Regional wave propagation in Tanzania, East Africa

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. B1, 2003, /2001JB000167, 2002 Regional wave propagation in Tanzania, East Africa Charles A. Langston 1 Center for Earthquake Research and Information, University of Memphis, Memphis, Tennessee, USA Andrew A. Nyblade Department of Geosciences, Pennsylvania State University, University Park, Pennsylvania, USA Thomas J. Owens Department of Geological Sciences, University of South Carolina, Columbia, South Carolina, USA Received 23 January 2001; revised 7 June 2001; accepted 25 June 2001; published 5 January [1] Crust and upper mantle structure under Tanzania, East Africa, is investigated using broadband waveforms and phase travel times collected from regional events recorded by the Tanzania Broadband Seismic Experiment. Broadband displacement waveforms from the ml 5.9 Rukwa graben earthquake (18 August 1994) are modeled using a wave number integration algorithm and a new phase time inversion technique to infer a very simple crustal and upper mantle model that can be used for waveform studies of other regional earthquakes in the area. Displacement amplitudes for all phases in the data are predicted quite well using source parameters determined from a previous study of teleseismic waveforms. The crust is parameterized by a linear gradient in velocity defined by surface and Moho P velocities, Poisson s ratio, and crustal thickness. This simple parameterization is sufficient to explain arrival times and waveshapes of the three-component waveforms recorded between 200 and 800 km at stations located on the craton and Mozambique belt. The S wave train consists of Sn, multiple Sn, and critically reflected S wave multiples in the crustal waveguide, in addition to the fundamental mode Rayleigh wave. High phase velocity, critical S wave reflections are seen to form the low group velocity Lg phase. Prominent sp depth phases are seen in the regional waveform data which can be used to infer accurate source depths for events in the region. The Tanzania craton and adjacent Mozambique belt crustal structure is simple and laterally homogeneous, showing few effects of rift disruption. High wave velocities in the uppermost mantle suggest little thermal modification from rifting processes of the East African Rift. INDEX TERMS: 7205 Seismology: Continental crust (1242), 7218 Seismology: Lithosphere and upper mantle, 7260 Seismology: Theory and modeling, 7203 Seismology: Body wave propagation; KEYWORDS: crust, wave propagation, upper mantle, earthquake, rift, Tanzania 1. Introduction [2] Continental rifting is a major tectonic process in the evolution of continents that precedes continental breakup and subsequent seafloor spreading. The processes of geologically young continental rifting are found today in the East African Rift (EAR) system where, for example, the spectacular rift escarpments within Tanzania developed within the last 1 Myr [Foster et al., 1997]. The processes that give rise to rifting in this region of the EAR have been the subject of speculation for some time. For example, some early gravity models [e.g., Fairhead, 1976] suggested that much of the lithospheric mantle under the EAR and cratonic area between the eastern and western branches has been eroded by asthenospheric upwelling. This mechanism is useful in explaining the origin of the high elevations of the East African plateaus through the mechanism of isostatic compensation, but other data sets, such as heat flow [Nyblade, 1997] and mantle xenolith geochemistry [Ebinger et al., 1997; Chesley et al., 1999], suggest that there is little 1 Formerly at Department of Geosciences, Pennsylvania State University, University Park, Pennsylvania, USA. Copyright 2002 by the American Geophysical Union /02/2001JB000167$09.00 thermal perturbation of the crust and upper mantle. It is difficult to reconcile these interpretations without basic constraints on crust and upper mantle seismic structure to give independent estimates of lithospheric thickness. [3] We utilize a high-quality waveform data set from earthquakes recorded by the Tanzania Broadband Seismic Experiment [Owens et al., 1995] to derive a velocity model of the crust and upper mantle of the Archean-age Tanzania craton and surrounding Proterozoic mobile belts (Figure 1) that are presently undergoing rifting. Very little was known of the seismic velocity structure in this region before deployment of this passive broadband experiment in There were no longrange refraction profiles to determine average properties of the crust and upper mantle, nor were there many permanent stations in this region to record local seismicity. [4] The Tanzania Broadband Seismic Experiment consisted of a 20-station broadband seismic network arranged in a skewed cross pattern across Tanzania (Figure 1), with the Archeanage Tanzania craton being the primary target of the experiment. The network was designed to record teleseismic body waves and surface waves to determine large-scale crust and upper mantle structure [Owens et al., 1995; Nyblade et al., 1996]. A number of studies have been completed using data from this experiment, including analysis of teleseismic receiver functions for crustal structure [Last et al., 1997], P and S wave mantle tomography [Ritsema et al., 1998], seismicity studies [Nyblade et al., 1996; ESE 1-1

