Geophys. J. Int. 1977 Pearce 381 94

Geophys. J. R. astr. SOC. (1977) 50,381-394

Fault plane solutions using relative amplitudes of P and pP

* R. G. PearCe School of Physics, The University, Newcastle-on-Tyne NEI 7RU

Department of Geophysics and Planetary Physics,

Received 1976 December 22; in original form 1976 October 22

Summary. One way of finding the fault plane orientations of small shallow earthquakes is by the generation of theoretical P-wave seismograms to match those observed at several distant stations. Here, a technique for determining the uniqueness of fault plane solutions computed using the modelling method of Douglas et al. is described. Relative amplitudes of P and pP, and their polarities if unambiguous, are measured on the observed seismograms to be modelled, and appropriate confidence limits are assigned to each measure- ment. A systematic search is then made for all fault plane orientations which satisfy these observations.

Examples show that if P and pP are not severely contaminated by other arrivals, a well-defined and unique fault plane orientation can often be computed using as few as three stations well distributed in azimuth. Further, even if pP is not identifiable on a particular seismogram, then an upper bound on its amplitude - deduced from the observed coda - still places a significantly greater constraint on the fault plane orientation than would be provided by a P onset polarity alone. Modelling takes account of all such information, and is able to further eliminate incompatible solutions (e.g. by the correct simu- lation of sP). It follows that if solutions can be found which satisfy many observed seismograms, this places high significance on the validity of the assumed double-couple source mechanism.

This relative amplitude technique is contrasted with the familiar first motion method of fault plane determination which requires many polarity readings, whose reliabilities are difficult to quantify. It is also shown that fault plane orientations can be determined for earthquakes below the magnitude at which first motion solutions become unreliable or impossible.

1 Introduction

The modelling method of Douglas et al. (Hudson 1969a, b; Douglas, Hudson & Blamey 1972) can be used to compute theoretical long-range P-wave seismograms for shallow earthquakes. The method assumes a doublecouple source mechanism over an extended fault *Present address: MOD(PE), Blacknest, Brimpton, Reading, Berks RG7 4RS.

by guest on July 24, 2013http://gji.oxfordjournals.org/

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382 R. G. Pearce plane of the type described by Savage (1966), and allows for the effects of a horizontal plane layered velocity structure at both the source and receiver. Account is also taken of anelastic attenuation, geometrical spreading and the response of the recording instrument. The aim is to vary the model empirically until the closest possible match is obtained between theoretical and observed seismograms at several recording stations simultaneously. In particular, a fault plane solution is obtained by searching for a source orientation which repro- duces the polarities and relative amplitudes of direct P and the free surface reflections pP and sP as observed on the seismograms.

Using this method, Douglas et al. (1974) were able to find a fault plane orientation which yielded theore tical P-wave seismograms closely resembling those recorded at three short period arrays from an earthquake in East Kazakhstan. Similarly, Cullen & Douglas (1975) modelled three earthquakes in Southeast Europe. However, because these models were determined by a process of informed trial and error, no measure of the confidence limits, or of the uniqueness of the resulting fault plane orientations could be given. Such a measure is clearly necessary in order to assess the value of fault plane Orientations deduced by modelling; the present paper a i m s to provide this.

2 Method

For a shallow earthquake, we expect P and pP to suffer the same fractional loss of amplitude along their paths, except near the source, where pP may encounter seismic discontinuities or scattering centres above the focus which are not traversed by P. If the earthquake is small (mb < 5.6) the source pulse is likely to last for less than one second, so that P and pP should be simple and well separated on a short-period seismogram. In such cases we expect the main signatures of the fault plane orientation on the seismogram to be the polarities and relative amplitudes of P, pP and sP. Therefore, provided an allowance can be made for any near- source differential effects between the direct and surface reflected phases, the range of fault plane orientations compatible with a particular seismogram can be computed.

