, but very few plane orientations fit the relative locations.
0 1995 RAS, GJI 123, 409-419
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The relative locations of 36 events of the swarm define a
well-constrained plane striking 213" and dipping 63" towards
west (Fig. 8). This strike is in excellent agreement with the
strike of mapped surface faults in this part of the rift zone
(JChannesson & Szmundsson 1989), i.e. N30°-35"E. The average dip of several hundred faults in the WVZ is approximately
7 0 (Gudmundsson 1992).The acceptable fault-plane solutions,
on the other hand, are highly non-unique (Fig. 8d), because of
the unfavourable station configuration. The earthquakes are
located outside the network and the azimuthal coverage is less
than 90". For 14 of the events no P-wave polarities could be
read, while for the remaining 22 events one to two unclear
polarities were used in the focal mechanism inversion.
The well-constrained fault plane from the relative locations
was used to estimate the optimal slip direction for the swarm.
Movement in the swarm is normal faulting, in good agree-
417
418
R. Slunga, S. Th. Rognualdsson and R . Bodvarsson
surface mapping, relative location may help to reveal the actual
extent of fracturing in the crust of southern Iceland.
The high-accuracy relative timing can also be used for
monitoring seismic velocities in the crust (e.g. Poupinet et al.
1984). For a network without a single central clock, a prerequisite for this application is the long-term stability of the
station clocks.
3.6
3.8
4.0
1
F
t
4.2 -
Y
I
4.4 L
+
ACKNOWLEDGMENTS
a 4.6 a
n 4.8
-
5.0 -
wt
5.41 ' l ' l ' l ' , ' , , , 7 , . , !
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Figure 9. The slip directions of the swarm in the rift zone in southern
Iceland (the WVZ). The fault dips 63"W and the optimal slip direction
is - 39", i.e. normal faulting, in good agreement with geological data
from exposed faults in the area.
very strong indication that these similar events represent
repeated slip on the same fault.
One obvious use of the method is to discriminate the fault
plane from the auxiliary plane given by fault-plane solution
algorithms based on point source assumptions. This use of
similar events also improves the ability to map active faults
by the use of microearthquakes. The dips of earthquake
fractures in the SISZ can rarely be observed directly. Studies
of earthquake fault-plane solutions and hypocentre distributions are the most promising geophysical methods for
determining the orientation of active faults in the area. A
magnitude 5.8 mainshock and 14 aftershocks that occurred at
the eastern end of the SISZ in 1987 were associated with
faulting on a near-vertical north-striking fault (Bjarnason &
Einarsson 1991). Shallow geothermal wells have been drilled
in several places in the SIL, often near water-bearing earthquake fractures. The results of drilling indicate that the fractures are steeply dipping, usually to the east, but westwarddipping fractures are not uncommon (Helgi Torfason 1994,
personal communication).
The nature of the SISZ has been the cause of some discussion
in recent years. At least three different models have been
suggested to explain the existence of an array of N-S trending
faults in an area where conventional wisdom would predict
a single E-W transform (Stefansson & Halldorsson 1988;
Einarsson 1991; Gudmundsson & Brynjolfsson 1993).
Numerical modelling (Hackman, King & Bilham 1990) suggests that bookshelf faulting on N-S trending faults within the
SISZ can accommodate the measured E-W transform motion
between the American and Eurasian plates, provided that the
faults are 20-25km long and spaced less than 5km apart.
Mapped surface fractures are spaced 1-6km apart and are
usually less than lOkm long (Einarsson 1994). The relative
location of microearthquakes seems to be a promising tool for
mapping active fractures in the area. Used together with
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5.2
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