Inversion of far-regional broadband P waves for the estimation of source parameters from shallow depth earthquakes

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112,, doi: /2006jb004724, 2007 Inversion of far-regional broadband P waves for the estimation of source parameters from shallow depth earthquakes Gene A. Ichinose 1 and Peter Goldstein 2 Received 31 August 2006; accepted 26 September 2006; published 15 February [1] Attempts in separating the earthquake source effect from complex upper mantle wave propagation effects have been unsuccessful due to band-limited World-Wide Standardized Seismograph Network data and limitations in the computation of accurate seismograms. In this study, we examine the potential for estimating source parameters using broadband P waves observed between distances of 10 and 30. We used the reflectivity method, which retains all of the rays, to compute synthetic Green s functions from the Earth-flattened global AK135 and regional T7 isotropic velocity models. We applied the moment tensor inversion and iterative dislocation grid search methods to estimate seismic moment, moment tensor, focal mechanism, and focal depth for three example seismic events, the 1995 (M w 5.7) west Texas, 1999 (M w 5.6) Scotty s Junction, Nevada, and 1999 southern Iran (M w 4.8) earthquakes. The west Texas and Scotty s Junction earthquakes were well recorded, and they had independently established source parameters. Independent estimates from different data sets and agencies were used to validate the inversion results. We selected the southern Iran earthquake to show the utility of the method at lower magnitudes. Selected vertical and radial component seismograms were windowed about the P wave arrival, corrected for instrument response, and converted to velocity, preserving the absolute amplitudes and periods within approximately 0.5 to 100 s. Both inverse methods were successful in separating the source effect with the use of the AK135 velocity model. The inversion results using the T7 model appear slightly biased and had worse waveform fits compared to AK135. More importantly, the use of two different velocity models resulted in biases in focal depths that were less than ±2 km, thereby providing a robust inverse method for focal depth. Utilizing far-regional P waves would be most useful for remote earthquakes not adequately recorded locally and too small in magnitude to be recorded beyond epicentral distances of 30 for teleseismic analysis. Citation: Ichinose, G. A., and P. Goldstein (2007), Inversion of far-regional broadband P waves for the estimation of source parameters from shallow depth earthquakes, J. Geophys. Res., 112,, doi: /2006jb Introduction [2] Inverting far-regional P waves to estimate focal mechanism and focal depth is valuable for discriminating between earthquakes and explosions [e.g., Goldstein and Dodge, 1999]. Focal depth can be used rapidly to flag a seismic event for further analysis in order to determine if the event was a fabricated explosion or natural earthquake. Depth can also be used to discriminate between damaging and nondamaging earthquakes [e.g., Sipkin, 2000]. Unfortunately, in routine earthquake location, focal depth is the least resolved due to sparse coverage of seismic stations in many parts of the world including North Africa, the Middle East, and eastern Asia. Utilizing far-regional P waves to 1 URS Corporation, Pasadena, California, USA. 2 Lawrence Livermore National Laboratory, Livermore, California, USA. Copyright 2007 by the American Geophysical Union /07/2006JB004724$09.00 monitor remote seismic events would be most useful for earthquakes not adequately recorded locally and too small in magnitude to be recorded beyond epicentral distances of 30 for teleseismic analysis. These earthquakes tend to occur more frequently and are plentiful compared to larger earthquakes. [3] Far-regional seismograms recorded within epicentral distances of 10 and 30 are usually avoided in earthquake source modeling because of the complexity due to the interaction of P waves with velocity changes across the transition zone, 410-km, and 670-km discontinuities. Helmberger and Wiggins [1971] and Wiggins and Helmberger [1973] originally modeled short-period P wave amplitudes and relative arrival times of upper mantle arrivals from earthquakes and explosions using the Cagniard-de Hoop method [e.g., Gilbert and Helmberger, 1972]. The results from these studies appeared promising in constraining upper mantle structure but complex crustal structure and source shapes prevented the complete separation between source and Earth structure effects. 1of21

