Tectonophysics, 209 (1992) 105-l 14 Elsevier Science Publishers B.V., Amsterdam

105

Waveform modelling of the May 20,199O Sudan earthquake

Domenico Giardini and Laura Beranzoli Istituto Nazionaie di Geofsica uia di iriita Ricotti 42, 00161, Roma, Italy

(Received May 7, 1991; revised version accepted August 5, 1991)

ABSTRACT

Giardini, D. and Beranzoli, L., 1992. Waveform modelling of the May 20, 1990 Sudan earthquake. In: C.J. Ebinger, H.K. Gupta and LO. Nyambok (Editors), Seismology and Related Sciences in Africa. Tectonophysics, 209: 105-114.

Vex-broad-band seismic waveforms were modelled to derive the moment tensor, the source time function and the depth of the May 20, 1990 Sudan earthquake. Long-period body waves, surface waves and broad-band displacement, recorded by the MEDNET regional network, were merged with digital data from global seismic networks, to compare fault geometries obtained by different methods and assess associated uncertainties. Our analysis indicates that the May 20 earthquake had a seismic moment of 5.3 X 10z6 dyne ’ cm and a depth of about 10 km; the focal mechanism shows a mixture of transcurrent geometry, with one plane striking NW-SE, and a smaller dip-slip component with the T axis oriented in the N-S direction. The fault geometry agrees with models calling for the recent re-activation of the NW-SE trending Aswa transform zone, marking the northern termination of the western branch of the rift. In contrast, the N-S tensional component, which also dominates the focal mechanisms of the aftershocks (Dziewonski et al., 19911, supports the evidence for the rotation of the regional Quaternary stress field to the north, in contrast with simple two-plate models of rifting in East Africa. ‘The Juba event allowed us to test the capability of the MEDNET regional seismic network to provide an accurate real-time description of the seismic source.

The development of global digital seismic net- works has lead to a revolution in seismological practice. Worldwide seismicity is now routinely analyzed using global data, and moment tensor catalogues have been compiled for about 9000 events since 1977, mainly by the Harvard group (Dziewonski et al., 1981) and by the United States Geological Survey (USGS) (Sipkin, 1986). For any large earthquake, we now find in the literature several moment tensor solutions derived from digital data, together with standard focal mecha- nisms retrieved from P-waves polarities; these solutions are often complemented by waveform modelling for the determination of depth and source time function.

Correspondence to: D. Giardini, Istituto Nazionale di Ge- ofisica via di Villa Ricotti 42, 00161, Rome, Italy.

Global seismic networks have led a major ef- fort to ensure the even geographical coverage needed for teleseismic studies. Several regional digital seismic networks are also in the planning or deployment stage (see Boschi et al., 1991 for a recent review of plans and distributions of re- gional and global seismic networks in North Africa). The standard seismological practice is to include ail available data, from regional and global networks, in source and st~ctural analyses. Here, we are concerned with the advantages and draw- backs of including patches of dense station cover- age from regional networks in the giobal data distribution used for moment tensor inversion.

In analogy to patterns observed in the stan- dard determination of focal mechanisms and in earthquake location, we find that the high spatial density of coherent information, provided by a regional network, dominates the varidnce reduc- tion and the fault planes geometry, j at the ex- pense of isolated stations. Therefore the data

HO-1951/92/$05.~ 0 1992 - Elsevier Science Publishers B.V. AI1 rights reserved

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distribution must be properly weighted. On the other hand, modelling teleseismic waveforms from a regional distribution of stations, with a distance between stations much smaller than the epicen- tral distance, has the advantage of smoothing out any path effect or distortion induced by structure in the station region. This proves to be most useful in rapid determination of focal parameters immediately after the event, when observations from only a few stations are available.

The May 20, 1990 Sudan earthquake provides the chance to explore the variability in moment tensor determination using waveform data and to evaluate the effect of merging data from the regional MEDNET network with the global data distribution. A second goal of this contribution is to verify if our modelling methods are suitable for real-time evaluation of significant earthquakes.