The possibility of utilizing the information contained in surface reflections in order to constrain fault plane orientations has also been suggested by Langston & Helmberger (1975). Honda & It8 (1951) and Kasahara (1963) compared observed and predicted amplitudes of principal phases from deep focus earthquakes, assuming previously computed fnst motion solutions. They concluded that the doublecouple mechanism was a reasonable model, though there was substantial variability in the consistency of their observations. Further, these authors did not use amplitude information to determine fault plane orientations, and no quantitative analysis was attempted. Randall & Knopoff (1970) tested the observed distribution of absolute P-wave amplitudes on the focal sphere against several source models. The difficulty of correcting each observation for the effects of the path and receiver regions - in p?rticular anelastic attenuation - restricts such studies to long-period seismograms, which in turn precludes the use of shallow earthquakes.

In the method introduced here a systematic search is made for all fault plane orientations which are compatible with a series of short-period P and pP observations from shallow earthquakes. By using relative amplitudes, the need to correct for anelasticity along the path is avoided, so permitting the use of short-period seismograms, in which P and pP are separated even for intracrustal earthquakes. Array stations are employed in order to improve signal to noise ratio, and because they are sited on simple, well determined crustal structures. Any single seismometer stations could also be used, remembering the preference towards good coverage of the focal sphere. The computational procedure is now described.

Let the seismic radiation from a point source be defined in spherical polar coordinates


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Fault plane solutions 383

Fwre 1. (a) Coordinate system used to define seismic source mechanism. (b) Double couple about the X, axis. (c) Polar diagram of far field P-wave radiation resulting from double couple source shown in (b).

(I, 8,#) about the source, where 8 = 0 is coincident with the X, Cartesian axis and 4 is measured in a right-handed sense from the X, axis - Fig. l(a). Then for a double-couple force system acting about the X, axis as shown in Fig. l(b), the time-dependent part of the far-field P-wave amplitude at unit distance from the source is given by (see, e.g. Honda 1957)

sin 28 COSG i A, (e; $1 = - - - 4n up A + 2 p K 1 1


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3 84 R. G. Pearce where X and I.( are L a m B s parameters, up is the P-wave velocity in the source medium, K is a constant dependent upon the magnitude of the couples, and P denotes the unit vettor. Similarly the S-wave amplitude is given by

K 1 1

4n us cc As@,@)=-- - - ( c o s ~ ~ cosdB-cosesin@+)

P Figure 2. (a) Definition of source orientation in space. (b) Definition of P-wave azimuth and take-off angle from the source.


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where us is the S-wave velocity in the source medium. The integrated effect over an extended source has little influence on the radiation pattern for the small faults discussed here, and will be neglected. It is clear from equations (1) and (2) that, although the ratio of P and pP amplitudes at the focal sphere is independent of all geophysical parameters, this is not true for P and sP. For simplicity, consideration is initially limited to P and pP.

Fig. l(c) is a polar diagram of the P-wave radiation Ap ( O , # ) ; we note the familiar degeneracy under interchange of the fault plane (arbitrarily chosen as the plane X2X3) and the auxiliary plane, X1X2. The source orientation is determined by the orientation of th is coordinate system in space, which is here defined by the dip 6 of the fault plane, the slip angle $ in this plane, and its strike u from north, as shown in Fig. 2(a). The direction of the P-wave emergence to a given station is defined by its azimuth E , and its angle of take-off (Y - Fig. 2(b).

To calculate the amplitude of P at source for a particular fault plane orientation, we require the direction vector x = { xl, x 2 , x3j of the P ray leaving the source expressed in the X coordinate system. This can be found by applying a series of rotations to the direction vector along X3, namely {O,O, l}. The required direction vector is given by

where q = [ - u is the azimuth of the recording station from the strike, and p = + 1 for P and - 1 for pP. The amplitude is then given by

K 1 1 A , = - - - sin (2 cos-' (x3)) cos (tan-' (XZ/XI))f.

