Mach wave properties in the presence of source and medium heterogeneity

Transcription

1 Mach wave properties in the presence of source and medium heterogeneity Journal: Manuscript ID GJI-S--0 Manuscript Type: Research Paper Date Submitted by the Author: 0-Aug-0 Complete List of Authors: Vyas, Jagdish; King Abdullah University of Science and Technology, ErSE Mai, Martin; King Abdullah University of Science & Technology, Physical Sciences & Engineering Galis, Martin; KAUST, Division of Physical Sciences and Engineering Dunham, Eric; Stanford University, Geophysics Department Imperatori, Walter; ETH Zurich, SED Keywords: Theoretical seismology < SEISMOLOGY, Earthquake ground motions < SEISMOLOGY, Coda waves < SEISMOLOGY, Computational seismology < SEISMOLOGY

2 Page of Mach wave properties in the presence of source and medium heterogeneity J. C. Vyas, P. M. Mai, M. Galis, Eric M. Dunham, and W. Imperatori King Abdullah University of Science and Technology, Stanford University, Swiss Seismological Service, ETH Zurich Jagdish.Vyas@kaust.edu.sa Summary We investigate Mach wave coherence for kinematic supershear ruptures with spatially heterogeneous source parameters embedded in D scattering media. We assess the Mach wave coherence considering: ) source heterogeneities in terms of variations in slip, rise time and rupture speed; ) smallscale heterogeneities in Earth structure, parameterized from combinations of three correlation lengths and two standard deviations for fixed Hurst exponent in a von Karman power spectral density; and ) joint effects of source and medium heterogeneities. Ground-motion simulations are conducted using a generalized finite-difference method, choosing a parameterization such that the highest resolved frequency is ~ Hz. We discover that Mach wave coherence is diminished at near fault distances (< 0 km) due to spatially variable rise time; beyond this distance the Mach wave coherence is more strongly reduced by wavefield scattering due to small-scale heterogeneities in Earth structure. Based on our numerical simulations and theoretical considerations we demonstrate that the standard deviation of medium heterogeneities controls the wavefield scattering in case of small Hurst exponent, rather than the correlation length. In addition, we find that peak ground accelerations in the case of combined source and medium heterogeneities are consistent with empirical ground motion prediction equations for all distances, suggesting that observed ground shaking amplitudes for supershear ruptures may not be elevated due to complexities in the rupture process and seismic wave-scattering.

3 Page of Key words: Mach wave; Kinematic rupture; D scattering media; Ground motion prediction equations. Introduction Seismological studies for crustal earthquakes report that the rupture front typically propagates at ~0% of the shear-wave speed (e.g. Heaton, 0; Mai and Thingbaijam, 0). However, the rupture speed may exceed the shear wave speed, as shown by theoretical and observational studies. For example, by analyzing strong motion records, it was shown that for the M W. Imperial Valley, California, earthquake (Olson and Apsel, ; Archuleta, ), the M W. Izmit and M W. Duzce, Turkey, earthquakes (Bouchon et al., 00), and the 00 M W. Denali Fault, Alaska, earthquake (Ellsworth et. al., 00; Aagaard and Heaton, 00; Dunham and Archuleta, 00) that the rupture locally propagated faster than the shear-wave speed (Vs). The analysis of seismic waveforms recorded at regional (< 000 km) or teleseismic distances demonstrated that the 00 M W. Kunlun, Tibet, earthquake (Walker and Shearer, 00; Vallee and Dunham, 0) and the 0 M W. Craig, Alaska, earthquake (Yue et. al., 0) also showed supershear rupture speed over parts of the fault plane. Both strong motion and teleseismic records suggest that the 00 M W. Qinghai, China, earthquake may have propagated at supershear speed (Wang and Mori, 0). Therefore, the seismic waveforms recorded in the near-field as well as at far-field distances from different earthquakes provide evidence for the existence of supershear ruptures. Andrews () has analytically shown that crack tip travelling at supershear speed will create a slip velocity pulse with lower high-frequency content compared to sub-rayleigh case. Ellsworth et al. (00) suggested that this might explain the observed deficiency of high frequencies in the ground acceleration, relative to expectations from empirical ground motion prediction equations (GMPEs), for a very-near-fault station (Pump Station 0) that recorded the 00 Denali Fault earthquake. However, other studies found that supershear ruptures create Mach cones with enhanced high frequencies (Bernard and

