Geophys. J. R. astr. Soc. (1981) 64,187-200
Complex P waveforms from a Gulf of Aden
earthquake
R.G . PearCe*Ministry of Defence, Procurement Executive, Blacknest,
Brirnpton, Reading, Berkshire RG7 4RS
Received 1980 May 22
Summary. It is shown that complex teleseismic P waveforms from a shallow
earthquake in a tectonic area can be interpreted using a simple source model
embedded in a plane layer velocity structure (with sea layer) whose details
are based upon independent evidence. This gives hope that structural complexity in tectonic regions may not always make distant P-wave seismograms
impossible t o interpret, and that, instead, source complexity may be
responsible for some of the many complex waveforms observed, even for
earthquakes below magnitude mb 5 . 5 .
1 Introduction
Interpretation of teleseismic short period P waveforms in terms of P , pP and sP has been very
successful for earthquakes which occur far from major tectonic zones, because a combination
of s m d simple source mechanism, simple shield-like velocity structure and high Q transmission paths produces exceptionally 'clean' seismograms between epicentral distances of
30" and 90", consisting primarily of only one, two or three discrete arrivals (see, e.g.
Mendiguren 1971; Douglas, Marshall et al. 1974; Douglas, Hudson et al. 1974; Pearce
1977a, b, 1980; Barley & Pearce 1977). Indeed, it is possible to compute source mechanisms
using the observed relative amplitudes of these three phases (Pearce 1977a, b, 1979, 1980)
and then to model the waveforms at each station using the method of Hudson (1969a, b)
and Douglas, Hudson & Blarney (1972), which considers a Savage (1966) type source with
homogeneous plane layered velocity structures near the source and receiver, and an average
anelastic attenuation for the whole path. The close similarity between theoretical and
observed waveforms which this process can achieve has done much to convince us that this
simple interpretation of such 'classic' seismograms is basically correct, and it has therefore
been possible in specific cases to infer from the waveforms such information as source size
and mechanism, focal depth, depth to the Moho, and the presence of low velocity surface
layers.
Unfortunately, short period seismograms observed from shallow earthquakes in tectonic
zones, whether beneath spreading centres, rift valleys or island arcs, are usually very
complex, even for earthquakes with mb below 5.5 when we might expect the duration of
Present address: National Coal Board, Denaby No. 2 Office, Doncaster DN12 4ED.
R. G. Pearce
188
seismic emission from the source to be well within the short period bandwidth. The signal
enhancement offered by seismic arrays provides us with many examples of complex waveforms down to mb = 5.0 and below. This complexity is a generally accepted feature of such
seismograms, usually being dismissed as due to structural effects near the source, and there
is no doubt that high anelastic attenuation, heterogeneous velocity structures, and various
types of scattering can all prevent us from extracting useful information from their waveforms.
In this paper seismograms from an earthquake less than 15 km from the ridge of the Gulf
of Aden are shown to be interpretable in terms of a simple source and structural model and
this success, albeit only for one earthquake, leads us to wonder how often the source, rather
than the transmission path, is responsible for complex seismograms which cannot be
interpreted in this simple way.
2 Fault plane solution
Fig. 2 shows phased array (P-wave) seismograms observed at Eskdalemuir (EKA), Gauribidanur (GBA) and Warramunga (WRA) for the eastern Gulf of Aden earthquake of 1971
a tC
e
%lt
2u
N
N
A
R
A
B
I
A
Figure 1. Location of the 1971 April 15 Eastern Gulf of Aden earthquake (ISC origin time 18.57.27.0,
location 12.79' N , 48.56' E, mb = 4.7). Major escarpments (shown with pecks facing downslope) are from
Laughton & Tramontini (1969). Supposed sections of Median Valley are shown with thick lines. The
location of refraction profie 167 (from Laughton 1966) is shown with a pecked line.