2 ESE 1-2 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA Figure 1. Map of East Africa showing locations (triangles) of stations deployed during the Tanzania Broadband Seismic Experiment. Data used in this study come from the four earthquakes whose locations are denoted by circled stars on the map. Major geological features are also shown. The outline of the Tanzania craton is the dashed stippled area. Major rift faults of the East African Rift are denoted by heavy lines. Proterozoic mobile belts surrounding the craton are named. The focal mechanism (lower hemisphere projection) of the Lake Rukwa earthquake is superimposed on the map and is from Zhao et al. [1997]. Langston et al., 1998], Pn tomography [Brazier et al., 2000], and study of upper mantle discontinuities from receiver function stacking [Owens et al., 2000]. In addition, new gravity measurements were made to fill in the gravity map of Tanzania and to add constraints on crustal thickness estimates [Tesha et al., 1997]. [5] In this paper we use a combination of travel time and waveform modeling to infer a surprisingly simple velocity model for the crust and mantle within Tanzania. In addition to inferring basic properties of the crust and upper mantle within Tanzania to constrain tectonic interpretations, we wish to develop a good wave propagation model that can be used in modeling local and regional earthquakes to infer accurate source parameters in subsequent seismotectonic studies. [6] We use the broadband waveforms from the 18 August 1994, Lake Rukwa earthquake first to infer the character of regional wave propagation within the crust and mantle and then to quantify the arrival times and amplitudes from a variety of observed seismic phases to produce a velocity model. The Lake Rukwa event was recorded at teleseismic distance and was the subject of a detailed source study by Zhao et al. [1997], who determined its source mechanism, source function, and depth. Because the source parameters are known for this event, it can be used to decipher the regional wave propagation across the network. The modeling approach incorporates the use of synthetic seismograms to verify phase interpretations, travel time studies to infer gross seismic velocities, and a new, general method for incorporating seismic phase times and waveforms in a formal inversion for structure parameters. This latter technique, called phase time inversion, is a simple method of modeling any time domain waveform or large collection of waveforms to determine a parameterized structure model. It avoids many of the problems of synthetic and data waveform comparisons that occur using cross-correlation or least squares methods. [7] The results show that it is possible to determine an accurate velocity model directly from regional waveform data that is useful in predicting times and amplitudes of regional seismic phases. Crustal structure within the craton is simple and consistent with past studies of surface wave dispersion and receiver functions. Mantle wave velocities are high and consistent with the inference that there has been little thermal modification of the upper lithosphere under Tanzania by rifting processes. Analysis of the waveforms from the Rukwa earthquake yield several insights into regional wave propagation including the mechanism for Lg wave propagation within the craton and use of sp depth phases to constrain earthquake source depths. 2. Data [8] Owens et al. [1997] give considerable detail on the deployment of stations of the Tanzania Broadband Seismic Experiment and collection, archiving, and quality of the resulting waveform

3 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA ESE 1-3 Table 1. Event Parameters Event Date Origin Time Lat., S Long., E Depth, km Local Magnitude Lake Rukwa Aug. 18, : Lake Tanganyika Nov. 12, : Mbeya Nov. 16, : Tarangire Feb. 12, : data. A typical station consisted of a PASSCAL Reftek 24-bit data logger, Omega clock timing system, 1-Gb hard disk, and an STS-2 broadband sensor. Two stations had CMG-3 broadband sensors, and several others employed GPS clocks as these became available. The 20-samples-per-second (sps) and 1-sps data were harvested from the disk in the field by writing to a digital audiotape. Station power was provided by deep-cycle truck batteries and solar panels. Nominally, 20 stations were running continuously during the experiment (Figure 1). [9] We gathered waveform data from some of the larger regional events that occurred within Tanzania (Table 1) as part of several local seismicity studies [Nyblade et al., 1996; Langston et al., 1998]. Waveforms from these events had high signal-to-noise ratios because of their relatively large magnitudes and were ideally suited for more detailed travel time analysis. [10] In this paper we concentrate on modeling waveforms from the Lake Rukwa earthquake because Zhao et al. [1997] determined detailed source parameters from its teleseismic body waves (depth 25 km, strike 135, dip59, rake 76, M dyn cm). Knowledge of source depth, mechanism, and far-field source time function is an essential ingredient in deciphering the regional waveforms written by this event. We use the source parameters of Zhao et al. [1997] as known quantities to predict the amplitudes of regional phases using a wave number integration technique [Barker, 1984] to compute synthetic seismograms. The event source mechanism, in particular, is very important in defining the character of regional waveforms because radiation pattern effects play a very important role in how stable certain waveform components remain over stations of the network. In particular, because the Rukwa event was a high-angle normal fault (e.g., see Figure 1), P-SV waveforms seen on the vertical and radial components did not change much with azimuth across the network. However, SH waveforms on tangential components had much more azimuthal variation. [11] The raw, 20-sps digital data for the Rukwa event were processed by removing the instrument response, scaling to ground displacement, and high-pass filtering with a causal two-pole Butterworth filter with a corner frequency of 0.01 Hz. An example of the data is shown in Figure 2 for station RUNG. The raw waveform data from the other events of Table 1 were used for timing of first arrivals. Waveforms from stations MTAN and INZA were not included in the analysis in this paper because of instrument malfunctions, although first-arrival travel times were picked. Locations and local magnitude determinations for all events are discussed by Langston et al. [1998] and Zhao et al. [1997]. 3. Regional Phases and Travel Times [12] Broadband waveforms from regional events in Tanzania show many clear and distinct seismic phases that can be correlated over long distances. Figure 2 shows velocity and displacement waveforms for the Rukwa event recorded at RUNG. This station was one of the closer stations that recorded useful data from the event. The data at RUNG illustrate the clarity of distinct seismic phases that show up in both the velocity and the displacement wave trains. Several interpretations of phases are shown in Figure 2 and will be discussed below. However, the initial problem we encountered when trying to understand these data was identifying the wave propagation involved in forming each phase. We approached the solution of this problem through a combination of particle motion analysis, construction of travel time curves in plausible plane-layered earth models, and calculation of synthetic seismograms using the Rukwa teleseismic source parameters as a constraint. Velocity (nm/sec) Displacement (nm) Lake Rukwa Event Recorded at Rungwa Station o Azimuth =75.9, Distance = 208 km Pn Pmp spmp SmS Sn ssms Time (sec) Vertical Radial Tangential Vertical Rayleigh wave Radial Tangential Figure 2. Three-component, 20-sps (top) velocity and (bottom) displacement data for the Lake Rukwa earthquake recorded at Rungwa, Tanzania (RUNG). Vertical (up), radial (away from the source), and tangential (clockwise around the source, looking downward) ground motions are shown. Note the excellent signalto-noise ratio and the wealth of distinct arrivals in the data. A number of phase interpretations are shown which were determined in the course of study of these waveforms and others recorded in the network.