4 Page of Baumont, 00; Dunham and Archuleta, 00). The study by Bizzarri and Spudich (00) confirmed that a crack tip propagating at supershear speed creates a slip velocity function with reduced high-frequency content compared to the sub-rayleigh case. However, they also demonstrate that Mach cone amplification of high frequencies overwhelms the reduction of high-frequency content in slip velocity for supershear ruptures, leading to a net enhancement of high frequencies for supershear ruptures. The theoretical and numerical studies predict larger ground-motion amplitude and higher frequency content for supershear ruptures. Furthermore, Dunham and Bhat (00) show that supershear ruptures radiate both shear and Rayleigh Mach waves that transmit large amplitude of ground motions even to large distances from the fault. Andrews (00) analyzed ground velocities from sub-rayleigh and supershear events for D models with same fracture energy and stress drop. The directivity beam generated in the sub-rayleigh case is concentrated in a narrow azimuth range around the fault having intense peak velocity, but attenuates as the beam diverges with increasing distance from the fault. The Mach wave originated from supershear ruptures forms a beam of parallel rays with constant amplitudes out to greater distances, and attenuates due to diffraction and scattering. In addition to the above findings, Bizzarri et al. (00) studied the effects of heterogeneous rupture propagation on shear and Rayleigh Mach wave coherence for supershear ruptures on a vertical planar fault embedded in a homogeneous medium. They found that heterogeneous rupture propagation reduces peak ground velocity, but the shear and Rayleigh Mach waves generated by supershear ruptures transmit larger ground motion much farther from the fault compared to sub-rayleigh ruptures. They utilized strong motion records from three supershear earthquakes to validate their numerical modeling results, investigating spectral acceleration (SA) at stations that presumably experienced Mach waves during the Imperial Valley, Izmit, and 00 Denali Fault earthquakes. Comparing to SA observed at non-mach-pulse stations for the same earthquake, they found no average elevation of spectral acceleration relative to ground motion prediction equations. This difference could arise either from the sparsity of the data (i.e., supershear ruptures do have larger ground motions, on average, but the few

5 Page of records are by chance biased toward lower ground motions) or there are additional processes that reduce ground motions from supershear ruptures (e.g., loss of Mach front coherence by additional source complexity and/or scattering along the wave propagation path). The purpose of this study is to investigate the discrepancy between observations and previous simulations through a set of simulations that explicitly take into account small-scale heterogeneities and the resulting wave scattering. Mach-wave observations are still rare in seismology. Either, Mach waves are generally not excited, because super-shear rupture propagation only infrequently occurs, or Mach-wave signatures are lost due to seismic-wave propagation effects. Heterogeneities present in the Earth s crust scatter seismic waves, and their impact on ground-motion have been subject of several numerical studies (Frankel and Clayton, ; Frenje and Julin, 000; Pitarka and Ichinose, 00; Hartzell et al., 00; Imperatori and Mai, 0; Bydlon and Dunham, 0). The effects of seismic scattering are more pronounced on S- waves than P-waves, and mainly distort the S-wave radiation pattern at frequencies above Hz (Pitarka and Ichinose, 00; Takemura et al., 00). The numerical simulations show substantial influence of medium heterogeneities on ground velocities (Hartzell et al., 00) and ground accelerations (Imperatori and Mai, 0). Moreover, scattering extends the duration of incoherent high frequency ground-motion and increases the root-mean-square acceleration, at least in D (Bydlon and Dunham, 0). However, these previous studies focused exclusively on sub-rayleigh ruptures, so do not directly inform the present investigation of ground motion radiated by supershear ruptures. To analyze the effects of medium heterogeneity and rupture complexity on Mach wavefront properties, we conduct a set of numerical experiments. We hypothesize that random heterogeneities in Earth structure and rupture complexities diminish or even destroy the coherence of Mach-waves and reduce their high frequency content. We perform ground-motion simulations using kinematic earthquake sources with specified spatio-temporal rupture evolution. The seismic wavefield is computed using a D finite-difference method. Wavefield signatures as well as ground-motion parameters are then analyzed with respect to Mach wave effects.