Complex P wavejonns
189
P 100 to 200, -ve
pP 00 to 150, we/-ve
sP 00 to 150 we/-ve
pP(ssf1 00 to 150; wel-ve
(a) EKA
C =328O
A = 582’
J
P 120to 220, -ve
pP 5.0 to 150; we/-ve
sP50 to 150; we/-ve
pP!ssfl 100 to 200, we
(b) GBA
= a50
A = 28J0
P80 to 200, -ve
pP80 to 150, we/-ve
sPOO to 50, we/-ve
pP(ssf) 100 to 200, we
(c) WRA
t :1100
A =905O
-
0
5
10s
Figure 2. Phased array seismograms observed at EKA, GBA and WRA for the 1971 April 15 Eastern Gulf
of Aden earthquake. Presumed identifications of phases are shown, with the amplitude bounds (in
arbitrary units) used for the fault plane determination by the relative amplitude method.
April 15, whose location and details are shown in Fig. 1 . These seismograms are clearly not
‘classic’ in the way defined above as they show continuous complex waveforms rather than
a series of discrete pulses. Moreover, the three seismograms differ in character, having
different signal durations and dominant periods. Apart from the initial P pulse at time t l , the
only common feature of these seismograms is the prominent arrival at t4, which is
provisionally identified as the p P type reflection from the sea surface - the most efficient
reflector above the source.
With this phase identification and an approximate knowledge of the sea depth, we know
the corresponding expected arrival times of PP and sP reflected from the sea bed (shown at
t , and t 3 respectively). By assigning bounds to the amplitudes of the five phases in arbitrary
units, the relative amplitude method of Pearce (1977a, 1979, 1980) can be used to find
those orientations of a presumed double couple radiation pattern which are compatible with
the polarities and relative amplitudes of the five phases - that is, we can determine a fault
plane solution. The assigned amplitude bounds for all five phases at the three arrays are
shown in Fig. 2. Corrections to the amplitudes of the surface reflected phases relative to
direct P are made to allow for the loss of amplitude of the former due to passage up and
down through the velocity structure of Fig. 4 (which is introduced later) but any amplitude losses below the source or elsewhere are neglected as they will have an equal effect on
all the five phases observed at any one station.
(b)
SLIP ANGLE IN FAULT PLANE
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Figure 3. Source orientations which are compatible with the relative amplitude observations at the three
seismic array stations shown in Fig. 2. (a) Shows the acceptable orientations plotted on a conventional
lower hemisphere equal area projection, while (b) gives a much clearer indication of the confidence limits
and non-uniqueness of the orientation, by means of a vectorplot as described by Pearce (1977a). The
orientation used to generate the theoretical seismograms of Fig. 6 is arrowed.
+
~
*
*
+
Complex P wavefomzs
191
Fig. 3(a) shows a lower hemisphere equal area projection depicting the source orientations
which are compatible with the relative amplitude data of all the three seismograms of Fig. 2 ;
the pole of each orientation is denoted by a square. Fig. 3(b) is equivalent to Fig. 3(a), but
shows the range of source orientations and their confidence limits in a more useful form.
This 'vectorplot' is displayed according to the method of Pearce (1977a), where each vector
represents an acceptable orientation, defined by its fault plane strike, u, angle of dip 6 , and
slip angle in the fault plane, $. Fig. 3(b) shows that the fraction of acceptable orientations
is much smaller than might be inferred from examining Fig. 3(a); indeed only 0.04 per cent
of orientation space is acceptable. The clusters represent near-normal faults with specific
angles of dip (see Pearce 1977a, Fig. 3). The confidence limits and non-uniqueness of the
mechanism determination are implicit in Fig. 3(b), being represented by the range of source
orientations which is acceptable. Moreover, the fact that there are any double couple
orientations compatible with all the measurements in Fig. 2 is itself strong evidence in
support of the phase indentifications, since the chance of any three randomly chosen seismograms being compatible with a double couple radiation pattern is extremely small (see
Pearce 1980).