The waveform modelling approach we devel- oped combines long-period body and surface waves to derive the moment tensor, and broad- band P and S, displacement pulses to model the source time function and constrain depth. The algorithms are only briefly described here (for details see Palombo et al., 1989; Beranzoli and Giardini, 1990).

The May 20,1!@0 Sudan earthquake

The Juba area in Southern Sudan was affected by a high-magnitude sequence of events in the period May-July 1990; the largest shocks oc- curred on May 20th 04, = 7.1-7.41, May 24th (MS = 7.0) and July 9th (MS = 6.4-6.6).

The Juba area lies to the north of the surface expression of the Western Rift system in East Africa; for a detailed review of the seismotecton- its of the rift and of Juba areas refer to Gaulon et al. (this volume). The earthquakes were lo- cated about 100 km north of the NW-SE trend- ing Aswa fracture zone, interpreted by some as a diffuse intracontinental transform zone connect- ing the western and eastern branches of the rift; this structure developed during the Mozam- biquian orogeny and may have been reactivated in the Tertiary (Kazmin, 1980; Gaulon et al., this volume).

Since no major seismicity has been reported by international catalogues for the Juba area, the 1990 sequence provides the opportunity for strengthening our understanding of the regional seismotectonic framework. Here we limit our analysis to the May 20 event, the largest event ever recorded in Africa (MS = 7.0-7.4). Focal parameters (depth, seismic moment and focal mechanism), issued by international agencies and research groups, display significant similarities and differences (see, for example, the NEIC Monthly Listings and Gaulon et al. (this volume)). For example, the focal mechanisms show a con- sistent component of strike-slip motion, but also marked differences in the strike and dip of the fault planes; the seismic moment ranges between 5.3 and 8.2 x 10z6 dyne * cm (extreme values ex- ceeding 102’ dyne 1 cm were also reported) and the depth estimates range between 10 and 30 km.

Moreover, focal mechanisms obtained by inter- national agencies shortly after the shock were, in some cases, substantially different from the final solutions published later by the same agencies. This is a not uncommon occurrence, which re- flects the dependence on the station distribution of many algorithms used in seismological practice and underlines the importance of developing reli- able methods for real-time processing of signifi- cant earthquakes.

Long-period waveform m&eWg

To describe the source properties of the May 20 earthquake we used digital data distributed by IRIS and by MEDNET, the broad-band seismic network installed in the Mediterranean region (Giardini et al., this volume). A map of Northern Africa is shown in Figure 1, including the distri- bution of the MEDNET network and the main elements of the African Rift; the four stations operating during the Juba sequence cover a small azimuth at an average distance of 4000 km.

We selected the 36 best traces for 16 GSN and MEDNET stations, which were characterized by exqellent signal-to-noise ratio and simple, uncon- taminated surface-wave trains. The stations used

were: AQU(Z,N,E), ANMO(Z), CMB(Z,N),

WAVEFORM MODELLING OF THE MAY 20,199O SUDAN EARTHQUAKE 107

CHTO(Z,N), CTAO(Z,N), GFA(N,E), GUMO(Z,N), HIA(Z,N,E,), HON(Z), HRV (N,E), KEV(Z,N,E), MAJO(N,E), PAS(Z,N,E), SNZO(Z,N,E), TOL(N,E) and VSL(Z,N,E). The station distribution achieves a good azimuthal coverage for surface-wave analysis.

The inversion for the moment tensor is based on the following elements (see Palombo et al., 1989; Beranzoli and Giardini, 1990):

(1) Six hours of three-component records, con- taining long-period body waves and the first 3 or 4 orbits of Rayleigh and Love waves were used.