4n up X + 2 p (4)

A computer program has been written to search systematically for all source orientations which are compatible with an acceptable range of P and pP amplitude ratios, deduced from an observed seismogram. Differential loss of amplitude of pP above the source is allowed for by a multiplicative factor, the calculation of which is discussed later. For each station 4' and (Y are known, and ($, 6, q) space is searched using a mesh size d (normally 5") within the bounds d < $ 6 n; d < 6 < n and d < q < 2n. This choice of bounds avoids duplication of orientations while maintaining the interchange of fault and auxiliary planes as separate solutions. The procedure can be repeated for observations at other stations; orientations which are acceptable at each station are transformed into the fixed system ($,ti, u) and only those acceptable at all stations are retained. The notion of dividing orientation space into acceptable and unacceptable regions is used in preference to the maximization of a criterion function, because the aim is+o establish the range of solutions which is compatible with the data. Anomalous observations which require explanation are then emphasized.

A clear representation of all acceptable orientations ( $ i , S i , ui) is provided by plotting each as a unit vector drawn at an angle ui from the Cartesian point ( $ i , S i ) as shown in Fig. 3. Different combinations of I) and 6 represent various types of fault, and these are indicated by lower hemisphere stereographic projections superposed on this plot. The projections are oriented for northerly strike (u = 360" - upward vector); other strike directions are interpreted by equivalent rotations. The positions of some important types of fault on the plot are shown in Fig. 3 - there is no need to consider the effect of interchanging fault and auxiliary planes, as the resulting fault types are represented elsewhere on the plot.


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386 R. C. Pearce

slip angle in fault plane CJ 5" 45" 90" 135" 180" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . + + + + + + + + + + + ?eO\-hy",0ntp' p.p +[vyti:al+dil: $!PI+ + + + + + + + + + + + + + + st r ,ke+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + q (r' . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................

a + + + + + + + c + + + + + + + %445"+ + + + + + +

+ t i + + + + - 3 + + + + + + + (0

+ + + + + + + + Lc + + + + + + +

O + + + + + + + 4 + + + , + + + + go".""h. + + + + +

lev? + + + +[si+nisty[ + + + shear

near-vertical

:trip $p+ + + + + + + + + + +

+ + + + + + +

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+ + + + + +

+ t

+ + + + + + + + + + + + + + + + + + + + + + + + + + + +

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+ + + + + + + + + + + + + + + + + + + + + + + + + + + +

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+

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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+ + + + ::e + + + + + + + + + + + + + + + + + + + + + + + + +

vertical strike slit

sinistral [dytyl],

+ + + +

shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

135". + + + + + + . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

180. + + + + + + + + + + + + + + + + + +

Figure 3. Method of representing acceptable fault plane orientations in terms of slip direction $ , dip 6 and strike u, as defiied in Fig. 2(a). Acceptable orientations are plotted as vectors from the Cartesian point defining $ and 6 , in the direction of the strike u. Lower hemisphere stereographic projections indicate the type of fault plane orientation represented by various combinations of $ and 6 , and are shown oriented for strike u = 360" (northerly). In each case the fault plane is shown by a thick line; the auxiliary plane by a thin line. Shaded quadrants are negative. Different parts of the plot characterize various fault types, and some of these are shown. Where the interchange of fault and auxiliary planes yields a different fault type, this is shown in square brackets.

3 Practical considerations

Before applying the relative amplitude method, a number of practical points must be discussed. Identification of pP is achieved by looking for a prominent phase following P, which is common to several seismograms - focal depths read from bulletins are not sufficiently reliable for this purpose. Where no clear pP-P time can be deduced for an earthquake, observation of the maximum amplitude in the P-wave codas on each seismogram can be used to set an upper bound to the pP amplitude.