In Fig. 3(b) the interchange of fault and auxdiary planes is represented on a different
part of the plot, so that the appearance of four clusters arises from only two distinct types
of orientation as shown in Fig. 3(a). These are both predominantly normal faults, with
different components of strike slip motion, but their existence implies that we are unable t o
determine which of the two solutions is correct using the three array seismograms alone. We
are also unable to specify which nodal plane is the fault plane without observing some effect
of rupture propagation along the fault.
3 Theoretical seismograms
An attempt is now made to reproduce the observed waveforms theoretically, with the aim
of simultaneously modelling other features of the seismogram in addition to the relative
amplitudes of P and the surface reflections. Fig. 4(a) shows the stations of interest plotted
on the focal sphere.
3.1
T H E W R A SEISMOGRAM
The attempt to model the waveforms begins with the WRA seismogram, as this appears to
have the hghest information content, showing both the most complex and the least
attenuated (highest frequency) signal. A theoretical seismogram is generated using the
method of Douglas et al., using a 1 km circular active fault of the type described by Savage
(1966), at one of the acceptable orientations as indicated in Figs 3(b) and 4(a). This source
is placed at a depth which is compatible with the relative times of P and the assumed
sea surface reflections, in an appropriate plane layer velocity structure. This velocity
structure consists of a sea layer whose possible range of depths is deduced from the
bathymetry of the epicentre, overlying surface layers with velocities and thicknesses to
match those found by a long range refraction profile within 50 km of the epicentre
(Laughton 1966, and Fig. 1) and a transition to upper mantle velocity beneath the source.
In addition the effect of the velocity structure beneath WRA (due to Underwood 1967)
is included and an average anelastic attenuation factor for the path is chosen to match the
dominant period of the signal. This is defined as the travel-time in seconds over the average
quality factor, Q, and is denoted by t*.
Figure 4. (a) Positions of stations on the focal sphere, assuming a source layer velocity of 6.9 km s'' as in the model. Note that a wide range of azimuths and takeoff
angles is included. The fault plane orientation is that used to compute Fig. 6 . (b) Shows the four additional orientations used to compute the seismograms of Fig. 7(i).
Complex P waveforms
193
The focal depth, sea depth and the source region velocities, layer thicknesses and densities
can then be perturbed from their initial values in order to maximize the waveform match
between theoretical and observed seismograms by trial and error. By following this procedure the model shown in Fig. 5 was obtained. This figure shows the corresponding
theoretical signal leaving the source region, and beneath it is the resulting theoretical seismogram. Comparison with the observed seismogram, also shown, indicates that an extremely
good waveform match is obtained, which is particularly encouraging in that the velocity
structure and sea depth are consistent with independent evidence, thus providing further
support for the interpretation of the seismic phases.
Fig. 5 also shows how the velocity structure gives rise to the different arrivals in the
theoretical seismogram. Several prominent features common to theoretical and observed
seismogram place important constraints on the model, and are worthy of comment. First,
the time separation of P and the surface reflections provides a focal depth determination
r - - - - - -
Velocity structure in the source region, as used
in the model
P
I
(not drown t o scale).
I
I
density gcm-'
velocity km s'
S velocity km s4
thickness km
A
A
Refraction profile
I 167 (for comparison)
P velocity k r n 9
I
thickness km
I
A
1.50
I
sea
2.22to
3.25
2.08 1.20
/\
\ \ \
_ .
2'4
0.28 to0.4
I
0.7
2.45
4.07
I
1.64to 2.36
I
6.91
I
,
\
\
computed P wove signa
lcovmg the source regio
attenuation
+
receiver+structure
seismometer
computed xismogram
observed seismogram
Y
-
0
5
10s
Figure 5. Computed and observed P-wave seismograms for WRA. This diagram illustrates how the source
region velocity structure gives rise to the different arrivals in the seismogram.
I
1 94
R . G. Pearce
whose only uncertainty is that of the seismic velocities above the source. This earthquake is
therefore concluded to be at a depth of 5.4 f 1.5 km below the sea bed (its uncertainty is
discussed in Section 4).