4 ESE 1-4 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA Travel Time, sec Travel Time, sec Distance, km a b Craton Stations Tarangire 8.45 Mbeya 8.44 Mozambique Belt Stations Tarangire 8.22 Pn Velocities Lake Tanganyika km/s Lake Tanganyika Rukwa 8.47 Mbeya 8.22 Rukwa Distance, km Figure 3. Pn velocities determined by regression of first-arrival travel times from four earthquakes recorded by the network. Pn velocities were determined for stations located (a) on the craton and (b) in the Mozambique belt. Standard errors and other velocity determinations are displayed in Table 2. The regression lines have been offset for viewing purposes. Pn velocities in the Mozambique belt are somewhat slower than within the craton but are not anomalously slow. [13] An initial model of crustal structure was constructed using results from teleseismic receiver functions and short-period surface wave dispersion analysis performed by Last et al. [1997]. Last et al. [1997] showed that cratonic crust within Tanzania was relatively high velocity, having average P and S wave velocities of 6.6 and 3.8 km/s, respectively, with an average thickness of km. The receiver function waveforms for most stations were very simple, implying that there were few crustal discontinuities other than the Moho. This result was similar to results obtained in Kenya for long-range refraction experiments off the rift axis [Kenya Rift International Seismic Project, 1987, 1991; Prodehl et al., 1994; Birt, 1996], which showed relatively simple, high-velocity crust in the northern part of the Tanzania craton and Mozambique mobile belt to the east. [14] We constrained upper mantle P and S wave velocities by performing travel time studies of first-arrival Pn waves from the events of Table 1 and Sn waves from Rukwa event waveforms [Langston et al., 1995]. Figure 3 shows results from a regression analysis of the Pn travel times for the events of Table 1, and Table 2 displays the numerical results. As Brazier et al. [2000] point out using a tomographic Pn velocity within the network is quite high at km/s, with the higher velocities found within the craton. The regression analysis shown in Figure 3 and Table 2 is consistent with their result. It also provides an independent check of the Pn tomography result since the regression analysis is largely independent of static timing errors imposed by unknowns in source location and origin time. Sn velocity, using picks from the Rukwa waveforms, is 4.75 km/s and is consistent with the high Pn wave velocity in the mantle. [15] Simply plotting the vertical- and radial-displacement waveforms in a reduced time section using the average Pn and Sn velocities yields important information on the nature of wave propagation across the network. Figure 4 shows a reduced time section for vertical-component arrivals before Sn. Clearly, these phases generally travel at Pn velocities and can be interpreted as Pn, spn, and multiples. Figure 5 shows the S wave train in a reduced time section using the average Sn velocity across the network. There is a remarkable succession of Sn and multiple-sn phases that can be traced across the network. [16] Identifying each phase in the Rukwa data was a straightforward matter involving calculating theoretical travel time curves in an ideal crustal model. Figure 6 displays a sketch of typical P and S wave ray paths in a simple single-layer-over-half-space crustal model. Travel time curves were computed for an earth model parameterized with a linear gradient in the crust over a homogeneous mantle (Figure 7). Parameters for this model are given in Table 3. The Rukwa source was located at 25 km depth within the lower half of the crust so that the P waveforms of Figure 4 are dominated by Pn, spn phases, and their multiples. The apparent low-velocity moveout of the later arriving energy in the P waveform data is the beginning of the regional PL wave [Helmberger and Engen, 1980]. [17] Calculating the travel time curves for S waves shows that the S wave train is dominated by Sn, ssn, and their multiples all across the network (Figure 6). The relatively large depth for the Rukwa event causes the Rayleigh wave to be a subdued, longerperiod pulse. It was remarkable to see how the various Sn head waves developed as multiple reflections go critical with distance. These critical reflections show up as high-amplitude, higher-frequency pulses on the seismogram and then decay with distance as a head wave. 4. Synthetic Seismograms and Phase Time Inversion [18] Early versions of the final earth model shown in Table 3 were very successful in predicting the general behavior of the Table 2. Pn and Sn Velocity Determinations a Event All Stations Craton Mozambique Belt Lake Rukwa (Pn) 8.29 ± ± ± 0.13 Lake Tanganyika (Pn) 8.28 ± ± ± 0.16 Mbeya (Pn) 8.07 ± ± ± 0.34 Tarangire (Pn) 8.58 ± ± ± 0.16 Lake Rukwa (Sn) 4.75 ± 0.13 a Measurements are given in km/s.