The method of specifying the pP/P amplitude ratio, and its reliability, was chosen to be compatible with the measurements that can be made from a seismogram. The possible ranges of both P and pP amplitudes are defined separately in arbitrary amplitude units. In addition, the polarities of these phases are each defined as positive, negative or uncertain - implying the inclusion of one or both senses for each amplitude range specified. Thus, for uncertain


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polarity observations, both a positive and negative amplitude range will be acceptable, and for small or 'nodal' observations, a lower bound of zero with an undefined polarity will cause a range of amplitudes about zero to be acceptable.

The need to specify a finite range of amplitudes arises from observational uncertainty caused by noise, by interfering arrivals, and from the need to allow for any differences in the frequency content of P and pP, which will affect their relative amplitudes as recorded by a short-period instrument. The aim is to specify 100 per cent confidence limits on the amplitudes, which will therefore usually be wide (typically spanning at least a factor of two for pP observations) but which will directly represent the observational reliability of each reading. Pearce & Barley (1977) have introduced a method of adding synthetic noise to theoretical seismograms in order to establish the amount of signal distortion that is attributable to noise on any given observed seismogram.

Changes in the relative amplitudes of P and pP between the source and receiver will, for shallow earthquakes, be limited to effects on pP above the source - the most likely causes being scattering, attenuation, and energy partitioning at seismic discontinuities other than the free surface. Where modelling (or independent evidence) provides a determination of the velocity depth structure, a correction can be made for the energy partitioning by computing the Zoppritz (1919) equations at successive discontinuities from the source layer to the surface, and back to the source layer. For intracrustal earthquakes which yield simple P-wave seismograms consisting primarily of P, pP and sP, calculation shows that such energy losses are small, provided there is no sea layer, and are neglected.

4 Application of the method

Two examples are now presented as a practical test of the relative amplitude method, both as a means of assessing the uniqueness of fault plane orientations already deduced by modelling, and as a means of computing fault plane solutions directly.

Figs 4(a), (d) and (g) show the P-wave seismograms observed teleseismically at the short period arrays YKA, WRA and GBA respectively, from an earthquake in East Kazakhstan (Earthquake 1 of Table 1). Douglas et al. (1974) used the computational method of Hudson (1969a,b) and Douglas et al. (1972) to generate corresponding theoretical seismograms assuming a focal depth of 25.4 km. This choice of depth enabled the second arrival at YKA and WRA (whose amplitude is too small to be measured at GBA) to be modelled aspP. By assuming dip slip on a fault dipping at SO" towards YKA, Douglas et al. (1974) were able to closely match the polarities, relative amplitudes and pulse shapes of P and pP at the three stations. Details of their model (designated Model 1) are given in Table 2, and their theoretical seismograms are reproduced in Figs 4(b), (e) and (h). The closeiiess of match provides adequate confirmation that pP has been correctly identified.

The question is now asked: 'what range of alternative fault plane orientations would yield theoretical seismograms whose P and pP pulses would also match the observed seismograms?'

Table 1. Earthquakes used in this paper (USCGS parameters).

Date Origin time Region Location m b h m s

1 1969May1 04 00 08.7 East Kazakhstan Lat. 43.98' N 4.9

2 1972 January 12 08 15 46.1 GulfofSuez Lat. 27.53' N 5 .1

Long. 77.86'E

Long. 33.75" E


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388 R. G. Pearce

P:6.0 to 8.0;we pP: 4.0 to ll.O;-Ve (a) observed

at Y K A c -6.0' A-73.3'

for YKA

I

(cIModel 2 computed for YKA

( 1 1 Model 2

for GBA computed I

P: 8.0 to lL.O;+ve

-

computed for WRA

I

P:l5 to 6.0:+vel-ve SR

A-30.3" Y

h I;


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Fault plane solutions 389 Table 2. Models used for East Kazakhstan earthquake (Model 1 taken from Douglas ef al. (1 974)).