Secondly, the time separation of pP and the sea surface reflection fixes the sea depth at
3.25 km since the sea layer velocity is known. That this depth lies within the known range
o f bathymetry immediately above the epicentre is a major strength of the model. Furthermore, because both the sea bed and sea surface have a high impedance contrast, successive
reverberations within the sea layer give rise to alternate polarity sea surface reflections whose
intervals are also related to the sea depth. These are observed at the correct time interval in
Fig. 5.
Thirdly, we note that the small negative first motion and the large negative overshoot of
the direct P wave have been reproduced in the model - this overshoot is caused by the
positive reflection from the discontinuity immediately above the source as shown in Fig. 5.
Finally, the seismogram is made much easier to interpret by the absence of sP type
phases, which generally make a seismogram much more complex for reasons discussed by
Pearce (1 980). Indeed it is possible that the presence or absence of upward-going S radiation,
as dictated by the source orientation, may often determine whether or not a short period
P-wave seismogram can be interpreted by relatively simple models of the type used here.
3.2
THE E K A AND G B A SEISMOGRAMS
A much stricter test of the model used for WRA would be to use the same model to
simultaneously generate theoretical seismograms for the EKA and GBA arrays. These,
together with WRA, are shown in Fig. 6, where the structures of Parks (1967) and Arora
(1969) have been used beneath the two stations respectively.
We conclude that the agreement at both GBA and EKA is also good, although the
predicted amplitudes of reflected phases at EKA are smaller than those observed. Another
important result is that a much larger average anelastic attenuation of t* = 1.5 s is needed to
reproduce the large dominant period of the GBA seismogram, compared with t* = 0.4 s
which is used for EKA and WRA. The implications of this are discussed in Section 4. As
expected, seismograms at the three arrays computed for the other allowable type of
orientation in Fig. 3 are very similar to those in Fig. 6 , and are not shown.
3.3
W W S S N S EISM 0 G RAM S
It is typical of predominantly dip slip earthquakes such as this that their radiation to teleseismic distances is generally similar towards all azimuths provided the fault plane is not
vertical. This follows from the nature of the double couple radiation pattern which displays
large antinodal regions both vertically upwards and downwards for a near 45" dip slip fault.
This basic similarity of relative amplitudes and polarities on the P-wave seismograms is seen
a t GBA and WRA, and we might expect a similar picture if more stations were examined. To
test this some vertical component short period WWSSN seismograms were examined.
Although the signal-to-noise ratio of single seismograph stations is generally much lower
than at the arrays, four of the best seismograms were chosen and corresponding theoretical
seismograms were generated using the same model as before. These stations are Shillong
(SHL), New Delhi (NDI), Bulawayo (BUL) and Nurmijavi (NUR), whose positions on the
lower focal hemisphere are shown in Fig. 4(a), together with those of the arrays. Theoretical
and observed seismograms are compared in Fig. 7.
Complex P waveforms
195
Icl observed
at GBA
(dl computed
tor GBA
t*=1.5~
,
If) computed
for WRA
1. O L S
u
10s
Figure 6. Observed and computed P-wave seismogramsfor EKA, GBA and WRA, showing the simultaneous
match that is achieved at the three stations, using the model of Fig. 5 . [ and A indicate azimuth of the
station from the earthquake and epicentral distance respectively.