2 [4] Past and recent studies of upper mantle structure used band-limited data and limited themselves to modeling only primary rays or relative amplitudes [e.g., Walck, 1984]. Most success in modeling upper mantle structure has been with studies by Helmberger [1973], Burdick and Helmberger [1978], and LeFevre and Helmberger [1989] which used longer-period P waves recorded by the World- Wide Standard Seismograph Network (WWSSN) across North America from both earthquakes and explosions. Recent studies by Goldstein et al. [1992] and Garnero et al. [1992] used digital broadband waveforms to examine the upper mantle velocity structure of Asia from nuclear explosions. Vidale et al. [1995] and Melbourne and Helmberger [1998] also used digitally recorded broadband and shortperiod P waves to examine the fine structure of the 410-km discontinuity across North America. Koch and Stump [1995] and Rodgers and Bhattacharyya [2001] have investigated the transition zone by using data recorded digitally from earthquakes and explosions across the United States. [5] In this experiment, we examined the potential to estimate the source parameters including seismic moment, focal mechanism, and focal depth from the inversion of P wave seismograms recorded between distances of 10 and 30. We used the previously published AK135 and T7 layered Earth velocity, attenuation, and density models to compute Green s functions using the reflectivity technique. The regional T7 velocity model was used to examine the variation in source parameter estimates due to a different upper mantle structure from the global AK135 model. Two different inversion schemes were used to estimate the source parameters of earthquakes, the dislocation grid search and moment tensor inversion methods. The dislocation grid search provides a detailed sensitivity and resolution analysis of the source parameters not capable by the moment tensor inversion method. These two inverse methods are well established and have been used to estimate source parameters for over 30 years. We will examine the 1995 west Texas (M w 5.7) and 1999 Scotty s Junction, Nevada (M w 5.6), earthquakes as two ideal test cases. Both were observed at regional and teleseismic distances by many stations. They also have independently established source parameters, estimated from different types of seismic data, methodologies, and agencies that are needed to validate the inversion results. We then examined a more realistic example from a smaller earthquake in southern Iran (M w 4.8) to tests the ability to estimate the source parameters down to lower magnitudes. 2. Broadband Waveform Data [6] The 14 April 1995 (M w 5.73) west Texas and 1 August 1999 (M w 5.61) Scotty s Junction, Nevada, earthquakes were recorded by several permanent seismic networks and two temporary arrays deployed by the Program for the Array Seismic Studies of the Continental Lithosphere (PASSCAL). The permanent stations included those from the United States National Seismic Network, University of California Berkeley Digital Seismic Network, Caltech s Terrascope, TriNet operated jointly by the U. S. Geological Survey (USGS), California Department of Mines and Geology, and Caltech, and stations, which are part of the Incorporated Research Institutions for Seismology (IRIS) and International Deployment of Accelerometers global seismic networks. The west Texas earthquake was recorded by stations from temporary PASSCAL arrays including those from the Missouri-to-Massachusetts (MOMA) experiment and the Colorado Plateau to Great Basin experiment. Figure 1 is a map of the locations for the west Texas and Scotty s Junction earthquake epicenters, seismic stations, and bounce points for the 410-km and 670-km discontinuities estimated using the AK135 velocity model. 3. Source Inversion Methodology [7] The moment tensor inversion method uses synthetic Green s functions formulated in terms of the fundamental faulting orientations. The Green s functions are ordered as a system of linear equations and solved using a least squares inverse for the moment tensor elements [e.g., Jost and Herrmann, 1989]. We neglect the isotropic component by only solving for a 5-degree of freedom deviatoric moment tensor. The alternate inverse technique requires formulating the synthetic Green s functions as a function of strike, dip, and rake. These parameters have a nonlinear relationship but can be easily solved using a brute force dislocation grid search scheme [e.g., Helmberger and Engen, 1980; Wallace et al., 1981; Wallace and Helmberger, 1982] to search for minima in the error parameter space. [8] We computed the Green s functions using the reflectivity method through a frequency and wave number summation technique [e.g., Zeng and Anderson, 1995; Thybo, 1989]. We first applied the Earth-flattening transforms of Müller [1977] on the one-dimensional (1-D) spherical AK135 and T7 isotropic velocity models (Figure 2). These transforms are needed due to the effect of the curvature of the Earth out to large source and receiver distances. We selected the reflectivity method over generalized ray theory in order to avoid ray truncation. With the generalized ray theory, only the primary interactions with each layer interface are retained otherwise the number of generalized rays that must be considered is prohibitively large. Both methods produce the same results [Burdick and Orcutt, 1979] except in cases where structures have strong velocity gradients or synthetics that are to be evaluated for extended times. [9] To avoid complex source time functions associated with larger earthquakes, we only examine earthquakes with magnitudes less than 6. We account for only simple spatial and temporal rupture effects with earthquakes of magnitudes greater than 4.5 by using a triangle source time function convolved on to the Green s functions. The source time function duration is controlled by the risetime (t r ) parameter, which is one half the total slip duration. These simplifications only allow for the resolution of the overall rupture process and not the details in the rupture of asperities along the fault plane. 4. Independently Estimated Source Parameters [10] Before examining earthquakes using far-regional P waves, we made additional estimates and collected published source parameters from the International Seismological Centre (ISC), Harvard (HRVD) centroid moment tensor (CMT), and National Earthquake Information Center 2of21