6 Page of The sections of the paper are organized as follows. First, we describe the computational model geometry and analyze the effects of source heterogeneities on Mach-wave properties. Next, we present the effects of medium heterogeneities on the seismic wavefield. Finally, we study the combined effects of source and medium heterogeneities on Mach wave. Model geometry and computational method The section describes the source and medium used as the reference case, receiver geometry, and numerical method employed to compute ground-motions.. Source model description We consider a 0 km long and km wide fault, and use a kinematic source description that specifies the spatio-temporal evolution of slip in terms of a discrete set of point moment tensor sources. The heterogeneous slip distribution (D) is characterized by a von Karman autocorrelation function (Mai and Beroza, 00), parameterized by correlation lengths in the along-strike (a x = 0 km) and down-dip (a z = km) directions, and Hurst exponent (H = 0.). Spatial variations in rise time (Tr) are generated assuming a correlation with slip, similar to previous studies (e.g., Schmedes et al., 00; Graves and Pitarka, 00). We also correlate rupture speed (Vr) variations with slip, based on the observation that ruptures propagate faster over fault areas of large slip (e.g., Oglesby and Day, 00; Guatteri et al., 00; Graves and Pitarka, 00). In the case of earthquakes with supershear rupture speed, the rupture front initially propagates at a sub-rayleigh velocity, but then transitions to supershear speed. Therefore, we assume that a sub-rayleigh rupture front arrives from some distance, and then transitions to super-shear speed propagation on the fault area of interest (0 km x km). Correspondingly, rupture onset times delineate an almost vertical rupture front (Figure -a). Since variations in rupture speed are correlated

7 Page of with the underlying heterogeneous slip model, the rupture-front contours are advanced over high-slip areas and delayed over zones of lower slip. Rupture speed variations over the fault plane range from.vs to.vs. The location of minimum rupture onset time denotes the hypocenter (black star, Figure -a). The heterogeneous slip model on the fault creates a seismic moment of. 0 Nm (Mw =.). Slip values range from 0. m -.0 m, and rise time from.0 s -. s. The temporal slip-rate evolution at each source point is described by the regularized Yoffe function (Tinti et al., 00) with fixed acceleration time (τ acc = 0. s). Strike and dip are 0, and the rake is uniformly set to 0 (left-lateral strike-slip). We then generate seven source models by combining heterogeneous and uniform rupture parameters (Table ), in which the uniform values are chosen as the corresponding average slip (. m) rise time (.0 s), and rupture speed (.Vs). We refer to the models using their heterogeneous parameters, e.g., H Vr denotes the model with heterogeneous (H) rupture speed (Vr), but uniform slip and rise time. Similarly, H DTr indicates heterogeneous slip (D) and rise time (Tr), but uniform rupture speed. The model with all parameters being heterogeneous is designated as H DTrVr. We also define a reference rupture model with uniform parameters (U DTrVr) with slightly increased rupture speed (.Vs). The final moment rate functions for the reference model and the heterogeneous source H DTrVr are thus comparable (Figure -b).. Receiver geometry and reference medium Supershear ruptures generate a planar Mach wave that is radiated off the fault at an angle θ (Bizzarri et al., 00): θ = sin ( Vs ). () Vr Using Eq., we compute the spatial limits in which the Mach waves travel for two different rupture speeds (Figure c; average Vr =.Vs for H DTrVr, and Vr =.Vs for U DTrVr). For our analysis, we

8 Page of examine simulated ground-motions at lines of receivers within the theoretical Mach region boundaries (Figure c), but ignore stations at the right end of these boundaries as they are affected by stopping phases. Receivers are spaced at 0. km in fault-parallel and km in fault-normal directions. Five additional locations (s to s, Fig. c) are used to investigate waveform differences for receivers inside and outside the Mach boundaries.. Computation of synthetic seismograms We use the Support Operator Rupture Dynamics (SORD) code, which is based on second-order accurate (in space and time) generalized finite-difference solver of the elastodynamic equations (Ely et al., 00). The reference medium is a homogenous half-space with uniform S-wave speed ( m/s), P- wave speed (000 m/s), and density (00 kg/m ), to which random velocity and density perturbations are added for studying scattering effects (Section ). The kinematic source is embedded as a point-cloud of local slip-rate functions over the designated rupture area. We use -points for the shortest wavelengths at a grid spacing of dx = 0 m, hence the maximum resolved frequency is Hz. The corresponding computational time step (dt = 0.00 s) is obtained by satisfying the numerical stability criteria (e.g., Ely et al., 00). Intrinsic attenuation ( Q ) is neglected in our simulations. Synthetic seismograms are lowpass filtered (using a fourth-order Butterworth filter) at f max = Hz to remove spurious numerical oscillations. Effect of heterogeneous source parameters Let us investigate the simulated ground motions with Mach front signatures for the heterogeneous source models, and compare those to waveforms for the uniform reference source. These eight