(2) Synthetic seismograms were generated by summation of normal modes at periods exceeding 100 s, computed for model PREM of Dziewonski and Anderson (1981) using a scheme of Wood- house (1988); complete seismograms include fun- damental modes and overtones, and model both body and surface waves; for a rapid analysis of

shallow events the summation can be restricted to fundamental modes and to the synthesis of sur- face waves.

(3) Inversion was performed in a narrow fre- quency band: 5-7 mHz; a weighting scheme was introduced where each trace was weighted by its norm and the moment tensor was constrained to have null volumetric component (following Dziewonski et al., 1981).

(4) A time correction was computed for each trace after the inversion for the moment tensor; the source half-duration was estimated as the time correction common to all traces; the residual time corrections accounted for hypocentral mislo- cations, the spatial extent of the source and man- tle heterogeneities.

(5) The depth was determined by variance minimization on different trials (Romanowicz and Suarez, 1983).

-r-

>

Fig. 1. MEDNET station distribution. All stations presently installed are shown, but only the stations which recorded the May 20, 1990 event are connected to the source area. The main tectonic elements of East Africa are indicated.

(6) A minimization scheme was applied to re- duce the instability associated with the M,, and M,, components of the moment tensor.

The last point is of particular relevance. The constraint we imposed involved the minimization of the moment tensor norm, weighted by a pa- rameter, E (see, for example, Menke, 1984); by varying the parameter E it is possible to explore the uncertainty and resolution associated with individual eIements of the moment tensor.

In Figure 2a the amplitude of the six elements of the moment tensor, for five inversions, per- formed with different minimization contraints (solutions MT,-MT,) are shown. Figure 2b lists the corresponding inversion and source parame-

ters: the constraint, E, the seismic moment, )2-I,,. the normalized variance, R (defined as the ratio of the variance over the norm of the data vector). and the fault plane geometry.

As is common for shallow events (Ekstrom, 1989), we observed a larger instability associated with the M,, and M,, components of the mo- ment tensor. A non-constrained solution (MT,) has a large seismic moment of 8.2 x It),, dyne .

cm, dominated by the M,, and 1w,, components, and reaches a good variance of R = 0.213. By increasing the constraint, the &f,, and Rrf,, com- ponents decrease significantly, as does the seis- mic moment; the other moment elements remain unchanged and the variance increases only

~ornen~ Tensof f kments

Fig. 2. (a) Absolute amplitude of the six elements of the moment tensor for five inversions performed with different minirniration contraints (MT,-MT,). (b) Fault mechanisms and inversion parameters for the five solutions in (a) and for a solution-obtained including only MEDNET data (MN); the constraint, E, seismic moment, MO (in dyne I cm), the normalized variance, R, and the fault

plane geometry (strike and sfip angles) are shown.

WAVEFORM MODELLING OF THE MAY 20.1990 SUDAN EARTHQUAKE 109

slightly. It is only with a very strong contraint (E = 1.0) that the solution (MT,) degrades consid- erably (R = 0.4491, and all moment tensor ele- ments are reduced (M, = 2 x lo,, dyne . cm).

The geometry of the focal mechanism reflects the proportions of the moment tensor elements (Figure 2b); unconstrained solutions are domi- nated by the dip-slip elements M,, and M,,, whereas more constrained tensors show a strike- slip geometry. The final solution, MT,, was cho-

sen on the basis of the resolution of the inversion procedure, and shows a superposition of dip-slip and strike-slip components. Figure 3 displays data

and synthetic seismograms obtained with the so- lution MT, at different stations around the world; the overall fit between data and synthetics is excellent, both in time and frequency domain.

To test the capability of the regional MEDNET

array to characterize a teleseismic source, we also obtained a moment tensor solution using only

VSL

PAS /

0 set 18000 0 mHz 8

Fig. 3. Long-period waveform modelling for the inversion of the moment tensor solution MT, (Fig. 2). Five of the ~~~MEDNET and GSN selected traces are displayed. In the windows on the left are filtered data (continuous line) and synthetic seismograms (dashed lines) for the station and component indicated; the corresponding frequency spectra are on the right. The frequency band included

in the inversion (5-7 mHz) is shown in bars.