3 Figure 1. Station map and 410-km and 670-km discontinuity bounce points for the 1995 west Texas and 1999 Scotty s Junction earthquake. (NEIC) earthquake catalogs. We also made our own independent estimates using regional and teleseismic waveform data (Table 1). These source parameters will provide validation of the far-regional inversion results, which we will expand upon in the discussion section Regional Wave Moment Tensor Inversion [11] One independent estimate of the source parameters was made using the long-period regional wave moment tensor inversion (RMTI) procedure similar to that by Ritsema and Lay [1995] and Pasyanos et al. [1996]. Seismograms recorded within 100 to 1000 km were instrument corrected to displacement and band-passed filtered between 50 and 100 s. Figures 3 (top) and 4 (top) show the complete waveform fits between the data and synthetics. The Green s functions were computed using the reflectivity method with the WUS velocity model [Ichinose et al., 2003] for stations in the tectonically active regions and CUS velocity model [Stewart, 1968] for the relatively stable central United States. Green s functions were computed for 1 km depth increments between 2 and 30 km, and the data were shifted in 1-s increments about the origin time estimated by the ISC or NEIC. We solve for the centroid depth and origin time using a grid search by minimizing the L2 norm objective function while maximizing the doublecouple component. At each iteration, we solve for the deviatoric moment tensor Teleseismic P Wave Dislocation Grid Search [12] The source parameters were also independently estimated using teleseismic P waves [e.g., Langston and Helmberger, 1975]. We perform a dislocation grid search for strike, dip, rake, focal depth, source duration, and seismic moment to find the best fit between data and synthetics for the P waves and depth phases. The Green s functions are computed using the generalized ray theory [Helmberger, 1974] with the AK135 velocity model [Kennett et al., 1995]. The observed teleseismic data were instrument corrected to displacement, filtered between 100 to 1 s and then aligned and windowed along the P wave arrival. Figures 3 (bottom) and 4 (bottom) show the teleseismic P and depth phase waveform fits and a depth resolution curves. We assume a single triangle shaped source time function and estimate the best half duration or risetime in the dislocation grid search. The risetime is 1 s for the west Texas and 0.75 s for Scotty s Junction earthquake. 3of21

4 Figure 2. (top) P wave velocity and attenuation profiles for the AK135 and T7 isotropic and spherical Earth models. (bottom) Enlarged plot at the two major upper mantle discontinuities to better illustrate the differences between the two models. We accounted for anelastic P wave attenuation using nominal t* value of 1 s [e.g., Langston and Helmberger, 1975]. [13] The independently estimated source parameters for the west Texas event, listed in Table 1, are within ±10 of strike, dip, and rake, and within ±0.1 magnitude unit. The depth estimates are on average within 2.6 km of the 17 km depth obtained from regional wave moment tensor inversion. The comparison is somewhat worse for the Scotty s Junction, Nevada, earthquake but all of the solutions consistently indicate that rupture occurred on a dip-slip normal fault oriented in a northeast or southwest direction at a depth between 6 and 10 km. 5. Upper Mantle Velocity Models [14] AK135, also known as IASP91, is an isotropic velocity model built using global P and S wave traveltime observations [Kennett and Engdahl, 1991; Kennett et al., 1995]. Below a depth of 120 km, the model represents a spherical average structure of the Earth and the top 120 km was modified with a primarily average continental structure (Figure 2). Montagner and Kennett [1996] estimated the density and attenuation from the inversion of free oscillations using the AK135 P and S wave velocities as constraints. Burdick and Helmberger [1978] developed the T7 P wave velocity model (Figure 2) for stations in North America using earthquake and explosion sources. They detailed how the model was perturbed from the starting model by trial and error to improve the fit of the synthetics to short-period P waves recorded by WWSSN stations. The main differences between the AK135 and T7 models are shown on Figure 2 (bottom). T7 has a low-velocity zone between 80 and 160 km depth absent in the AK135. The discontinuity, commonly referred to as the 410-km, is shifted from 420 km in AK135 to 390 km in T7. The last major difference of T7 is the gradual gradient of the 660 km 4of21