5 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA ESE 1-5 Distance (km) Data PL Reduced Travel Time T - Distance/8.3 sec Reduced Travel Time T - Distance/8.3 sec Pn P PmP ppn Pn 2 spn ppn 2 Pn 3 spn 2 ppn 3 spn 3 PmP 2 ppmp 3 spmp 3 Synthetic Figure 4. (left) Reduced velocity profiles of vertical-displacement data from the Rukwa earthquake and (right) synthetic waveforms from the final inversion model. The data and synthetics have been windowed to exclude the S wave train. Note how all waveforms are dominated by waves that travel at Pn velocity. Travel time curves for major P and sp waves are superimposed on the plot. The largest amplitude phases in the data are spn-type head waves. Refer to Figure 6 for ray path diagrams. Pn 2 and Sn 2, for example, are mantle head waves associated with PmP 2 and SmS 2 crustal multiples, respectively. All wave number synthetic seismograms in this paper were computed using 2048 time points with a 5-sps sampling frequency. broadband waveforms when synthetic seismograms were calculated using the Rukwa source parameters. Relative amplitudes and times of the different head waves and crustal multiples were roughly correct, showing good similarity between data and synthetic. However, it proved difficult to come up with a method to use all the data simultaneously to find an optimum structure model. [19] Several schemes were attempted to refine the velocity model. Because the wave number integration algorithm is CPU Distance (km) Reduced Travel Time T - Distance/4.75 sec Red ced Travel Time T - Distance/4.75 sec Sn ssn SmS Sn 2 2 ssn SmS 2 Sn 3 ssms 2 ssn 4 ssn 3 Sn 4 SmS 3 ssms 3 SmS 4 Rayleigh Wave Figure 5. (left) Reduced velocity profiles of vertical-displacement data from the Rukwa earthquake and (right) synthetic waveforms from the final inversion model for the S wave train. Travel time curves for important S wave ray paths are superimposed on the waveform sections. These waveforms contain both Sn-type head waves and postcritical-angle multiple S wave reflections. ssms 4

6 ESE 1-6 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA P PmP spmp Pn P head wave Moho S SmS ssms SmS 2 ssms Sn, Sn, ssn, ssn, etc. S head wave Moho Figure 6. Schematic ray paths for various (top) P and (bottom) S waves within the Tanzania crust and mantle. intensive [Barker, 1984], multimode surface wave summation was used initially to construct an accurate synthetic for the S wave train [e.g., Harkrider, 1964, 1970]. Because this is a much faster process (by 2 orders of magnitude in speed), many more earth models could be tested. We used a normalized cross-correlation function to determine the fit between data and synthetic [e.g., Wallace and Helmberger, 1982]. However, the multimode summation we used was not appropriate for the P wave part of the wave train. Furthermore, it was difficult to fit important, relatively high frequency pulses in the wave trains of many records because there were significant time shifts between the data and synthetic pulses when the fit was dominated by the longer-period portions of the seismogram. [20] An attempt was made to calculate wave number integration synthetics using a coarse grid search algorithm in the crustal structure parameters to regain the P wave train portion of the seismogram. Normalized cross correlation was then used on specific time windows in the data and synthetics in an attempt to model various individual phases. Again, modest time shifts between data and synthetic arrivals placed these arrivals outside of the correlation time window even though the pulse shapes were not very different. We also discovered that there were consistent absolute time shifts between the data and synthetic waveforms that were probably due to details in the Rukwa source time function or errors in the origin time. These time shifts compounded the problems with the correlation operator windows. Clearly, the similarity of data and synthetics showed that the basic wave propagation was understandable, yet it was difficult to quantify the earth model using features of the data waveforms. [21] As usual, a little thought instead of brute-force numerical analysis yielded a simple way to incorporate all important data features into a simultaneous inversion for structure parameters. The regional waveform consists of multiple body waves and surface waves, many of which interfere with each other in complex ways. Whichever way the amplitudes work out, travel times of these waves are straightforward functions of crustal velocity structure and thickness. We noticed that many synthetic seismograms for differing earth models often looked similar, with the major differences occurring in arrival time for the various component phases within them. Since these features changed their travel time when model parameters changed, we decided to use these time differences as data in a formal generalized inversion for velocity parameters. [22] Figure 7 illustrates implementation of the process using vertical-component data from station MTOR. The earth model is parameterized as shown in Figure 7 (bottom) as a linear velocity gradient in the crust defined by surface P wave velocity, v 1,a basal P wave velocity, v 2, and crustal Poisson s ratio, s c. Crustal thickness h is also a parameter. Mantle P and S wave velocities are fixed by the travel time regression of the Rukwa Pn and Sn data. Using an initial guess for the earth model, a synthetic seismogram is constructed (the reference model synthetic in Figure 7) and compared to the original. Note that the source parameters are fixed. [23] Phase times are defined as the arrival time of some easily recognizable peak or trough associated with a particular seismic phase arrival. For example, in Figure 7, T j is associated with the trough of Sn, and T j +1 is associated with the peak of ssn. Because the reference model is not perfect, corresponding peaks and troughs on the synthetic (T j o, T j +1 o, etc.) do not occur at the same times for these phase time picks. [24] An iterative inversion problem can be set up to simultaneously solve for a new set of model parameters using the phase time misfits (Appendix A). The phase times for the data waveforms, starting model synthetic, and model perturbation synthetics are all picked manually using an interactive graphical interface (Figure 7). This has both drawbacks and natural efficiencies. Obviously, this process introduces biases in the interpretation of the data and synthetics. A choice is made to fit a particular arrival in the data, and it is assumed that waveshape for the arrival does not change appreciably across the synthetics. Picking the wrong phase in the synthetics will create problems since the inversion system will have inconsistent data. Another drawback is that picking the phase time manually introduces some error in the time estimate that will affect estimates of the model parameters. Furthermore, this process is not easily made automatic since each iteration of the system requires picking a new set of phase times for the updated model and perturbation synthetics. [25] However, fitting the phase times directly is the intuitive process that a waveform analyst attempts when fitting data with synthetic seismograms. The phase time itself is just a generalization of ray arrival time applied to some consistent feature of the waveform. Reduction of a highly sampled time series with thousands of points to a few pieces of data is a great economy in setting up the inversion problem. For example, we applied this technique to 56 broadband waveforms with 3000 points