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MEDNET data. The solution, indicated as MN in Figure 2b, is quite similar to the MT, and MT, solutions obtained from global data, indicating that, even with few stations from a high-quality array, it is possible to evaluate in real-time signif- icant earthquakes (see EkstrGm et al., 1986).

Broad-band waveform modelling

We turned to broad-band modelling to con- strain the fault geometry and to evaluate the source time function and depth. The inversion for

NEIC

h=15 km

USGS

h=12 km

7.4 x 10”

CMT

h=15 km

5.3 x 1018

MEDNET

h=lO km --_J 5.3 x 10’6

GEOSCOPE

a

the moment tensor was based on the following elements (see Palombo et al., 1989; Beranzoli and Giardini, 1990):

(1) The source time function was inverted to model P and S, displacement pulses in shape and amplitude; synthetic seismograms were gen- erated by classic ray theory CLangston and Helm- berger, 1975). Stations in the 30-90” distance range were used.

(2) The focal mechanism was given by long- period analysis. The depth was evaluated by trial- and-error modelling of the surface reflections pP and sP. The seismic moment obtained from long-

Fig. 4. Waveform modelling for five source mechanisms obtained for the May 20th event by different agencies and research groups: the fault plane solution by NEIC, the long-period moment tensor obtained by the USGS and the CMT solution (all liked in the May Monthly Listing of the NEIC); the MT, solution obtained here (Fig. 2) and the GEOSCOPE solution (Gaulon et al., this volume). For each solution we show: (a) the fault mechanism, with the location of the MEDNET BNI station ind_jca@d on the fecal sphere; (b) the elementary synthetic wavelet produced hy a single 4 s pulse at the depth listed; 6.9 the wavuforzn modellingat the BNI station, obtained from the source time function inversion carried out with the MEDNET stations BNI, AQU and VSL (data are

indicated with continuous line, synthetic seismograms with dashed line).

WAVEFORM MODELLING OF THE MAY 20.1990 SUDAN EARTHQUAKE

period analysis was taken as a limit on the source

time function integral (Ekstrom, 1989). (3) We parameterized the source time function

as a sequence of triangular elements (Nabelek, 19841, of 4 s length, and impose a positivity con- traint in the inversion.

(4) Attenuation was introduced with a t * of 1 s for P waves and an initial t * of 4 s for S, waves (N’abelek, 1984); t* can be adjusted for S, waves to obtain the same shape and duration of the source time function for both P and S, waves.

In Figure 4 the source mechanisms obtained for the May 20 event by various agencies and research groups are compared: the fault plane solution by NEIC, the long-period moment tensor obtained by the USGS and the centroid moment tensor (CMT) solution (all listed ip the May Monthly Listing of the NEIC), the MT, solution obtained here and the GEOSCOPE solution (Gaulon

et al., this volume). For all five mechanisms we modelled the P

displacement pulse at the MEDNET stations, com- puting a source time function for the focal mech- anism and the depth reported by each source (listed in Figure 4).

For each solution we show the following re- sults for station BNI:

(1) the fault mechanism, with the location of the BNI station indicated on the focal sphere;

(2) the elementary synthetic wavelet produced by a single 4 s pulse;

(3) the waveform modelling. The successful modelling depends on the given

depth and focal mechanism. Due to the critical location of the MEDNET stations on the focal sphere, close to both nodal planes, the NEIC and CMT mechanisms do not reproduce correctly the relative amplitudes or the sign of the main P pulse and the surface reflections and do not achieve a satisfactory modelling of the data. The GEOSCOPE, USGS and MEDNET solutions obtain a better fit, although the 13 km depth of the GEOSCOPE solution (Gaulon et al., this volume) makes the main pulse too broad. Our modelling indicates that a depth of 10 km produces the best fit.