5 Table 1. Source Parameters a Origin Time, UTC Latitude, deg Longitude, deg Z, km M m b, dyn cm NP1 NP2 f, deg D, deg L, deg f, deg D, deg L, deg PDC RT, s Agency/ Method West Texas 14 April :32: M w % RMTI 17 M w % 1.0 TELEP-GS 00:33: M w % 1.7 HRVD CMT 00:32: M w % USGS 00:32: m b 5.6 NEIC 00:32: M s 5.6 ISC Far-regional P 18 M w % 1.0 FRGS-AK M w % 1.0 FRMTI-AK M w % 1.0 FRGS-T7 18 M w % 1.0 FRMTI-T7 Scotty s Junction 1 August 1999 Independent 16:06: M w % RMTI 10 M w % 0.75 TELEP-GS 16:06: M w % USGS 8 M w % Berkeley-RMTI 16:06: M w % 1.7 HRVD CMT 16:06: M e 5.6 NEIC 16:06: m b 5.5 ISC Far-regional P 8 M w % 0.8 FRGS-AK M w % 0.8 FRMTI-AK135 8 M w % 0.4 FRGS-T7 8 M w % 0.8 FRMTI-T7 Southern Iran 30 April 1999 Independent 04:20: <10 M w % RMTI 45 M w % 1 HRVD CMT 4 M w InSAR 04:20: m b 4.9 ISC Far-regional P 2 M w % 0.2 FRGS/AK135 2 M w % 0.4 FRMTI/AK135 a Fault strike, f; fault dip, d; fault rake, l; seismic moment, M o ; focal depth, Z; body wave magnitude, m b ; surface wave magnitude, M s ; moment magnitude, M w ; RMTI, regional wave moment tensor inversion; TELEP, teleseismic P wave grid search inversion; HRVD CMT, Harvard University centroid moment tensor; USGS, U.S. Geological Survey moment tensor; ISC, International Seismological Centre; NEIC, National Earthquake Information Center; FRGS, far-regional grid search; FRMTI, far-regional moment tensor inversion; InSAR, interferometric satellite aperture radar [Saikia et al., 2003]. discontinuity between 610 and 670 km, which is sharp in AK135 at 660 km. [15] We computed a record section of synthetic seismograms and compared them to MOMA array observations from the west Texas earthquake in order to illustrate the ability of reflectivity method and AK135 to produce realistic P wave synthetics for the far-regional range. The synthesis of complete waveforms by the reflectivity method has been proven to predict regional ground motions for frequencies up to 1 Hz across relatively stable tectonic regions of India [e.g., Saikia, 2000] and eastern Africa [e.g., Langston et al., 2002]. The fits of broadband waveforms in these studies required the use of only relatively simple 1-D crustal models with independently estimated source parameters. Figure 5a shows a record section of instrument corrected velocity seismograms observed for distances between 12 and 27 along the MOMA array from the west Texas earthquake. Figure 5b shows a record section of synthetic velocity seismograms along the MOMA array computed from the AK135 model. We assumed the source parameters estimated from RMTI (Table 1) and convolved a triangle shaped source time function with the synthetics estimated from modeling teleseismic P waves. The traveltime curves for P waves and depth phases, pp and sp, are calculated from AK135 for a focal depth at 17 km. Traveltime curves were computed using the TauP software [Crotwell et al., 1999]. 6. Results 6.1. Test Case Results Dislocation Grid Search Results From Far-Regional P Waves [16] The data were corrected for instrument response to velocity and resampled at 4 samples per second to match the Green s functions. The Green s functions are convolved with a triangle source time function to account for the finite source rupture duration. The L2 norm of the residual vector is used as an objective function to estimate the fit between the data and synthetics. This is applied to a window 10 s before and 20 s after the first arrival for each waveform component. The short window length is set to include only the relevant direct, surface reflected, and triplicated P waves but longer window times would be necessary for deeper 5of21

6 Figure 3. Independent estimates of source parameters for the west Texas earthquake. (top) Moment tensor inversion results from long-period regional waves ( s). We performed an iterative grid search to estimate the origin time and centroid depth. (bottom) Focal mechanism, rupture duration, and focal depth estimated from forward modeling teleseismic P waves and depth phases. earthquakes. Using longer windows for shallow earthquakes would unnecessarily include complex coda waves from crustal structure and degrade the resolution of the source parameters. A pass over the dislocation grid estimates the orientation of one of the two focal mechanism nodal planes by searching strike, dip, and rake in 10 increments. Multiple grids are used to include a range of depths in 2 km increments, a range of risetimes in 0.1 s increments, and a range of seismic moments in increments of 0.1 magnitude units. An additional pass can be made about the best fitting solution using a finer grid spacing Test Case 1: The 1995 West Texas Earthquake [17] Vertical and radial component P waveforms were selected from 24 stations for the inversion of source parameters of the 1995 Texas earthquake. Figure 6 shows the waveform fits at 42 available stations for the west Texas event including the 24 stations used in the inversion. We selected the stations so that the focal sphere was evenly sampled avoiding biases from any one azimuth. The best fitting source parameters are listed in Table 1. The synthetic and observed vertical and radial P waveforms shown in Figure 6 illustrate that the AK135 was adequate in gener- 6of21

7 Figure 4. Independent estimates of source parameters for the Scotty s Junction, Nevada, earthquake (see Figure 2 for details). 7of21

8 Figure 5. Record section of (a) data observed along the MOMA array from the 1995 (M w 5.7) west Texas earthquake for distances between 12 and 27 and (b) synthetic seismograms computed using the Earth-flattened AK135 velocity model. The synthetics are computed assuming the west Texas seismic source estimated using long-period regional wave moment tensor inversion, a 17 km focal depth, and a 2-s duration source time function estimated teleseismic P waves. The traveltimes for P, pp, and sp phases are overlaid. ating Green s functions capable producing the effects of the 410-km and 670-km discontinuities on the P, pp, and sp phase triplications. The most difficult region is between 18 and 22 where both triplications overlap to produce a very complex P coda (see stations NEW, LON, LTY, MM08, and CEH). Outside of this range, the direct P and sp phases dominate. In addition, a reflective phase from either the 410-km or the 670-km discontinuity interferes with the first arrival. There appears to be misfit of the sp and later arriving phases at stations FFC, MM05, EYMN, and SSPA indicating either changes in velocity gradients or changes in the depth of the velocity discontinuities between the central United States compared to the western United States. [18] We show the sensitivity of the solution to changes in the source parameters: strike, dip, rake, and focal depth in Figure 7. The larger size of the focal mechanisms indicates solutions with smaller errors. These plots show that focal depth is well resolved at 18 km. The errors in waveform fits at 18 km are much smaller than at 16 km and there are also significant differences in the focal mechanism solutions between these two focal depths. On closer inspection of the parameter error space at 18 km depth, there are two local minima associated with the strike angles of the two nodal planes shown by the arrows in Figure 7. The dip angles have two minima closely located to each other while the rake angle has a minimum error at 90. The error appears less sensitive to changes in the rake, which has a wider minima than for strike or dip parameter error space. Figure 8 shows the same sensitivity of the focal mechanism solution using the T7 velocity model. The focal depth is resolved to within 16 and 18 km depth although the depth at 16 km provided better waveform fit with little change in focal mechanisms. The use of the T7 velocity model provided comparable solutions to those estimate by AK Test Case 2: The 1999 Scotty s Junction Earthquake [19] For the second test case, we applied the dislocation grid search to the velocity seismograms from the Scotty s Junction earthquake. We selected P waveform data from 12 stations available within the range of 10 30, half of 8of21