7 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA ESE 1-7 Figure 7. (top) Illustration of picking phase times from observed and synthetic regional waveforms. Verticalcomponent data from Kwa Mtoro (MTOR) station are shown, followed by a synthetic seismogram ( reference model ) computed using the starting earth model and by four other synthetics that are computed using perturbations of the starting earth model. (bottom) Earth model parameterized by a linear gradient in the crust over a mantle half space. Arrival times are a function of the assumed source and structure parameters. Phase times are picked using obvious peaks or troughs for various arrivals in the data. For example, each phase time shown corresponds to Sn (T j ), Sn 2 (T j + 1 ), ssms 2 (T j + 2 ), and the Rayleigh wave (T j + 3 ). The corresponding peak or trough is picked on the synthetic waveforms to form the phase time residual and partial derivatives. each from the Rukwa event. Using only unambiguous picks of phase times between data and synthetics, these 180,000 data points were reduced to 91 phase time picks. There is also an economy in the computation of synthetic seismograms since synthetics for only five different models need to be computed to form the reference synthetic seismogram and the perturbation seismograms. Implicit in the formulation are smoothing constraints imposed by the form of the crustal model. Rather than parameterizing a model with many thin layers, simple ideal velocity profiles, like the linear gradient used here, can be investigated. This simplifies the inversion setup and reduces likely problems in parameter resolution when velocity and

8 ESE 1-8 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA Table 3. Inversion Model Parameters v 1, km/s v 2, km/s s c h,km t 0,s Starting model All stations 5.84 ± ± ± ± ± 0.2 Craton Stations a 5.97 ± ± ± ± ± 0.4 Mozambique Stations b 5.64 ± ± ± ± ± 0.4 a Fifty-five phase times are used from RUNG, URAM, MITU, PUGE, MBWE, SING, MTOR, and BASO. b Thirty-six phase times are used from KOND, KIBA, TARA, KIBE, KOMO, and LONG. thickness parameters of many thin layers in a model trade off with one another. If a more complicated model is needed to fit the data, the model can be made incrementally more complex. [26] Synthetic tests of the technique worked remarkably well by yielding the correct velocity model in a single iteration. Relatively large perturbations of the earth structure parameters produced stable partial derivatives. The method also worked quite well for single-station synthetic tests. Errors in picking the phase times were found to be a minor problem and did not degrade the model parameter estimates significantly. Picks could be made to within 0.5 s for the synthetic data with the model parameter variance being, at most, 0.01 km 2 in crustal thickness. Variance for the other parameters was a little larger than numerical noise levels. [27] Figure 8 shows the results of applying the phase time inversion to the Rukwa waveform data. Table 3 displays the starting model and final inversion model parameters. The strategy used in picking phases was to use clear, isolated peaks in the vertical waveforms and a few of the tangential waveforms. Phase time picks from the radial waveforms are redundant since they contain the same arrivals as those on the vertical components. Because the tangential waveforms were more affected by azimuthal radiation pattern effects in the Rukwa source (SH wave nodes for both up- and down-going waves sweep through the network), we generally avoided picking details in the tangential waveforms and attributed tangential waveform complexity to the influence of scattering and to the greater effect of unknowns in the source mechanism on amplitudes near wave nodes. We also did not pick phase times from complicated regions of the vertical waveforms where it was obvious that many arrivals were interfering with each other. It was heartening to see after inversion that these complex portions of the seismogram at certain stations improved in fit. [28] One iteration was required to produce a stable model. Table 3 shows that there were only small changes in the earth structure parameters and origin time needed to improve the alignment of numerous phase picks. A variance of 1 s was assumed for the phase time picks for the estimate of model parameter variance. Figure 7 shows a typical misfit between the data and starting model synthetic. [29] In addition to the origin time and crustal velocity structure parameters determined by the inversion, seismic moment for the Rukwa event was estimated from the final waveform fits by waveform correlation. Seismic moment is a multiplicative scalar quantity in the synthetic seismogram calculation where the ground displacement can be represented by M 0 S(t) for a suitably normalized S(t). The optimum least squares estimate of M 0 can be found through cross correlation of S(t) with the data seismogram O(t). M 0 ¼ ½OðtÞSðtÞŠ t¼0 ; ð1þ ½SðtÞSðtÞŠ t¼0 where the circled cross denotes cross correlation and the value at zero lag time is taken. Using all radial- and verticalcomponent waveforms in Figure 8, a seismic moment of dyn cm is obtained for the Rukwa event. This is 40% of the moment found by Zhao et al. [1997] using teleseismic body waves. 5. Nature of Regional Wave Propagation Within the East African Plateau [30] A perusal of Figure 8 shows that the combination of teleseismic source parameters for the Rukwa event and a simple layer-over-half-space model for the Tanzania crust and upper mantle yields synthetic seismograms which reproduce many details of the observed waveforms at all distance ranges. Arrival times, waveshape, and relative amplitudes fit remarkably well for most vertical and radial components and for many tangential components. These fits allow an in-depth understanding of the wave propagation within the East African plateau that has been difficult to achieve elsewhere. [31] Returning to Figures 4 and 5, it is apparent that the P and S wave trains at regional distances are dominated by critical reflections and head waves from discrete up- and down-going reflections in the Tanzanian crust. The depth of the Rukwa source and its normal fault mechanism combine to create a succession of discrete Sn-type head waves on vertical and radial components of the S wave train. Figure 5 shows how high-amplitude critical S wave multiple reflections apparently decay in amplitude with distance as the head wave propagates away from the critical distance. This happens over and over as progressively higher order multiples go critical with increasing distance. [32] This observation has interesting implications for the propagation mechanism for the higher-frequency Lg phase. Lg is a phase which is of interest in Comprehensive Test Ban Treaty monitoring since it often travels great distances in the crustal waveguide, is the largest phase seen in high-frequency regional seismograms, and can be used to estimate seismic moment and magnitude [e.g., Herrmann and Kijko, 1983; Kennett, 1986; Hanson et al., 1990; Campillo, 1990]. The study of Lg has an extensive literature, but its propagation mechanism has been difficult to understand because of unknowns in crustal structure and use of relatively limited, single-station data sets. [33] Figure 9 displays a profile of the vertical-component velocity waveforms from the Rukwa event showing a typical interpretation of Lg in regional data. It is a high-amplitude S phase with a velocity indicative of the upper crust, here at 3.5 km/s. If this empirical travel time curve is superimposed on the travel time curves for multiple S waves (Figure 10 ), we see that the beginning of Lg is composed of post-critical Moho reflections with later portions of Lg composed of higher-order post-critical Moho reflections. Phase velocity for these post-critical reflections is high, being 4.2 km/s, since they have near-grazing incidence angles at the Moho. [34] Figure 10 (bottom) shows group velocity dispersion curves for the final crustal model. Modal explanations for Lg are equally valid as the ray explanation since adequate S wave synthetic seismograms can be computed using normal mode summation. The group velocity dispersion shows that there is a tangle of higher modes that interfere with each other near 3.5 km/s over a wide