9 Page of simulations are run using the homogeneous medium and identical receiver geometry to focus on source effects only.. Synthetic seismograms and wavefield snapshots Figure compares fault parallel (FP), fault normal (FN), and vertical (Ver) components of ground acceleration for source H Tr and the reference source U DTrVr at stations s - s (Fig. c; recall that s, s and s are within the Mach boundary, s and s are outside). Sites s and s clearly show the S-Machwave and Rayleigh-Mach-wave, while at site s there is no clear separation between the two Mach waves. The Rayleigh-Mach-wave is most strongly developed on the Ver component, while the S Mach wave is only expressed on the horizontal components. Mach waves from U DTrVr arrive earlier than those from H Tr due to faster rupture speed of the uniform rupture model. The overall horizontal-component Mach-wave amplitudes from H Tr are smaller than from U DTrVr, especially close to the fault (sites s and s), illustrating the effects of rise time heterogeneities. The longer rise times on the fault close to the Earth surface reduce peak slip-velocity for fixed τ acc and given slip, leading to reduced ground-motion amplitudes for H Tr. For both sources, site s shows significantly lower ground acceleration than site s (~ times on the FN, and ~ times on the Vercomponent), although s is closer to the fault than s. The ground-velocity amplitudes for sources H Tr and U DTrVr at these two sites show similar characteristics (Figure S), indicating larger ground-motions for locations inside the Mach boundaries than outside. Figure displays snapshots of ground acceleration for source models U DTrVr and H Tr, illustrating the planar Mach waves due to supershear rupture propagation and a strong stopping phase from sudden rupture arrest at the right fault edge (nicely seen on FP at s and beyond). The FP and FN components

10 Page of both show the S-Mach-wave and Rayleigh-Mach-wave, while the Ver component only contains the Rayleigh-Mach-wave. Mach-wave amplitudes almost remain unchanged as the waves propagate, even at larger distance from the fault due to their planar nature (perfect planar in D and more complex in D). The wavefield of ground velocity exhibits similar Mach-wave characteristics as the acceleration wavefield (Figure S); for both sources, Mach waves travel large distances without significant attenuation. However, Mach wave velocity/acceleration amplitudes are smaller for model H Tr than for the reference source U DTrVr.. Peak ground acceleration (PGA) To further quantify ground-motion characteristics due to the effects of source complexity on Mach wave coherence, we calculate peak ground acceleration (PGA) as the maximum magnitude of the two horizontal components, and GMRotD0 (Boore et al., 00; calculated by stepwise rotating the two orthogonal horizontal components by increments from to 0, computing the geometric mean for each pair, and taking PGA as the median of 0 geometric means). Examining the mean and standard deviation of PGA at all stations at some given fault-perpendicular distance (Fig c), we observe that the mean PGA computed from the maximum magnitude of horizontal components (henceforth PGA MaxM) is larger than mean PGA computed as GMRotD0 (PGA GMrot); however, the overall trends are consistent (compare Fig. and Fig S). Figure compares PGA GMrot values for the eight source models as a function of distance, showing also the PGA-estimates using the GMPE of Boore and Atkinson (henceforth BA00). The mean PGA GMrot values computed using eight sources fall outside the -sigma bounds of BA00 at

11 Page 0 of distances of 0 km and beyond. However, at a distance of km the PGA estimates from the GMPE and our simulations are comparable. The overprediction of the simulated PGA GMrot values at the larger distances is likely due to the omission of both intrinsic attenuation and scattering in these simulations. Figure reveals that the mean PGA GMrot for U DTrVr remains almost constant with distance, because the planar Mach wave has negligible attenuation over the modeled distances. The mean PGA GMrot for H D, H Vr, H DTr, and H TrVr are close to those of the reference model. Source models with heterogeneous slip and rupture speed (H DVr and H DTrVr) generate higher mean PGA GMrot, compared to the reference model, which is already evident in the corresponding wavefield snapshots (compare Figure S with Figure ). H Tr has lower (~%) mean PGA GMrot values compared to U DTrVr due to longer rise times on the near-surface parts of the fault, reducing peak slip velocity and peak slip acceleration for fixed τ acc. This is due to the sensitivity of the Mach wave observed at the surface to the near-surface part of the fault in case of vertical rupture front. The correlation between rupture parameters also influences PGA GMrot; e.g. for H DTr, the larger slip near the surface increases PGA GMrot, whereas longer rise time near the surface lowers them, resulting in net ground-motions comparable to U DTrVr. In general, we observe that the source rise time heterogeneities can lower the PGA values from supershear ruptures in near-fault distances ( 0 km).. Average Fourier Acceleration (AFA) To investigate the spectral characteristics of the seismic wavefield, we calculate Fourier spectra of unfiltered acceleration time series at each site. We then compute the average Fourier acceleration (AFA) as the mean of the spectra for multiple sites at a given distance from the fault. Figure compares AFA for the FP- and FN-components for all eight sources. The AFA obtained for H D, H Vr, H DTr, and H TrVr 0