We also tested the capability of the MEDNET regional array to parameterize the source process

I I I I I 1 I , , 0 al 40

111

H=9Km

Time (set)

Time (set)

Fig. 5. P waveform modelling at the three MEDNET stations telemetered to Rome in real time for the May 210 event: BNI, AQU and VSL. The preferred mechanism is obtained from long-period analysis of the same stations (solution MN, Fig.

2). The source time function is also shown.

of teleseismic events. To do this we modelled P pulses for the three MEDNET stations teleme- tered to Rome on May 20: BNI, AQU and VSL. We used the focal mechanism MN in Figure 3, obtained by inversion of long-period MEDNET data. The results are shown in Figure 5. The early part of the signal, containing the cantributions from the source, is well modelled on all three traces; the later portion shows high-frequency undulations which are different for each station and are produced by reverberations under the station.

The response of the structure under the sta- tion to incoming waves can be determined and deconvolved from the data (e.g., Clarke and Sil- ver, 1991). Without this deconvolution, the inver- sion algorithm also maps in the source time func- tion that part of the signal which is dub to station

117

structure. This effect will be more pronounced when the source time function is derived only from one station or from a sparse distribution of stations.

The use of data from a regional array offers an alternative solution. As seen in Figure 5, the source time function models all coherent details of the waveforms, produced by source complexity, but is not able to reproduce the structural effects, since the synthetic waveform varies very smoothly across the focal sphere. There is no need to stack the data, traces to extract the coherent part of the signal produced from the source, since the smoothing is carried out directly by the inversion procedure; indeed, the smoothed waveform is represented by the synthetic seismogram. In this manner the inversion for the source time function is very stable, even when performed by a small number of stations.

Seismotectonic interpretation

As seen in the previous discussion, the focal mechanisms of the May 20th event and of its largest aftershocks (Dziewonski et al., 1991) show: (1) left-lateral transcurrence in the NW-SE di- rection and (2) N-S dip-slip extension. We are interested in the coherence of this style of defor- mation with the state of stress shown by the seismicity of East Africa; we do not present here a complete tectonic framework, see Strecker and Bosworth (1991) and Gaulon et al. (this volume) for a more detailed discussion.

Figure 6 displays a map of East Africa with the T axes of moment tensor solutions for events since 1964, reported by various sources (CMT solutions from the quarterly letters of the Fhysics of the Earth and Planetary Interiors, including the parameters for the Juba sequence from Dziewonski et al. (19911, and other solutions from Shudofsky (1985) and Wagner and Langston (1988)). The shaded areas in Figure 6 cover the main rift branches (after Chorowicz et al., 1987).

As shown by the location of significant events (m 2 5.2) in the last 20 years, extension and rift- ing involve a large portion of East Africa; all events display an approximately horizontal T axis, and most of them have a nearly vertical P axis.

Significant extension takes place also outside of the main rift branches.

On the basis of the T axes orientation, we can distinguish six different regions of coherent stress geometry:

(1) the Afar triangle (AT), with the well-know separation of the Arabian peninsula to the north-northeast;

(2) the central Ethiopian portion of the east- ern branch (EB), showing ESE-WNW extension;

(3) the Kenyan portion of the eastern branch and the Gregory Rift (GR), where contrasting focal geometries show an average NE-SW exten- sion;

(4) the coastal basins, from Kenya down to the Karimbas basin (KB) and the Lacerda basin-(LB) recently identified along the coast of Mozam- bique (Mougenot et al., 1986), displaying uniform WSW-ENE extension which also involves struc- tures in Madagascar;

(5) the western branch of the rift, with exten- sion consistently perpendicular to the main rift structure from its northern end at Lake Mobutu (ML) down to Lake Malawi (MA);

(6) the area of diffuse WNW-ESE extension to the southwest of the rift.