Although it is less certain that these stations lie above simple crust and upper mantle
structures, a general similarity between theoretical and observed seismograms is seen. This
extends to the polarity and pulse shape of direct P, and the position and amplitude of the
sea surface reflection, which is observed at all the stations. A most significant result is the
prediction by the model of a nodal onset at BUL (Fig. 7f), and this is indeed observed. Any
station close to a nodal plane for P is highly sensitive to small changes in source orientation,
so three other neighbouring acceptable orientations, shown in Fig. 4(b), were also used to
compute seismograms at BUL (Fig. 7i). One of these shows a positive first arrival whch
agrees best with observation. By contrast, the alternative type of orientation gives a large
positive direct P wave as shown in the last example of Fig. 7(i). Also the alternative type
gives large amplitude sP radiation at NDI and SHL (not shown), which is not observed. So
196
R . G. Pearce
observed
at SHL
{=6 6 O
A.42.F
computed
for SHL
t*= 1.0s
i
observed
at
NDI
t=550
A=31.00
computed
for NDI
tg=0.6s
observed
at BUL
f=2110
A=382'
computed
for BUL
tr=0.6s
observed
at NUR
c = 345O
A=507O
compu t ed
for NUR
t*= 0 . 6s
computed
lor BUL
l o r other
oriontat ions
1.
2. -
3.
Figure 7. Observed and computed seismograms for four WWSSN stations, using the model of Fig. 5. Note
that the source orientation determined using only the three array stations correctly predicts the low
amplitude direct P-wave a t BUL.
197
orientations of this type, whde not precluded by the three array stations, are less consistent
with the four WWSSN stations used here.
Complex P waveforms
4 Discussion
Despite the wealth of long range refraction profiles, gravity and magnetic traverses and rock
sampling carried out at sea, and despite the number of earthquake studies which have been
done, the processes beneath the crests of ocean ridges are still only poorly understood. Not
least of these processes concerns the role of the ridge seismicity, so the successful matching
of theoretical and observed seismograms achieved above provides 11s with some results of
geophysical significance which are deduced by a novel method for such studies.
First, the reproduction of sea surface reflections using the known correct sea depth is
good evidence that we have the correct waveform interpretation. Other authors (e.g.
Mendiguren 1971 ; Duschenes & Solomon 1977) have previously identified reflections from
the sea surface, and this modelling of their characteristic appearance offers an accurate way
of fixing the focal depths of shallow undersea earthquakes, since the arrival time of pP can
be deduced once sea surface reflections have been identified with certainty. Focal depth
determinations for shallow earthquakes beneath the oceans have normally only been possible
using arrays of ocean bottom seismographs, or sonobuoys; depths determined by those
methods have been restricted to microearthquakes (Prothero et al. 1976; Francis, Porter &
Lilwall 1978; Lilwall, Francis & Porter 1978; Jones & Johnson 1978). Teleseismic location
studies are unable to constrain the depths of shallow earthquakes, and identification of
surface reflections on individual seismograms is often unambiguous or uncertain. Only by
the successful modelling of several seismograms simultaneously can pP be identified with
sufficient confidence to justify its use to determine the focal depth of intra-crustal earthquakes. Aside from the present paper, Weidner & Aki (1973) provide the only depth
determination of teleseismically recorded earthquakes on an ocean ridge, theirs being
computed from Rayleigh wave amplitude and phase spectra.
The depth determination of 5.4 km below the ocean floor for this Gulf of Aden earthquake is well inside the range of depths deduced in the other studies of ocean ridge
earthquakes (which have generally put depths at less than 10 km). This depth cannot be in
error by more than f 1.5 km - an error which could arise from incorrect specification of
velocities in the model of Fig. 5; this is discussed later.
The second result of interest is the focal mechanism. Although we are unable to
distinguish the fault plane and the auxiliary plane from the seismic evidence, the nodal
planes with strikes near 70" and 100" are consistent with a ridge event on the axis of the
Gulf. The alternative nodal planes, w h c h strike approximately north/south, would be
inconsistent with this interpretation. The set of orientations with strikes of near 100" are
more in accord with the strike of the Median Valley (Fig. 1) whereas the WWSSN seismograms favour the 60" striking set of orientations. It is usual for the strike of normally faulted
earthquakes to be poorly constrained or even unconstrained from teleseismic observations;
here the three array seismograms alone eliminate a half of all possible strikes (Fig. 3a).