9 Figure 6. Broadband far-regional P waves recorded from the 1995 west Texas earthquake. The synthetics were computed using the AK135 velocity model. The source was determined using the dislocation grid search method. Stations used in the inversion are marked with a star. The vertical (Z) and radial (R) observations and synthetics are plotted using the same scale in velocity units. 9of21

10 Figure 6. (continued) the number of stations used for the west Texas earthquake. We performed the same data selection, processing, and inversion procedure as above and obtained a solution listed in Table 1. Figure 9 shows the waveform fits between the data and synthetics obtained from the best solution. All stations fit well except for station SIUC. Again stations around 20 were more complex due to the overlapping triplications (see stations CCM and FFC), while the direct P and sp phases were most dominant outside this range. [20] We show the sensitivity of the solution to changes in the strike, dip, rake, and focal depth shown in Figure 10 for the AK135 velocity model. These source parameters are all well resolved indicated by the range of the focal mechanisms with the smallest errors. The focal depth is resolved between 8 and 10 km although the depth an 8 km has a lower error in the waveform fits. The focal mechanism solutions between these two depths are similar. Inspection of the parameter error space for a focal depth of 8 km indicates that the solution is very sensitive to all the parameters with well-defined global minima for each of the nodal planes shown by the arrows in Figure 10. The sensitivities of the solutions using the T7 model are shown in Figure 11. The focal depth is still well resolved at 8 km although the overall errors are relatively larger than those obtained using the AK135 model Far-Regional P Wave Moment Tensor Inversion Results [21] The same data selection and processing procedures used in the dislocation grid search were followed for the farregional moment tensor inversions (FRMTI). The data were instrument corrected to velocity and the reflectivity method was used to compute the synthetic Green s functions. The focal mechanisms from the moment tensor solutions (see Table 1) for both test cases are within in strike dip and rake but the seismic moments and moment magnitudes tend to be slightly under estimated by a factor of 2 relative to independent estimates. Figure 12 shows L2 norm error versus depth for the west Texas earthquake estimated by iterating the inversion at 2 km depth increments. There is a minimum error at 18 km depth using the AK135 velocity model and 18 km using the T7 velocity model. The solutions obtained are similar to those obtained in the previous section using the dislocation grid search. Figure 13 shows the error for the moment tensor inversion of the Scotty s Junction earthquake at 2 km depth increments. The best fitting depth is 10 km using the AK135 velocity model and 8 km using the T7 velocity model. The focal mechanisms, obtained from the moment tensor inversion and dislocation grid search for the Scotty s Junction earthquake, are rotated in a counterclockwise direction relative to the solution obtained using the AK135 model. The AK135 model also resulted in moment tensor solutions with lower errors although the focal mechanisms and focal depths were not significantly different between the two models. [22] The waveform fits tend to be slightly better in the FRMTI than with the grid search method because of the increase in degrees of freedom in the moment tensor over a purely double couple source. The percent double couple is 94% for the west Texas moment tensor and 94% for the Scotty s Junction moment tensor (Table 1) using the AK135 model. The percent double couples obtained for these two earthquakes using the T7 model are 94% and 48% respectively. The problem with the moment tensor inversion is that 10 of 21

11 Figure 7. Dislocation grid search results from the inversion of far-regional P waves for the 1995 west Texas earthquake using the AK135 velocity model. The solution and relative error sensitivities to the individual source parameters are shown as a grid of focal mechanisms and as a function of fault strike, dip, rake, and focal depth. The sizes of the focal mechanisms are scaled with the normalized error. The focal depths at 16 and 18 km show the solutions with the smallest errors. The arrows indicate the solutions with the global minima. it will map uncertainties into the solution, including those from the velocity structure, errors in the location of the earthquake, complex source effects, and noise. Our preference is to show the percent double couple only as a measure of these uncertainties because there are no indications that either earthquake required a source with nondouble-couple components including compensated linear vector dipole or isotropic components. 7. Applicability to Smaller Magnitude Seismic Events [23] The applicability of this method at lower magnitude events is of great importance in showing the utility of farregional P waves. The problem with smaller magnitude seismic events is that there will be fewer stations and higher noise. We first examined a simple scenario of having a sparse number of stations by removing stations from the data set used in the FRMTI. We then examined an earthquake in southern Iran as a realistic test case to show the utility of inverting far-regional P waves for estimating source parameters. [24] We were able to retrieve a moment tensor and seismic moment of the Scotty s Junction earthquake to within the range of solutions listed in Table 1 with only a single component from station LTX (D = 13.9 ). LTX has a raypath that is near nodal on the P wave radiation pattern. We obtained a strike of 35, dip of 57, rake of 91, and a 11 of 21