(a) Source parameters

Focal depth = 25.4 km Radius of fault plane = 1.25 km (circular) Stress drop across fault = 100 bar Fracture velocity = 0.6 us, where us = source layer S-wave velocity

Dip of fault plane 6 = 130" 90" Direction of slip in the fault plane J, = 90" 180"

Model 1 Model 2

Strike of fault plane u = 96" 101"

(b) Source structure

P-wave velocity S-wave velocity Density Thickness kmls km/s g cm-3 km

Layer 1 4.80 - 2.7 1 .o Layer 2 6.15 3.5 2.8 30.6 Layer 3 8.2 - 3.3 00

Where S wave velocity (us) is not listed us = up/J3 where up is the P-wave velocity.

(c) Receiver structures

YKA - Hasegawa (1971); WRA - Underwood (1967);CBA - Arora (1969).

Realistic bounds on the possible amplitudes and polarities of these two phases are specified in Fig. 4, in the manner developed above. Because of the simplicity of the observed seismograms, any loss of pP energy above the source is assumed to be negllgible. The acceptable fraction of orientation space acceptable at each station is shown in Table 3, and Fig. 5 shows a plot of all fault plane orientations compatible with these three observations, displayed as described in Fig. 3. These acceptable solutions occupy only 1.7 per cent of orientation space - which shows that as few as three seismograms can contain enough information to severely constrain the orientation of an assumed double-couple.

Nearly all the acceptable orientations are clustered around that used by Douglas et al. (1974) (shown with a single arrowhead together with its 'degenerate partner' resulting from interchange of fault and auxiliary planes). This cluster centres on the reverse thrust 45' dip slip type of fault (see Fig. 3), and some features familiar to any first motion worker can be clearly seen. While the dip is constrained to within +15' and the slip direction to within a maximum of ? 45", the strike is very poorly defined - as the angular spreads of up to 180" in Fig. 5 indicate. When observed in first motion solutions of dip slip faults, this effect is caused by the absence of any nodal plane passing through the teleseismic annulus on the focal sphere, within which observations are available. A more general case of the same phenomenon occurs here: that is, there are no large P-wave amplitude differences within this

Figure 4. P-wave seismograms from East Kazakhstan earthquake, 1969. (a), (d) and (8) are observed at Yellowknife (YKA), Warramunga, (WRA) and Gauribidanur (CBA) respectively; azimuth and epicentral distance A to each station are shown. Bounds on acceptable amplitudes and polarities of P and pP as used in the fault plane search are also indicated, with amplitudes in arbitrary units. (b), (e) and 01) show corresponding theoretical seismograms computed using the model of Douglas ef al. (1974) (Model 1). (c), (0 and (i) are corresponding theoretical seismograms computed using Model 2. Note that, although Model 2 generates a good match for P and pP at all three stations, its predictions of sP are in poor agree- ment. 1* (the ratio of travel time to anelastic quality factor Q) is assumed to be 0.2 s for each seismic path.


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390 R. G. Pearce Table 3 . Constraint on fault plane orientation imposed by relative amplitudes of P and pP.

Station Fraction of orientation space acceptable

East Kazakhstan earthquake Gulf of Suez earthquake (%) (%I

16.0 EKA - GBA 50.0 5.4 WRA 10.2 - YKA 8.1 6.1 At three stations 1.7 0.3

annulus - or within the equivalent upper hemisphere annulus, which is an additional part of the focal sphere sampled by this method.

A small group of vertical strike slip solutions are also acceptable (Fig. 5 ) highlighting the importance of testing models for uniqueness. While empirically perturbing the orientation of the dip slip model to achieve the closest match, the possibility of the fundamentally different dynamic processes implied by a vertical strike slip fault might be entirely overlooked, although such a model may fit the observations.