The dips of the nodal planes are defined to within 15", and if the above inference is correct
then the fault plane dips at about 70" towards the south, implying an epicentre on the
northern side of the Median Valley. The ISC location is within 5 km of the ridge axis as
inferred from the bathymetry, so its confidence limits include both flanks of the Median
Valley. The errors in the computed source orientation of Fig. 3 (remembering the usual
a priori assumption that the source radiates as a double couple) are completely defined
in Fig. 3(b) and represent only 0.04 per cent of orientation space. (Indeed here it comprises disconnected regions.) It is pointed out that, as with fault plane solutions computed
198
R . G. Pearce
b y all methods, the 100 per cent confidence volume can have any shape in orientation
space. It is always an incomplete description of the error merely to place independent
confidence limits upon the dip and strike of each nodal plane. Moreover, it must be
emphasized that a reliable first motion solution could not have been obtained from an
earthquake of this (low) magnitude; this again suggests that modelling and relative amplitudes could have a wider application in the determination of source orientations for ocean
ridge earthquakes. Many of the solutions computed for larger such earthquakes are published
with no quantitative estimate of their confidence (e.g. Fairhead & Girdler 1970; Sykes 1970;
Forsyth 1975 ; McKenzie, Davies & Molnar 1970).
The third important result concerns the widely differing values of anelastic attenuation
factor t* whch are needed to match the dominant periods of the three array seismograms
shown in Fig. 2. It is important to note that these differences in dominant period cannot be
explained by directional variation in the source spectrum. This is clear from the fact that
there is no temporal variation in dominant period on any of the records, as would be
expected if a different duration of pulse were emitted to the lower and upper hemispheres.
Furthermore, it has been shown that the seismograms can be modelled using a 1 km radius
Savage fault, and to formulate a model in which the observed difference in dominant periods
were created by the source itself, and which could also reproduce the observed waveforms,
would be very difficult. In particular we note the absence of high frequency arrivals on the
highly attenuated GBA seismogram. Doppler effects resulting from elongated fault planes
(Bollinger 1968; Douglas, Hudson & Marshall 1981) would tend to produce stopping phases
on a short period seismogram, which could not be modelled using the type of formulation
employed here. In any case, it would be unlikely for an earthquake as small as this to have a
sufficiently large fault plane to generate such effects.
Hence we conclude that the observed differences in dominant period are indeed the result
of anelastic attenuation, and the high value of t* used at GBA implies an extreme effect
along that path. We would expect the magnitudes to corroborate this, and qualitatively this
is found to be so for GBA and WRA, whose observed mb’s are 5.0 and 5.8 respectively.
Unfortunately the calibration voltage at EKA for the relevant time period is unknown, so
that a confident magnitude determination is not possible.
The final geophysically interesting aspect of this model concerns the velocity structure
which is used (Fig. 5). Here it is important to remember that although the focal depth,
mechanism and anelastic attenuation factors are well constrained by the need to match
model with observation, there are other model parameters in Fig. 5 which are only poorly
constrained by the seismograms, or which are merely given arbitrary but reasonable values.
This applies to some aspects of the velocity structure, each detail of which must be
considered separately.
The velocity structure beneath the sea bed in Fig. 4, which is based in part on the long
range refraction profile shown, is typical of an oceanic profile inasmuch as it has a three
layer crust underlain by material with upper mantle velocity (see, e.g. Keen & Tramontini
1970, for the western Atlantic). It is an important general observation that these realistic
velocities and thicknesses have been shown by modelling to be consistent with the observed
seismograms; models which contain a different number of layers above the source would not
in general allow a match of theoretical and observed waveforms at WRA and GBA. However,
since it is only travel-time differences that are resolved explicitly by the model, it cannot
be said that the modelling has excluded all other possibilities. In particular, an increase in
velocity with depth within layer 1 (which is likely to be present for unconsolidated
sediments) would have little effect on the theoretical waveforms.
Although a wide range of velocities have been measured for layer 2 the value of 4.01
Complex P waveforms
199
km s-' used here is low. However, the waveform does not critically depend on this velocity
and if a value of 5 .O km were used the layer thickness (and the earthquake depth) would be
increased by only 0.7 km, and the effect on reflection coefficients would be small.