9 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA ESE 1-9 (202, 74) (262, 8) (299, 59) (340, 28) Figure 8. Panels showing observed (top) and synthetic (bottom) regional seismograms for the Lake Rukwa earthquake. Vertical (Z), radial (R), and tangential (T) waveforms are shown for each station. Station distance (km) and azimuth from the source (degrees) are shown in parantheses. Seismograms have been normalized for plotting, and the absolute amplitude (microns) is given in the upper right of each seismogram. The arrows denote phase time picks used in the inversion. Note that the timescale generally changes with station distance. Phase picks were taken from GOMA data because the propagation path was generally along the western branch of the East African Rift. Phase picks were not taken from HALE data since this station is at the coast and is likely to have thinner crust. Nevertheless, phase arrival times and waveshapes are matched well by the synthetics at both stations.

10 ESE 1-10 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA (202, 74) (262, 8) (299, 59) (340, 28) Figure 8. (continued)

11 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA ESE 1-11 (509, 48) (528, 58) (582, 67) (614, 51) Figure 8. (continued)

12 ESE 1-12 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA (673, 71) (679, 55) (756, 47) (795, 73) Figure 8. (continued)

13 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA ESE 1-13 Vertical Component Velocity "Lg" at 3.5 km/s Distance (km) Reduced Travel Time T - Distance/4.75 sec Figure 9. Vertical-component velocity waveforms from the Rukwa earthquake plotted in a reduced velocity profile at the average Sn velocity. This profile shows the empirical Lg wave interpretation of the S wave train data. Lg is an apparent phase that travels at 3.5 km/s. frequency band. However, this relatively low group velocity does not mean that the Lg phase propagates entirely in the upper crust. Basically, the interference of separate modes in the modal summation gives rise to discrete arrivals that can be interpreted as individual rays. This explanation reinforces empirical array studies of the Lg phase performed by Vogfjord and Langston [1990, 1996] using high-frequency data from the Norwegian seismic arrays. Using array beams, they decomposed the Lg wave field to show that low group velocity Lg waves were composed of high phase velocity turning waves and post-critical reflections within the Scandinavian crust. 6. Discussion [35] The velocity model determined here for the crust and upper mantle in Tanzania is very simple. Standard errors for the model parameters are small for the phase time pick variance of 1 s. However, the reduced velocity profiles shown in Figures 4 and 5 point out that there are numerous small time shifts between observed and theoretical arrival times. Scrutiny of waveform detail shows small misfits at most stations. Thus there is evidence of velocity heterogeneity that cannot be modeled by these methods at present. Brazier et al. [2000] performed a Pn tomography and showed 4% heterogeneity in Pn velocities between cratonic and Mozambique belt upper mantle. There is probably similar heterogeneity in crustal velocity and thickness. For example, Last et al. [1997] show that there are small changes in the average velocity and/or crustal thickness over stations of the network in the receiver function data. However, as seen in the Last et al. [1997] study, it is remarkable how well a simple crustal model explains the waveform data. [36] Surprisingly, one crustal model fits data for stations on the craton and to the east within the Mozambique belt. The phase time data for these two groups of stations were inverted separately (Table 3), but there were few significant differences in resulting models. The inversions suggest that crust of the Mozambique belt is somewhat slower and thicker than crust of the craton. This is in agreement with studies of regional gravity [Tesha et al., 1997] and constraints on average velocity and crustal thickness determined by Last et al. [1997]. However, the differences are small, and it is not clear how lateral changes in crustal structure affect the propagation of individual phases in the regional waveforms. Ray paths for longrange multiple reflections will sample both structures, and phase times will be significantly affected by both. Clearly, modeling the phase times with a single plane-layered crustal model may only be suggestive of differences in structure. A more robust method of treating lateral heterogeneity is needed. [37] Data from two stations located within the Rukwa rift zone, TUND and PAND, could not be modeled adequately with any plausible earth model (Figure 11). These stations are at a distance