12 Page of are very close to the reference case; for H Tr, the AFA is lower compared to U DTrVr for all distances. Rupture models with heterogeneous slip and rupture speed (H DVr and H DTrVr) lead to higher AFA than the reference model. In agreement with our previous observations, model H Tr, with rise time heterogeneity has the lowest AFA. Effects of scattering medium In this section we investigate the effects of seismic scattering on Mach-wave characteristics by computing the seismic wavefield for U DTrVr embedded into realizations of heterogeneous D Earth media. The resulting ground-motions are analyzed analogous to the homogeneous-medium case.. Realization of D random media Small-scale heterogeneities in Earth structure cause seismic scattering that leads to wave-front distortion, redistribution of wave energy, and pronounced changes of seismic waveforms. Frankel and Clayton () studied scattering of elastic and acoustic waves in D random media characterized by variations in seismic wave speeds. They considered three different correlation functions (Gaussian, exponential, and self-similar von Karman), and observed that D self-similar random media with % velocity fluctuations and correlation lengths of 0 km (or greater) may explain travel-time anomalies across seismic arrays and the coda waves of micro earthquakes. Ritter et al. () analyzed teleseismic P-wave recordings to determine scattering-media parameters of the lithosphere. For their study region

13 Page of (central France), they proposed a model of the lithosphere as a heterogeneous layer of 0 km thickness with correlations lengths of km and velocity fluctuations of %. These values are in agreement with Rothert and Ritter (000) who determine the small-scale heterogeneous structure of the upper lithosphere beneath the Grafenberg array, Germany, and find wave-speed perturbations of % and correlation lengths of 0.. km. We introduce small-scale heterogeneities in our homogeneous background model by adding a spatial random field, characterized by an isotropic von Karman autocorrelation function, following the approach of Imperatori and Mai (0). The power spectral density of the von Karman function is described as, p(k) = σ ( πa) Γ(H +.) Γ(H) ( + k a () )(H+.) where a, H, σ, k, and Γ are correlation length, Hurst exponent, standard deviation, wave number, and the Gamma function respectively. We generate six realizations of the D random field using three correlation lengths (.0 km,.0 km, 0. km), and two standard deviations (%, 0%) for fixed Hurst exponent (H = 0.). The choice of these parameters values is motivated by data analysis using borehole logs and seismic reflection data (e.g., Dolan and Bean ; Bean et. al., ). The six realizations of randomized D Earth models (having variations in velocity as well as density) are referred to as M to M (Table ), shown in terms of surface slices of S-wave speed to illustrate the effects of different correlation lengths and standard deviations (Figure ). We place the reference source U DTrVr in six different random media, and conduct ground motion simulations for the same receiver geometry as before. Due to regions of lower shear-wave speeds in these

14 Page of random-media realizations, we have to reduce the spatial grid size to dx = m, and the computational time steps to dt = 0.00 s and dt = 0.00 s for media with standard deviations of % and 0%, respectively.. Synthetic seismograms and wavefield snapshots Figure compares FP, FN, and Ver components of ground acceleration at sites s to s (Fig c) for M (a =.0 km, σ = %) and M (a =.0 km, σ = 0%) with the homogeneous-medium case, using the uniform source model. S-wave Mach amplitudes at station s on the FP and FN components are smaller for M than for the homogeneous medium. As the S-Mach waves propagate away from the fault, amplitudes are further reduced for M compared to the homogeneous medium due to the cumulative effects of seismic scattering. The S-Mach wave amplitudes at sites s and s for M are comparable to scattered-wavefield amplitudes arriving after the S-Mach wave, suggesting that medium scattering may potentially obfuscate Mach-wave detection in real earthquakes. Scattering of the S-wave Mach waves is stronger for M than for M, due to the higher standard deviation of the random wave-speed fluctuations. Sites outside the Mach boundaries (s and s) also experience larger scattering for M than M. Rayleigh-Mach-waves on the Ver components of s and s have comparable amplitudes for all three media, but have smaller amplitude at site s for media M and M compared to the homogeneous medium. Ground-motion velocities at the five stations s to s for media M and M exhibit generally similar scattering effects as seen in ground acceleration (Figure S). In general, Mach-wave amplitudes are reduced in media with small-scale random heterogeneities (especially for σ = 0%), compared to the homogeneous medium, since the elastic scattering redistributes the wave energy in space and time.