An additional constraint can be placed on the fault plane orientation using the relative amplitudes of P and 9. Douglas et al. (1974) noted that, using their model, the second arrival observed at GBA - Fig. 4(g) - was reproduced closely as sP. This is clearly not true of all orientations shown in Fig. 5 . For example, the solution designated Model 2 in Table 2 (which is shown with a double arrowhead in Fig. 5 ) incorrectly generates the sP observations, while the P and p P pulses are, of course, still compatible - see Fig. 4(c), (f) and (i). This testifies to the importance of sP in fault plane determination.

slip angle in fault plane C,J 5" 30" 60" 90" 120" 150" 180" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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+ + + + + +

a + + + + + + + - + + + + t + + t t t t t t + + + + + + + + + + + + + + + 73 + + ~ + + + + + + + , + + + + + + + + C + + + t + + + + + + + + + + + +

+ + + \ ,, + + + + + + t + + + + + * + i + + + + + + t t t + + t +

.- ++++++++++++++++++++++++++*+++*,+++++++++

+ + + + + + + + + + + + t + + + + + + + + + + + + + t t + + +

1 8 O y + + + + + + + + + + + + + + i + + + + + + t + + t + + + + + + + t t + + Figure 5. East Kazakhstan earthquake 1969. Fault plane orientations which are compatible with the polarities and relative amplitudes of P and p P in all three observed seismograms, as specified in Fig. 4. Note the separate group of vertical strike slip solutions at extreme left and right edges of plot. Single and double arrows show orientations used for Models 1 and 2 respectively (accurate to the nearest increment in the mesh). Because either nodal plane may be the fault plane, each orientation appears twice.


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Fault plane solutions 39 1

(a) observed at YKA t = 345.9O A= 86.6'

Ib) correlogram at YKA

k) computed for YKA t * = 0 . 6 ~

Id) observed at GBA t 199.80 A= 43.0'

(el correlogmm at GBA

It) computed tor GBA t'= 0.7s

Ig) observed at EKA

C = 326.5O A = 38.5O

(hl correlogram at EKA

I iI computed for EKA t *= 0.5s

t2 P 15to20,+ve

P: 0.9 to 1.1: -ve

Figure 6. P-wave seismograms from Gulf of Suez earthquake 1972. (a), (d) and (g) are observed at YKA, GBA and Eskdalemuir (EKA) respectively, annotated as in Fig. 4 . @), (e) and 01) are the corresponding correlograms, indicating the arrival of energy with the correct azimuth and phase velocity. (c), (0 and (i) are corresponding theoretical seismograms, computed using the model of Table 4.


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392 R. G. Pearce Apart from providing a clear assessment of the uniqueness of a fault plane solution com-

puted by modelling, the relative amplitude method offers a means of computing fault plane orientations directly. Moreover, in another example it is shown to be effective in doing t h i s using seismograms with low signal-to-noise ratio, where first motion observations are unreliable or impossible.

Fig. 6(a), (d) and (g) show observed seismograms at the three arrays YKA, GBA and EKA respectively, from a shallow earthquake in the Gulf of Suez, with mb = 5.1 (Earthquake 2 of Table 1). The corresponding correlograms, indicating the arrival of phased energy, are also shown - Fig. 6(b), (e) and (f). The second arrival at CBA (labelled t l ) is tentatively identified as pP. On t h i s assumption, realistic bounds on the amplitudes, and polarities where unambiguous, are included in Fig. 6 for each station. Because pP is not clearly seen at either YKA or EKA, an upper limit on its amplitude is deduced from the noise amplitude alone. Any loss of pP energy above the source is again assumed to be negligible. It is important to realize that even with these very wide constraints on possible relative amplitudes, each station places a substantial constraint on the fault plane orientation. Table 3 shows the fraction of orientation space acceptable, assuming the measurements made in Fig. 6. The orientations compatible with a l l three stations are plotted in Fig. 7. One of these orientations (shown with an arrowhead in Fig. 7) is used as input to the modelling program, in order to test the reproducibility of other features of the seismograms, such as the interfering waveform of the pP and sP pulses. The model parameters used are shown in Table 4 and the resulting theoretical seismograms are shown in Fig. 6(c), (f) and (i). The match between theoretical and observed seismograms is good, and it is seen that the third arrival at GBA (marked as t2 in Fig. 6) models well as sP. Again, not all the orientations shown in Fig. 7 exhibit this additional match of sP; in fact the absence of any significant energy following P in the YKA seismogram indicates that the null vector - Fig. l(c) - is oriented near to the upper hemisphere take-off angle to YKA. However, even without sP information, the assumption of a double-couple has allowed the fault plane to be constrained to within 0.3 per cent of orientation space, using three low signal-to-noise ratio seismograms for an mb 5.1 earthquake.