12 Figure 8. Same as Figure 7 but for dislocation grid search results using the T7 velocity model. The focal depths at 16 and 18 km show the solutions with the smallest errors. The arrows indicate the solutions with the local minima. seismic moment of dyne cm. The percent double couple was 15% indicating that the uncertainties are very high for any single station. The accuracy of the solution obtained from station LTX could not be reproduced as well for other stations. One reason that LTX fit better is that nodal stations have large variations in P wave amplitudes and polarities making them very sensitive to changes in focal mechanism parameters. Another reason is that LTX was not within the zone of overlapping upper mantle triplications where multiple complex P wave arrivals are observed at epicentral distances of about 16 to 24. [25] Saikia et al. [2003] originally examined the 30 April 1999 earthquake in southern Iran (M w 4.8) as a test case for making ground truth locations using a combination of Interferometric Synthetic Aperture Radar (InSAR) and seismic data (Figure 14). We also use this event as a realistic test case for the applicability of the far-regional P wave inversion at lower magnitudes. This event is an ideal example of the many seismic events in remote locations of the Middle East and Asia with magnitudes that are too small to be recorded at teleseismic distances. However, this particular earthquake was recorded by 5 broadband-instrumented stations within the far-regional range. This earthquake was of additional interest because it generated surface deformation detected by InSAR indicating that it was a very shallow depth earthquake (depth = 4 km) given an approximate fault area dimensions of 2 2 km [Saikia et al., 2003]. They estimated the source parameters independently using long periods recorded by stations RAYN, GNI, and ATD with the RMTI method (Figure 14). These estimates were consistent 12 of 21

13 Figure 9. Broadband far-regional P waves recorded from the 1999 Scotty s Junction earthquake. The synthetics were computed using AK135 velocity model. The source was determined using the dislocation grid search method. The vertical (Z) and radial (R) observations and synthetics are plotted using the same scale in velocity units. All of the P wave arrivals are aligned at 10 s. Note the complexity of the P wave at distances between 20 and 24 relative to distances beyond 30o (see stations SSPA and DWPF) due to the triplications from the 410-km and 670-km discontinuities. with those estimated from the modeling of InSAR data and CMT solutions from HRVD (Table 1). The earthquake has a reverse faulting mechanism with dipping fault planes oriented in a northwest and southeast direction. [26] We then performed a dislocation grid search and moment tensor inversion on the far-regional P wave windows from velocity seismograms recorded at the five stations using the same procedure described for the previous examples. The dislocation grid search results and solution parameter sensitivities are shown in Figure 15 using the AK135 velocity model. The focal depth with the minimum error is at 2 km. There is another local minimum at the focal depth of 6 km but with a higher error relative to the global minimum at a focal depth of 2 km. The best fitting solutions had a focal mechanism with rake angles rotated clockwise by 35 to 45 relative to the focal mechanisms obtained from RMTI and InSAR. The waveform fits using the grid search results are shown in Figure 16. The focal depth for the best fitting moment tensor solution is at 2 km with a double couple component of 36% (Figure 17). The very shallow depths estimated by both inversion methods are consistent with the surface deformation observed by InSAR [e.g., Saikia et al., 2003]. [27] Saikia et al. [2003] note that for the current configuration of the seismic networks, the focal depth between 35 and 45 km for the 1999 southern Iran event was 13 of 21

14 Figure 10. Dislocation grid search results from the inversion of far-regional P waves for the 1999 Scotty s Junction earthquake using the AK135 velocity model. The solution and relative error sensitivities to the individual source parameters are shown as a grid of focal mechanisms and as a function of fault strike, dip, rake, and focal depth. The sizes of the focal mechanisms are scaled with the normalized error. The focal depths at 8 and 10 km show the solutions with the smallest errors. The arrows indicate local minima. incorrectly estimated by the NEIC and ISC (Table 1). Their RMTI results using only a sparse number of long-period regional waves could only resolve the focal depth to within 0 to 10 km. The resolution of the focal depth from the use of broadband far-regional P waves for the 1999 southern Iran earthquake illustrated the important utility of these methodologies down to magnitudes of 4.8. The answer to the question of applicability of the method at even lower magnitudes may depend on the calibration of velocity models to fit higher frequencies. Further work is needed to test and calibrate global velocity models including AK135 to improve the resolution and accuracy of the focal mechanism solutions down to lower magnitudes. 8. Discussion [28] We applied dislocation grid search and moment tensor inversion methods to test the potential of inverting farregional broadband P waves for estimating source parameters. The grid search results using the AK135 model revealed at most two local minima associated with the two nodal planes of the focal mechanism rather than associated with any 14 of 21