14 ESE 1-14 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA Reduced Travel Time T - Distance/4.75 (sec) ssms SmS SmS 3 ssms 2 SmS 2 ssms 4 SmS 4 ssms 3 S Wave Ray Travel Times "Lg" at 3.5 km/s Distance (km) ssn Sn Rayleigh Wave Dispersion 3 Sn ssn 3 Sn 2 ssn 2 a ssn 4 4 Sn b 4.0 higher modes Group Velocity (km/s) "Lg" at 3.5 km/s fundamental mode Frequency (Hz) Figure 10. (a) Ray and (b) mode explanation of the Lg phase. Figure 10a contains important S wave ray travel times for the final earth structure model developed here. The crustal velocity gradient causes shear wave multiples to have distinct cutoffs with distance where they become grazing rays at the Moho. Superimposed is the empirical Lg travel time curve of the data. Lg is composed of multiple post-critical S wave reflections in the crust that have relatively high phase velocities. There is no single propagating S wave with a low phase velocity of 3.5 km/s. Lg is composed of different waves at different distances. Rayleigh wave dispersion curves for all modes between 0 and 1 Hz show that the high-frequency portion of each of the higher modes interferes quite extensively for group velocities near 3.5 km/s. As shown by the synthetic seismogram computation, interference of each mode with the others gives discrete phase arrivals which are the wave S crustal multiples. where first-arrival P and S waves should be Pn and Sn head waves, respectively. However, the data show impulsive, relatively high frequency P and S arrivals that look nothing like the synthetics. The Rukwa graben has extensive basin fill [Baker et al., 1972; Zhao et al., 1997], so models with thick sections of near-surface sediments were tested. These improved some aspects of the P wave train but did nothing for the S waves and surface waves. Models predict large, free-surface S wave reflections that do not seem to be in the data. Because these two stations are at similar distances, we cannot come up with constrained earth structures for the graben path, and we leave these anomalies for future field experiments. [38] Because the Rukwa earthquake source was so deep at 25 km, it is likely that we have missed details of near-surface crustal structure. In particular, the Rayleigh wave is pulse-like

15 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA ESE 1-15 Rukwa Graben Paths (231, 152) ssms Sn ssms Sn (237, 136) Figure 11. Observed and synthetic waveforms for stations in the Rukwa rift zone, formatted as in Figure 8. Waveforms for these stations show anomalous behavior with respect to the final earth model, suggesting significant differences in structure of the crust and upper mantle. Synthetic seismograms predict large free-surface reflections that are not in the data. and shows little evidence of dispersion even at 800 km distance. Higher-frequency fundamental mode surface waves will not be excited because of the large source depth, so we cannot investigate dispersion for higher-frequency surface waves. These waves exist for other earthquakes recorded by the experiment and will be investigated in a companion study of earthquake sources. [39] The crustal model developed here will be very useful in modeling other East African earthquakes for source parameters. The Rukwa data show spectacular sp-type phases (Figure 2) that are excellent indicators of source depth [Langston, 1987, 1996] in local/regional data. The simplicity of the crustal model predicts simple waveforms at most distances. Particle motion and phase travel time studies can be used to locate small events using the waveforms from a few stations, and amplitude modeling can yield the source mechanism [e.g., Helmberger and Malone, 1975; Wallace and Helmberger, 1982; Dreger and Helmberger, 1990; Zhao and Helmberger, 1993, 1994; Zhu and Helmberger, 1996]. This opens up the Tanzania data set for seismotectonic studies of faulting and source mechanisms in this area of nascent rifting. [40] It is not known whether the discrepancy in seismic moment determined in this study and by Zhao et al. [1997] is significant. Zhao et al. [1997] used a teleseismic Q model for P and S waves parameterized by t* of 1.0 and 4.0, respectively. Using lower values (less attenuation) would decrease the estimate of the teleseismic moment and possibly lengthen the teleseismic source function. Both effects would tend to bring the teleseismic and regional moment estimates in line. Estimating the seismic moment from low-pass filtered regional data only increased the estimate by 10%, suggesting that the teleseismic t* value used by Zhao et al. [1997] may be too large. [41] The phase time inversion process used here was surprisingly robust in determining a velocity model. The problem behaved as a linear problem even though the method of computing synthetic seismograms is quite nonlinear in the model parameters. On the other hand, the wave propagation involved nearly horizontally propagating seismic waves in which it is reasonable to suppose that small changes in model slowness will result in a linear change in arrival time. The strength of the inversion is that it is an intuitive process that reduces large, highly sampled waveform data sets into small, but precise, phase time data sets. This method should be useful for many kinds of waveform data sets when the wave propagation and source properties are adequately understood or where there is great heterogeneity in the data set. For example, it could be useful in combining tomographic ray methods with waveform methods for determining earth structure.