Unlike the thicknesses of layers 1 and 2, that of layer 3 is constrained by the need for a
discontinuity immediately below the source, which is required by the model in order to
produce an S to P conversion beneath the source, which can generate the observed P
waveforms at both WRA and GBA. (This S to P conversion has been invoked in other
examples of modelling, and has been interpreted as occurring at the Moho beneath intracrustal earthquakes (Pearce 1977b).) In this model the discontinuity is assumed to be the
'Moho', which has implied a thickness of 2.4 km for layer 3 . Although the thickness of layer
3 averages 5 km and is fairly constant away from ridge axes, we have little knowledge of its
behaviour beneath the ridge itself. Fowler (1976) gives a Mid-Atlantic Ridge structure in
which layer 3 has a thickness of 4 km, but with considerable thinning at the ridge axis.
It is the velocity of layer 3 which governs the take-off angles of rays from the source
(Fig. 6) so that an incorrect assumption of this velocity would reduce the simultaneous
waveform match at all stations.
From this modelling alone we conclude that there is a sharp impedance contrast at this
depth beneath the source, and that there are no other major impedance contrasts beneath it.
The inclusion of an upper mantle with a velocity of 8.1 km s-' merely serves to ensure a
transition to standard upper mantle velocity at some depth, to achieve the correct ray angles
in the mantle halfspace. In practice there is more likely to be a lower velocity immediately
below layer 3 , especially at the ridge axis, as reported by many authors, including Laughton
& Tramontini (1971) for the axis of the Sheba ridge in the Gulf of Aden. It is important
to realize that no constraint is imposed on this velocity by the theoretical waveforms, which
do not change significantly if this velocity alone is changed.
Finally, we conclude that the earthquake must have occurred within layer 3 -both the
inferred number of discontinuities above it, and its absolute depth indicate this.
5 Conclusion
The modelling has shown that complex P waveforms from this earthquake can be interpreted
using a Savage type source in a homogeneous plane layered velocity structure. A closer
examination of more earthquakes in similar settings will be necessary in order to establish
how widely these ideas might be applicable to seismograms from other mid-ocean ridge
earthquakes. Arrays are well-suited to this as they enable good quality seismograms to be
obtained from the smaller, and therefore hopefully simpler sources.
References
Arora, S. K., 1969. Crustal structure near Gauribidanur Array,Proc. Symp. on use of Gauribidanur Array
for Seismological Research, pp. 4-36, Bhabha Atomic Research Centre, Bombay.
Barley, B. J. & Pearce, R. G., 1977. A fault plane solution using theoretical P wave seismograms, Geophys.
J . R . astr. Soc., 51,653-668.
Bollinger, G. A., 1968. Determination of earthquake fault parameters from long period P waves, J.
geophys. Res., 73,785-807.
Douglas, A., Hudson, J. A. & Blarney, C., 1972. A quantitative evaluation of seismic signals at teleseismic
distances - 111. Computed P and Rayleigh-wave seismograms, Geophys. J. R . asfr. SOC.,28, 385410.
Douglas, A., Hudson, J. A., Marshall, P. D. & Young, J. B . , 1974. Earthquakes that look like explosions,
Geophys. J. R . astr. Soc., 36,227-233.
Douglas, A., Marshall, P. D., Young, J. B. & Hudson, J. A., 1974. Seismic source in East Kazakhstan,
Nature, 248,743-745.
2 00
R. G. Pearce
Douglas, A . . Hudson, J. A. & Marshall, P. D., 1981. Earthquake seismograms that show Doppler effects
64,163-18s.
due t o crack propagation, Geophys. J . R. astr. SOC.,
Duschenes, J . D. & Solomon, S. C., 1977. Shear wave travel time residuals from oceanic earthquakes and
the evolution of the oceanic lithosphere. J. geophys. Res., 82, 1985 2000.