15 Figure 11. Same as Figure 10 but for dislocation grid search results using the T7 velocity model. The focal depths at 8 km show the solutions with the smallest errors. The arrows indicate the solutions with the local minima. nonuniqueness in the solution (Figures 7, 10, and 16). The results from the west Texas and Scotty s Junction earthquakes are compared to independent estimates. Figure 18 compares the focal mechanisms and moment tensor solutions from each method and different agencies. If the long-period RMTI solution is considered as a reference solution, then by simple visualization of the focal mechanisms, the far-regional P wave dislocation grid search and FRMTI methods, along with the AK135 velocity model, appear successful in separating out the source effect. Specifically, the strike and dip of the nodal planes were within the scatter of other independent estimates and within 20 in orientation of the RMTI solution. Rake was different by as much as 60 from the RMTI solution for the Scotty s Junction and southern Iran earthquakes using either the AK135 or T7 velocity models. Ichinose et al. [2003] documented average biases of as much as 13 in strike, dip and rake, between RMTI and HRVD CMT focal mechanisms and average biases of as much as 15 between RMTI and P wave first motion focal mechanisms. [29] The grid search results and moment tensor inversions revealed single global minimum error for focal depth. This minimum had a width of about 2 km, the size of the depth sampling increment, indicating that focal depth was well resolved. The focal depths are also estimated within the range of 2 km from independent estimates (Table 1). More importantly, the use of two drastically differently upper mantle velocity models resulted in biases in focal depths that are less than ±2 km, thereby providing a very robust inverse method. [30] Far-regional P waves can be inverted for earthquake source parameters using various standard inversion methods and reasonable velocity models. We attribute this success to 15 of 21

16 Figure 12. Depth-error curves estimated from the far-regional moment tensor inversion for the 1995 west Texas earthquake using the AK135 and T7 velocity models. The best fitting depth and moment tensor is at 18 km depth with the AK135 and T7 models. Figure 13. Depth-error curves estimated from the far-regional moment tensor inversion for the 1999 Scotty s Junction earthquake using the AK135 and T7 velocity models. The best fitting depth and moment tensor is 10 km using the AK135 model and 8 km using the T7 model. 16 of 21

17 Figure 14. (top) Map of seismic stations, which recorded the 1999 earthquake in southern Iran (M w 4.8) from Saikia et al. [2003]. The focal mechanism shows the RMTI inversion result. (bottom) Observed and predicted regional waves filtered to long periods ( s). The filtered seismograms were used to invert for the moment tensor. the use of broadband seismograms and the use of the more accurate reflectivity method to compute synthetic Green s functions. Previous studies used band-limited WWSSN data and generalized ray theory rather than f-k reflectivity technique. The advantage of computational speed far out weighed the need for higher accuracy from more rays and higher frequencies. Higher accuracy is needed in the computation of Green s functions in order to take advantage of the resolution now available from modern broadband waveform data. The ability of far-regional P waves to resolve focal depth is due to the same underlying principle that applies to teleseismic depth phases with the important exception that the complex reflection and refraction interactions with the upper mantle discontinuities need to be included and accurately modeled Velocity Model Uncertainty [31] Up to this point, we have only focused on the ability to estimate and resolve source parameters and neglected the implications toward understanding upper mantle Earth structure. We initially assumed that the AK135 velocity model produces realistic waveforms and reserve detailing its performance for future research. Although this model was not intended for use in specific regions, we were fortunate that it did well in modeling the phase arrival times and absolute amplitudes for upper mantle triplicated phases across North America (see Figures 5, 6, and 9). We have 17 of 21

18 Figure 15. Dislocation grid search results from the inversion of far-regional P waves for the 1999 southern Iran earthquake using the AK135 velocity model. The solution and relative error sensitivities to the individual source parameters are shown as a grid of focal mechanisms and as a function of fault strike, dip, rake, and focal depth. The sizes of the focal mechanisms are scaled with the normalized error. The focal depths at 4 km show the solutions with the smallest errors. The arrows indicate the solutions with the global minima. 18 of 21