It is difficult to reconcile this detailed picture in any simple two-plates model of the rifting processes in East Africa, unless a large portion of the events in Figure 6 have been discarded as being due to local gravity tectonics and therefore insignificant for the definition of the regional stress pattern (as in Chorowicz et al., 1987; Chorowicz, 1990; Gaulon et al., this volume). The interpretation of the Aswa fracture zone (AFZ) as a main intra-continental transform element entails the application of tectonic concepts char- acteristic of fast oceanic spreading centres to slow, oblique continental rifting (with relative plate velocities smaller by a factor of 30-50). It also presents controversial aspects: for example, the Aswa fault is also claimed to be a controlIing factor in the offset between the two main rift branches, in open contrast to its supposed left- lateral transform nature (Chorowicz, 1990; Gaulon et al., this volume).

The Juba sequence indicates that transcurrent dislocation take place to the north of the western

WAVEFORM MODELLI~G OF THE MAY 20,199O SUDAN EARTHQUAKE 113

rift branch termination (Fig. 61, as it is expected to accommodate the deformation produced by the active rifting process. There is no evidence

for the re-activation as transform fault of the whole Aswa fracture zone down to the Kenyan rifts (GR). Instead, there is ample evidence for recent NNE-SSW trending dip-slip extension (Chorowicz et al., 1987). Indeed, the presence of widespread NNE-SSW trending tensional stresses is recorded on both rift branches (see Chorowicz, 1990) and there is general consensus

for the Quatemary rotation of the regional state of extension from a roughly E-W direction to a more northerly orientation (see also Sttecker and

Bosworth, 1991). The T axes of the, Juba se- quence also show N-S extension, in agreement with this regional framework.

Conclusions

Tbe use of broad-band seismic data recorded by the MEDNET regional seismic network allows a

Fig. 6. Map of Eastern Africa with the T axes of moment tensor solutions for events since 1964, reported by various ‘sources. CMT solutions from the quarterly letters in the Physics of the Earth and Planet Interiors, including the parameters for the fuba sequence from Dziewonski et al. (1991) and other solutions from Shudofsky (1985) and Wagner and Langston (1988). The shaded areas cover the main Rift branches. Significant tectonic elements are indicated: AT = Afar triangle; EB = Eastern Rift Rift; KB = Karimbas basin; LB = Lacerda basin; WB = Western Rift branch; ML = Lake Mobutu; MA = Lake

Aswa fracture zone.

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reduction in the uncertainties associated with source parameters obtained by waveform mod- elling of global digital data and the acquisition of an accurate real-time description of the seismic source.

The May 20th, 1990, Juba earthquake had a seismic moment of about 5.3 X 10” dyne. cm and a depth of about 10 km. Its mechanism shows a mixture of strike-slip dislocation, with one plane striking NW-SE, and N-S dip-slip extension.

The May 20th event occurred in a key area of the African Rift, which had not been affected by major seismicity in this century, and offers the chance to test existing tectonic models. The ge- ometry of the fault mechanism lends some sup- port to models calling for the re-activation of the NW-SE trending Aswa transform zone, to the north of the western rift branch. The N-S exten- sion, shown both by the main event and by the aftershocks, agrees with estimates of the recent re-orientation of the regional state of stress to a northerly direction.

Acknowledgements

We are indebted to the MEDNET Data Center and to the NEIC, who collected and made avail- able the digital seismic data needed for this re- search. We thank Prof. Enzo Boschi for his lead- ing role in the development of MEDNET and his continuous support. Roland Gaulon provided useful comments and Cindy Ebinger showed much patience in carefully reviewing the manuscript and suggesting useful references. We thank Daniela Riposati for help in drafting the figures.

References

Beranzoli, L. and Giardini, D., 1990. Analisi dei segnali sismici a larga banda: il terremoto de1 Rift Africano de1 20 Maggio 1990. Proc. 9th Conv. Gruppo Nat. Geofis. Terra Solida (in press).