Fairhead, J . D. & Girdler, R. W., 1970. The seismicity of the Red Sea, Gulf of Aden and Afar Triangle,
Phil. Trans. R . SOC. Lond.. 261,49-74.
Forsyth, D. W., 1975. Fault plane solutions and tectonics of the South Atlantic and Scotia Sea, J .
geophys. Res., 80, 1429-1443.
Fowler, C. M . R., 1976. Crustal structure of the Mid-Atlantic ridge crest at 37" N, Geophys. J. R. astr.
SOC.,41,459-491.
Francis, T. J . G., Porter, I. T. & Lilwall, R. C., 1978. Microearthquakes near the eastern end of St Paul's
Fracture Zone, Geophys. J . R. astr. Soc., 53, 201-217.
Hudson, J. A . , 1969a. A quantitative evaluation of seismic signals at teleseismic distances - I . Radiation
from point sources, Geophys. J. R. astr. SOC.,18, 233-249.
Hudson, J . A., 1969b. A quantitative evaluation of seismic signals at teleseismic distances - 11. Body
waves and surface waves from an extended source, Geophys. J. R. asfr. SOC.,18, 353-370.
Jones, P. R. & Johnson, S. H.. 1978. Sonobuoy array measurements of active faulting on the Gorda
Ridge,J. geophys. Rex, 83,3435-3440.
Keen, C. E. & Tramontini, C., 1970. A seismic refraction survey on the Mid-Atlantic Ridge, Geophys.
J . R. astr. SOC.,20,473-491.
Laughton, A . S. 1966. The Gulf of Aden,Phi[. Trans. R. Soc., A259, 150-171.
Laughton, A. S. & Tramontini, C., 1969. Structure of the Gulf of Aden, Tectonophysics, 8, 359-37s.
Lilwall, R . C., Francis, T. J. G. & Porter, I . T., 1978. Ocean bottom seismograph observations on the
Mid-Atlantic Ridge near 45" N - further results, Geophys. J . R. astr. SOC.,
55, 255-262.
McKenzie, D. P., Davies, D. & Molnar, P., 1970. Plate Tectonics of the Red Sea and East Africa,Nature,
226, 243-248.
Mendiguren, J . A., 1971. Focal mechanism of a shock in the middle of the Nazca Plate, J. geophys. Res.,
76, 3861-3879.
Parks, R., 1967. Seismic refraction networks in the study of the Earth's crust, PhD thesis, University of
Edinburgh.
Pearce, R. G., 1977a. Fault plane solutions using relative amplitudes of P and pP, Geophys. 1. R. astr.
Soc., 50, 381-394.
Pearce, R. G.. 1977b. A study of earthquake modelling with applications to the East African Rift System,
PhD thesis, University of Newcastle-upon-Tyne.
Pearce, R. G., 1979. Earthquake focal mechanisms from relative amplitudes of P,pP and sP:method and
computer program, A WRE Report No. 0 41 f 79, HMSO.
Pearce, R. G., 1980. Fault plane solutions using relative amplitudes of P and surface reflections: further
studies, Geophys. J. R. astr. Soc., 60,459-487.
Prothero, W. A., Reid, I., Reichle, M . S. & Brune, J. N., 1976. Ocean bottom seismic measurements on the
East Pacifk Rise and Rivera Fracture Zone, Nature, 262, 121-124.
Savage, J. C., 1966. Radiation from a realistic model of faulting, Bull. seism. SOC.Am., 56,577-592.
Sykes, L. R., 1970. Seismicity of the Indian Ocean and a possible Nascent Island arc between Ceylon and
Australia,J. geophys. Res., 75,5041-5055.
Underwood, R., 1967. The seismic network and its applications, PhD thesis, Australian National
University, Canberra.
Weidner, J. D. & Aki, K., 1973. Focal depth and mechanism of mid-ocean ridge earthquakes,J. geophys.
Res., 78,1818-1831.
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