15 Page of Figure shows snapshots of ground-motion acceleration at different times for media M (a =.0 km, σ = %) and M (a =.0 km, σ = 0%). The corresponding snapshots of ground velocity are provided in Figure S, but the seismic scattering is more prominently visible in the acceleration wavefield. As the Mach wave travels away from the fault, its amplitude decreases and its coherence is reduced. In fact, the scattering effects are so strong for M that the plane-wave structure of the Mach wave is difficult to identify after s and beyond. In addition, the amplitudes of the scattered wavefield and the Mach wave become comparable (as seen already on seismograms s to s).. Peak ground acceleration (PGA) Following our previous approach, we quantify the effects of seismic scattering in heterogeneous media using PGA GMrot values as a ground-motion intensity measure, noting that PGA MaxM yields larger mean PGA than PGA GMrot also for heterogeneous media (compare Figure with Figure S), in agreement with our earlier observation. Figure displays PGA GMrot values for the six scattering media M-M and the homogeneous medium for simulations with the uniform source model; PGA GMrot computed using BA00 facilitates the comparison. As our simulations are elastic, the mismatch between GMPE-estimates and simulations can partially be attributed to the absence of intrinsic attenuation in our simulations. Mean PGA GMrot values for M and M (σ = %) are near or just outside the -sigma bound of BA00 for all distances, while mean PGA GMrot for M and M (σ = 0%) are within the -sigma bound of BA00. For distances larger ~0 km, mean PGA GMrot values from BA00 and our simulations begin to converge. The standard deviation of medium heterogeneities seems to control the seismic scattering rather than correlation length for small H ( 0.), The correlation length of 0. km for media M and M is smaller than the minimum physical

16 Page of wavelength corresponding to background homogeneous medium (./ ~ 0. km) leading to very weak scattering of the Mach wave. In summary, we find that seismic scattering due to small-scale random heterogeneities in the Earth destroys the coherence of Mach waves, and thus complicates their observation in nature.. Average Fourier Acceleration (AFA) Let us examine the spectral characteristic of scattered Mach waves by comparing AFA spectra computed as mean amplitude spectra for stations at a given distance from the fault. Figure 0 depicts AFA spectra as a function of frequency for the horizontal components of motion for the homogeneous and six heterogeneous media. All AFA spectra are similar, on both components, at km distance, showing that scattering is relatively unimportant at these close distances. With increasing distance, AFA spectra for scattering media decrease more rapidly than for the homogeneous medium, at all frequencies above Hz, due to the cumulative nature of scattering effects. We also observe that AFA spectra for M, M, and M (σ = 0%) decrease more rapidly than for M, M, and M (σ = %), indicating that seismic scattering is controlled by the standard deviation of the velocity fluctuations. Effects of combined source and medium heterogeneities The Mach wave coherence is affected by rise time heterogeneities at close fault distances (< 0 km), whereas the influence of seismic scattering becomes dominant beyond certain distances (> 0 km). Now, we combine both source and medium heterogeneities to examine their overall effects on the Mach

17 Page of wave. We place H Tr source in random medium M due to its strongest impact on Mach waves as discussed in sections and. Then, we analyze the synthetic ground-motions at several receivers.. Synthetic seismograms and wavefield snapshots Figure compares FP, FN, and Ver components of ground acceleration from H Tr in M to U DTrVr in a homogeneous-medium at locations s-s. The S-Mach wave amplitudes on FP and FN at s are now even smaller, because of the combined source and medium heterogeneities, compared to considering each case individually (compare Fig. with Figs. and ). The Rayleigh-Mach wave amplitudes on the Ver component are lower for H Tr in M than in the reference case at station s, but are comparable at sites s and s. Therefore, they are mostly affected by medium heterogeneities, while the source heterogeneities have smaller effects. The particle velocities are also lower at stations s, s, and s for H Tr in M than in the reference case (electronic supplement, Figure S). The FP, FN, and Ver components of ground-acceleration (Figure ) and ground velocity (electronic supplement, Figure S) are displayed for H Tr in M. The scattering effects are more prominent in the acceleration wavefield compared to velocity wavefield. Nevertheless, the planar structure of the Mach pulse is harder to recognize in acceleration/velocity snapshots at s and beyond.. Peak ground acceleration (PGA) We apply the same approach as before and compute PGA GMrot to examine the effects of combined source and medium heterogeneities, which yields smaller mean PGA GMrot than PGA MaxM (compare Figure with Figure S0), consistent with earlier observations (in the sections. and.). Figure compares PGA GMrot values from H Tr in M for four rupture speeds (Vr =., 0., 0., 0. Vs; one supershear and three subshear scenarios; denoted using numbers to respectively, e.g. H Tr