Boschi, E., Giardini, D. and Morelli, A., 1991. MedNet: the Broad-Band seismic network for the Mediterranean. II Cigno Galileo Galilei, Rome.

Chorowicz, J., 1990. Dynamics of the different basin types in the East African Rift. J. Afr. Earth Sci., 10: 271-282.

Chorowicz, J., Le Fournier, J. and Vidal, G., 1987. A model for rift development in Eastern Afriea. Geol. J., 22: 49S- 513.

Clarke, T.J. and Silver, P.G., 1991. A procedure for the systematic interpretation of body wave seismdgrams-I.

Application to Moho depth and crustal properties. Geo- phys. J. Int., 104: 41-72.

Dziewonski, A.M. and Anderson, D.L., 1981. Preliminary reference earth model, PREM. Phys. Earth Planet. Inter.. 25: 297-356.

Dziewonski, A.M. Chou, T.-A. and Woodhouse, J.H., 1981. Determination of earthquake source parameters from waveform data for studies of global and regional seismic- ity. J. Geophys. Res., 86: 2825-2852.

Dziewonski, A.M., EkstrBm, G., Woodhouse, J.H. and Zwart,

G., 1991. Centroid moment tensor solutions for April-June 1990. Phys. Earth Planet. Inter.. 66: 133-143.

Ekstriim, G., 1989. A very broad band inversion method for

the recovery of earthquake source parameters. Tectono- physics, 166: 73-100.

Ekstriim, G., Dziewonski, A.M. and Steim, J.M., 1986. Single station CMT: application to the Michoacan, Mexico, earthquake of September 19, 1985. Geophys. Res. Lett., 13: 173-176.

Kazmin, V., 1980. Transform faults in the East African Rift System. In: Geodynamic evolution of the Afro-Arabic Rift System. Atti Convegni Accad. Naz. Lincei, 47: 65-73.

Langston, C.A. and Helmberger, D.V., 1975. A procedure for modeling shallow dislocation sources. Geophys. J.R. As- tron. Sot., 42: 117-130.

Menke, W., 1984. Geophysical Data Analysis. Academic Press, London.

Mougenot, D., Recq, M., Virlogeux, P. and Lepvrier, C., 1986. Seaward extension of the East African Rift. Nature, 321: 599-603.

N’abelek, J.L., 1984. Determination of earthquake source parameters from inversion of body waves. Ph.D. Thesis, Mass. Inst. Technol., Cambridge, Mass.

Palombo, B., Beranzoli, L. and Giardini, D., 1989. Tecniche di inversione per i parametri deih sorgente sismica da sismo- grammi a larga banda. Proc. 8th Conv. Gruppo. Nat. Geofis. Terra Solida (in press).

Romanowicz, B. and Suarez, G., 1983. On an improved method to obtain the moment tensor and depth of earth- quakes from the amplitude spectrum of Rayleigh waves. Bull. Seismol. Sot. Am., 73: 1513-1526.

Shudofsky, G.N., 1985. Source mechanisms and focal depths of East African earthquakes using Rayleigh-wave inversion and body-wave modelling. Geophys. J.R. Astron. Sot., 83: 563-614.

Sipkin, S., 1986. Estimation of earthquake source parameters by the inversion of waveform data: global seismicity, 1981- 1983. Bull. Seismol. Sot. Am., 76: 1515-1541.

Strecker, M. and Bosworth, W., 1991. Quaternary stress-field change in the Gregory Rift, Kenya. EOS, Trans. Am. Geophys. Union, 72: 17-22.

Wagner, G.S. and Langston, CA., 1988. East African earth- quake body wave inversion with implications for continen- tal structure and deformation. Geophys. J. Int., 94: 503- 518.

Woodhouse, J.H., 1988. The calculation of eigenfrequancies and eigenfunctions of the free oscillations of the Earth and the Sun. In: D.J. Doombos (Editor), Seismological Algorithms. Academic Press, London, pp. 321-370.