19 Figure 16. Vertical component broadband far-regional P wave recorded from the 1999 southern Iran earthquake. The synthetics were computed using the AK135 velocity model. The source was determined using the dislocation grid search method. estimated source parameters using the global AK135 and regional T7 upper mantle velocity models (Figure 4) to show the effect on the focal mechanism and focal depth from the use of incorrect velocity models. Unfortunately, the correct velocity model is unknown but the results here show that AK135 provided a more consistent solution with an improved waveform fit than T7 to the independent solutions used for validation in Table 1. More importantly, the use of two reasonably different upper mantle Earth structures in computing Green s functions for the source inversion will still provide accurate focal depths to within ±2 km as shown by the earlier two test cases. The focal mechanisms appear less accurate or biased with the use of the T7 model therefore calibration may be necessary when there is an indication that the assumed model drastically deviates from the real Earth structure. [32] Burdick and Helmberger [1978] indicated that T7 is more appropriate for long-period far-regional P waves and not for modeling broadband waveforms. One of the major differences between the two velocity models is that T7 has a more gradual velocity gradient across the 410-km and 670-km discontinuities. Recent waveform modeling for the fine structure of the 410-km discontinuity by Vidale et al. [1995] and Melbourne and Helmberger [1998] suggest that the velocity jump is sharp and occurs over a depth range of km. Modeling of the 670-km discontinuity by Walck [1984] suggested that it is also sharp from 620 to 660 km depth. These discontinuity transition thicknesses have implications for the mantle composition [e.g., Gaherty et al., 1999], which can be better improved by the broadband frequency response to the discontinuity s reflectivity Risetime Estimates [33] The interpretation of risetime is difficult not only because of the possible trade-offs with attenuation and seismic moment, but also complications with directivity and rupture propagation effects. These rupture effects are obvious at larger magnitudes but the magnitude at which these effects become negligible is highly variable. Nevertheless, risetimes estimated using far-regional P waves are consistent with those estimated from teleseismic P waves suggesting that this methodology is at least capable of resolving the risetime as well as other methods. Figure 17. Depth-error curves estimated from the far-regional moment tensor inversion for the 1999 southern Iran earthquake using the AK135 and T7 velocity models. The best fitting depth and moment tensor is at 18 km depth with the AK135 and T7 models. 19 of 21

20 equations give risetimes of 1.1 s for west Texas, 0.9 s for Scotty s Junction, and 0.3 s for the southern Iran earthquakes, which are all within 0.1 s of the inverted estimates shown in Table 1. Figure 18. Focal mechanism and moment tensor solutions estimated from independent methods compared to those obtained using far-regional broadband P waves. We used two methods, the GS, dislocation grid search applied to farregional P waves, and FRMTI, far-regional moment tensor inversion methods using both AK135 and T7 velocity models. Other independent estimates are TELE, teleseismic P waveform modeling; USGS, U.S. Geological Survey moment tensor solution; HRVD CMT, Harvard University centroid moment tensor solution; RMTI, regional wave moment tensor solution; InSAR, modeling surface displacements measured from interferometric synthetic aperture radar. [34] We compared risetimes with scaling relations estimated from various strong ground motion studies compiled by Somerville et al. [1999]. In order to predict a risetime for the total rupture process with the assumption of bilateral instead of unilateral rupture, we use the relationships between fault area (A) in km and seismic moment (M o )in dyne cm, A = M o 0.79, and fault area and risetime, t r ¼ 0:5 p ffiffiffi A where v r is the average rupture velocity of 3 km/s. We take the square root of the fault area to for the fault length and multiply this by one half for bilateral ruptures. These v r 9. Conclusions [35] We were successful in extracting focal mechanism and depth from broadband P waves recorded from shallow earthquakes (M w ) between distances of 10 and 30 with a large and small number of stations. Most success in modeling far-regional seismograms has been with WWSSN long-period P wave seismograms [e.g., Helmberger, 1973; Burdick and Helmberger, 1978; LeFevre and Helmberger, 1989] and the study of modern broadband and short-period waveforms have been limited to modeling only primary rays [e.g., Goldstein et al., 1992; Garnero et al., 1992; Vidale et al., 1995; Melbourne and Helmberger, 1998]. We used the reflectivity method, which retains all of the rays to compute synthetic Green s functions up to 2 Hz. We used an Earthflattened global AK135 velocity model, which generates realistic P wave ground motions within this distance range. We also used the regional T7 upper mantle velocity model to examine the variation of solutions using different models. [36] We applied both grid search and moment tensor inversion methods for far-regional broadband P waves generated by the 1995 west Texas and 1999 Scotty s Junction, Nevada, earthquakes. These two earthquakes were selected as test cases because they were well recorded and had independently established source parameters. These source parameters were used to validate the inversion results. Vertical and radial component digital records were included in both inverse procedures. These records were corrected for instrument response and converted to velocity, preserving the absolute amplitudes and frequencies between approximately 100 s and 2 Hz. The solution obtained for the west Texas and Nevada events were within of the RMTI solution and within the scatter of other independent solutions (Table 1). We also examined the applicability of the method at lower magnitudes. We applied dislocation grid search and FRMTI methods on a more realistic test case for an M w 4.8 earthquake remotely located in southern Iran. The solution sensitivities indicated that the focal depth is well resolved but that the focal mechanism is biased in rake angle compared to independent estimates. [37] Far-regional P waves are useful in estimating focal mechanism and focal depth. The focal depth was well resolved and accurately estimated to within ±2 km with use of two different velocity models. This illustrates the potential of these methods to estimate focal depth across different tectonic environments similar to the utilization of teleseismic depth phase. [38] Acknowledgments. This study was partially funded by the Defense Threat Reduction Agency grant DTRA01-01-C We thank three anonymous reviewers for help in improving the manuscript. The Berkeley Seismological Laboratory at the University of California Berkeley provided BDSN broadband waveform data. The facilities of the Incorporated Research Institutions for Seismology data management system and specifically the data management center were used for access to waveform data required for this study. We obtained source parameter information from the International Seismological Centre (online bulletin, 2001, Plots were made using GMT plotting software [Wessel and Smith, 1991]. 20 of 21

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