16 ESE 1-16 LANGSTON ET AL.: REGIONAL WAVE PROPAGATION IN TANZANIA, EAST AFRICA [42] The East African plateau is an active tectonic area with a relatively high seismicity rate [Langston et al., 1998]. The surrounding Proterozoic mobile belts and east margin of the Tanzania craton are being actively rifted. Nevertheless, the results of this study of crustal and upper mantle velocity structure show that seismic velocities are generally high in the mantle and similar to ancient cratonic regions elsewhere in the world [Christensen and Mooney, 1995]. These high mantle velocities imply that there has been no thermal perturbation of the uppermost mantle under most of the region. [43] We performed several numerical experiments to see if the data could put any significant constraints on upper mantle velocity gradients. It is well known that head wave amplitudes are affected by velocity gradients [e.g., Hill, 1971]. Using the crustal model from the inversion, we tested several upper mantle models that were parameterized by an increasing linear velocity gradient with depth. There was some indication that a positive velocity gradient of 0.004/s might be resolvable in the data since Pn and Sn waves at the farthest distances started to become higher-frequency and higher-amplitude turning waves in the synthetics. However, most of the data are not sensitive to gradients <0.004/s and are most simply explained by a constant velocity half space. [44] Seismic velocities are also relatively high in the crust and are consistent with cratonic crustal structure elsewhere [Christensen and Mooney, 1995]. Although we found that crustal structure is simple, velocities do need to increase with depth so that lower crustal P wave velocities attain values of 7.0 km/s. Travel times and critical distances of the various crustal multiples observed in the Rukwa waveform data are a sensitive function of the velocity gradient and velocity in the lower crust. Because source/station distances are so great, small changes in average crustal velocities yield large changes in arrival times for these phases. [45] Aside from wave paths in the Rukwa graben, there was not much evidence for severe disruption of the crust or the mantle. Waveform data for stations on the craton and to the east in the Mozambique mobile belt seemed to be explained equally well by the same earth model. Clearly, there are rift faults along the eastern edge of the craton, and these faults may cut through the crust and into the upper mantle. However, it appears that these structures do not have enough offset or intrinsic heterogeneity to affect significantly the regional wave propagation across them. This is consistent with the relatively high efficiency of wave propagation implied by the attenuation characteristics of the local magnitude scale found by Langston et al. [1998]. Wave propagation across the East African plateau has few losses and is very clean, making it an ideal laboratory for the study of local and regional earthquakes. 7. Conclusions [46] It was possible to derive a crust and mantle velocity model from regional waveform data recorded from the Lake Rukwa earthquake and from first-arrival time data picked from other large regional events. The model is very simple, consisting of a crust characterized by a linear velocity gradient over a mantle half space (Table 3) and is consistent with previous crustal structure studies in the area. The crust and mantle velocity structure of the Tanzania craton is similar to velocity structure in other Archean cratonic areas in that it has high average crustal velocities, high velocities near the Moho, and relatively high upper mantle velocities. These velocities imply that much of the crust and upper mantle has not been thermally modified by rifting processes of the East African Rift Zone. [47] A simple, intuitive method for inverting large data sets of regional waveform data has been developed and is called phase time inversion. This method minimizes the misfit between the arrival times of discrete phases on observed and synthetic seismograms. It is similar to tomographic methods except that there is no reliance on ray travel times or explicit formulations of ray geometry. Any seismic phase can be used as long as accurate synthetic seismograms can be computed. Application to the Rukwa regional waveform data showed that in this case, the inversion problem behaved in a linear fashion. Earth models can be parameterized in terms of simple ideal systems to minimize the number of model parameters while preserving basic understanding of the wave propagation involved. [48] The results of the crustal structure study are being used to perform more detailed seismotectonic studies of local and regional events within Tanzania through waveform modeling. Phase time inversion should be useful in many other studies of broadband waveforms where there is interest in wave propagation mechanisms and in determining earth structure parameters. Appendix A [49] Suppose we have j = 1... n phase time picks that we want to fit. Each is given by Tj ¼ tjða Þ; ða1þ where the model phase times, t j, are functionals of the model parameter vector a, with where a ¼ðs 1; s 2 ; s C ; h; t 0 Þ; s 1 ¼ 1=v 1 s 2 ¼ 1=v 2 ða2þ ða3þ are the surface and basal crustal P wave slownesses and t 0 is event origin time. [50] Expand the phase times around a starting model: where or T j ffi T 0 j T 0 j j a 0 a k ; ða4þ k ¼ T j a 0 Þ ða5þ ðt j Tj 0 Þ¼@T j a 0 a k : ða6þ k The partial derivatives are calculated numerically using a finite difference, j ¼ T jða 0 þ a k^e k Þ T j ða 0 k a ¼ 1: ða7þ ða8þ