18 Page of is H Tr having Vr = 0. Vs) to U DTrVr in the homogeneous medium. The PGA GMrot from BA00 are plotted to facilitate comparisons. Recall that the GMPEs are derived using records from many earthquakes, most of which are subshear ruptures. Therefore, the ground-motions computed using subshear scenarios are expected to better match with BA00 than the supershear scenarios. The mean PGA values from H Tr in M are close to BA00, whereas those from U DTrVr in the homogeneous medium remain significantly higher. The physical explanation is the presence of source effects in the near-field (< 0 km), while medium scattering effects are dominant only beyond a certain distance (> 0 km), leading to overall diminished Mach wave amplitude at all distances. Additionally, the PGA at stations s and s (which are outside the theoretical Mach cone boundary) for H Tr in M are within the one-sigma bounds of BA00, indicating that our choices for source and medium parameterizations are reasonable. The mean PGAs from H Tr and H Tr in M are also within the one-sigma bounds of BA00, while estimates for H Tr in M are outside. Due to directivity effects, especially the FN component of ground acceleration for H Tr and H Tr in M show large amplitudes in the forward direction (Figure S). The directivity pulse is seen by receivers at km distance, where mean PGAs from H Tr in M are comparable to BA00, while H Tr in M overpredicts the shaking levels (Figures and Figure S). Overall we find that for scenarios with combined source and medium heterogeneities, the Mach wave coherence is strongly reduced, which in turn leads to the effect that PGA-levels are not elevated when compared to a GMPE. Therefore, source and medium complexity destroy the theoretically expected stronger shaking for supershear ruptures.. Average Fourier Acceleration (AFA)

19 Page of Figure illustrates the AFA for FP and FN components of ground acceleration for H Tr,,, (Vr =., 0., 0., 0. Vs) in M and U DTrVr in the homogeneous medium. The AFA for H Tr in M is close to U DTrVr at km distance. The source effects are masked by medium scattering already at km distance; otherwise, lower AFA is expected due to rise time heterogeneities as previously found for H Tr in the homogeneous medium (see Figure ). The AFA decreases with increasing distance for H Tr in M faster than the reference case beyond Hz, but the decline from combined source and medium heterogeneities is comparable to what is seen in the case of medium heterogeneities only (compare Figure with Figure 0). At km (and beyond), the AFA from H Tr in M approaches H Tr in M. Overall, we find that heterogeneities in source and medium collectively lead to lowered AFA from supershear ruptures within the Mach cone region. Discussion The ground-shaking computed by considering variations only in source parameters illustrate that rise time variability can lower the Mach wave coherence in near fault distances (< 0 km). Bizzarri et al. (00) investigated the effects of rupture complexity, arising from heterogeneities in initial shear stress in their dynamic source models, on Mach waves. They observed reduced peak ground velocity (PGV) due to variations of rupture speed and spatially less correlated slip velocity time histories, but the PGV decrease was not significant. However, we notice nearly % decrease of PGA (using H Tr) in close distances to the fault (< 0 km). The differences could be because of large slip-weakening distances used in their simulations, which may weaken the effects of stress heterogeneities. Their Fourier amplitude spectrum ratio between homogeneous and heterogeneous supershear rupture is nearly one. In contrast, we find a decline of the average Fourier amplitudes for H Tr compared to U DTrVr, indicating a significant effect of source complexity on the spectral ratios.