slip angle in fault plane t,) 5" 30" 60" 90" 120" 150" 180" + + + C h < , \ + + + + + + + + + + + + + + + + + + + ) + + + + + + + + . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A < , + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + i

Fault plane solutions Table 4. Model used for Gulf of Suez earthquake.

(a) Source parameters

Focal depth = 7.8 km Radius of fault plane = 1.0 km (circular) Stress drop across fault = 100 bar Fracture velocity = 0.6 us Dip of fault plane 6 = 15' Direction of slip in the fault plane I) = 2" Strike of fault plane u = 96"

@) Source structure

P-wave velocity S-wave velocity km/sl km/s

Layer 1 6.0 3.1 Layer 2 6.1 - Layer 3 8.1 -

(c) Receiver structures

YKA and GBA as in Table 2; EKA - Parks (1967).

Density g cm-)

2.8 2.9 3.4

393

Thickness km

18.1 18.0 00

5 Comparison of the relative amplitude and first motion methods

Since the relative amplitude method provides a means of directly computing fault plane solutions, it is important to compare it with the first motion method. Although no detailed comparison between these methods is given here, several fundamental advantages of the relative amplitude method are worthy of note.

The use of amplitude information enables the maximum source information to be extracted from seismograms, even if the P-wave first motion polarity cannot be read unambi- guously. The above examples show that if a double-couple mechanism is valid (an assumption widespread in first motion studies) then fault plane solutions can be computed at much lower mb (- 5.0) and with far fewer seismograms (as few as three) than is possible using the first motion method. It follows that if many observations are available, the large redundancy of information could be used to confidently confirm or reject any assumed radiation pattern. Moreover, because confidence limits on the amplitudes are specified, it follows that a realistic assessment of the reliability of each observation is implicit in the input data - this is impossible to achieve with first motion observations. The need to design Q posteriori weighting factors, based on the mutual consistency of the data (e.g. Ingram 1959; Knopoff 1961) is thereby entirely avoided. Barley & Pearce (in preparation) have made a detailed comparison of fault plane solutions computed using both methods for one earthquake.

Conclusions

Examples have demonstrated that the relative amplitudes and polarities of P and pP can be used to provide a clear measure of the uniqueness of fault plane orientations deduced by the modelling of shallow earthquakes. As a means of computing fault plane solutions directly, it has been shown that the relative amplitude method is capable of providing a well- constrained fault plane orientation using only a small number of P/pP observations, and that in some cases SP can provide a further useful constraint on the orientation. Several advantages of the relative amplitude method over the first motion method have been noted; these suggest that the relative amplitude method has a wider field of application than that of first motions.


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394 R. G. Pearce In a future paper, the relative amplitude method will be applied to 'a larger number of

earthquakes, and sP observations will be included in the computations. By using long-period seismograms, which are affected less by the effects of the propagation paths of each phase, the extension of this method to the study of fault plane orientations of deep focus earthquakes will be considered.

Acknowledgments

I should like to thank Dr H. I. S. Thirlaway and his colleagues for facilities provided at MOD Blacknest, where this work was carried out. In particular, I thank A. Douglas and J. B. Young for useful discussions. The Natural Environment Research Council is acknowledged for financial support.

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Zoppritz, K., 1919. h e r Erdbebenwellen VIIb, Cottinger Nachrichren, p. 66-84. sity, Canberra.


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