20 Page of The Mach wave coherence beyond 0 km distance is reduced due to wavefield scattering from small-scale heterogeneities in the Earth. Bydlon and Dunham (0) show that seismic scattering increases the duration of incoherent high frequencies, and hence elevates the root-mean-square acceleration, at least in D. However, the Mach pulse is an extremely coherent high-frequency seismic wave, therefore, scattering lowers the PGA by redistributing the frequencies in the entire D medium. Imperatori and Mai (0) observe PGA decrease with increasing epicentral distance as a result of wavefield scattering for sub-rayleigh ruptures. This supports our finding of medium scattering being responsible for the decline of Mach front coherence at large distances for supershear ruptures. Ground-shaking levels in terms of PGA from supershear ruptures (in the Mach cone region) with both medium and source heterogeneities are in overall agreement with BA00. The GMPEs inherently have intrinsic attenuation, whereas our simulations are elastic; incorporating anelastic attenuation will slightly reduce the shaking levels. Our findings explain the observation of Bizzarri et al. (00) that spectral accelerations (SA) were not elevated at stations that experienced Mach waves, compared to stations unaffected by the Mach pulse, during the Imperial Valley, Izmit, and 00 Denali Fault earthquakes. Our simulations are kinematic, in order to be able to precisely control the rupture complexity and the occurrence and spatial extent of supershear propagation. Thus, we do not attempt to study the precise processes of when and why supershear rupture happens. This is achieved by means of dynamic simulations with large-scale fault segmentation and/or small-scale fault roughness, which may provide more insight into rupture heterogeneity and ground-motion complexity from supershear earthquakes. Fault segmentation may control rupture nucleation, rupture arrest, and the seismic moment release for sub-rayleigh speeds (Oglesby and Mai, 0; Aochi and Ulrich, 0). Fault roughness causes localized acceleration/deceleration of the rupture front due to local stress perturbations leading to high frequency radiation (Madariaga, ) that is important for engineering purposes and seismic-hazard estimation. Therefore, dynamic simulations with realistic variations in initial stress, friction on the fault, off-fault

21 Page 0 of plasticity, D medium heterogeneities, non-planar fault geometry, and fault roughness are needed to gain a deeper understanding the Mach wave coherence and resulting ground-shaking properties. Conclusions Ground-motion simulations reveal that the Mach wave coherence is diminished in the near-field (< 0 km) by spatial variations of rise time, while wavefield scattering reduces coherence at larger distances (> 0 km). Theory predicts larger ground-motion amplitudes and higher frequency content for supershear than sub-rayleigh ruptures, whereas PGAs from our simulations (H Tr, H Tr and H Tr in M) are almost consistent with BA00 for both kind of ruptures. We speculate that local supershear ruptures might be more common in nature than reported, but not easily detectable due to wavefield scattering and rupture complexity. Acknowledgements The research presented in this article is supported by King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia, grants BAS//-0-0 and AEA Earthquake rupture and ground-motion simulations have been carried out using the KAUST Supercomputing Laboratory (KSL), and we acknowledge the support of the KSL staff. 0

22 Page of References Aagaard, B. T., & Heaton, T. H. (00). Near-source ground motions from simulations of sustained intersonic and supersonic fault ruptures. Bulletin of the Seismological Society of America, (), 0-0. Andrews, D. J. (). Rupture velocity of plane strain shear cracks. Journal of Geophysical Research, (), -. Andrews, D. J. (00). Ground motion hazard from supershear rupture. Tectonophysics, (), -. Aochi, H., & Ulrich, T. (0). A probable earthquake scenario near Istanbul determined from dynamic simulations. Bulletin of the Seismological Society of America. Archuleta, R. J. (). A faulting model for the Imperial Valley earthquake. J. geophys. Res, (), -. Bean, C. J., Marsan, D., & Martini, F. (). Statistical Measures of Crustal Heterogeneity from Reflection Seismic Data: The Role of Seismic Bandwidth. Geophysical Research Letters, (), -. Bernard, P., & Baumont, D. (00). Shear Mach wave characterization for kinematic fault rupture models with constant supershear rupture velocity., (), -. Bizzarri, A., & Spudich, P. (00). Effects of supershear rupture speed on the high frequency content of S waves investigated using spontaneous dynamic rupture models and isochrone theory. Journal of Geophysical Research: Solid Earth, (B). Bizzarri, A., Dunham, E. M., & Spudich, P. (00). Coherence of Mach fronts during heterogeneous supershear earthquake rupture propagation: Simulations and comparison with observations. Journal of Geophysical Research: Solid Earth, (B).

23 Page of Boore, D. M., & Atkinson, G. M. (00). Ground-motion prediction equations for the average horizontal component of PGA, PGV, and %-damped PSA at spectral periods between 0.0 s and 0.0 s. Earthquake Spectra, (), -. Boore, D. M., Watson-Lamprey, J., & Abrahamson, N. A. (00). Orientation-independent measures of ground motion. Bulletin of the seismological Society of America, (A), 0-. Bouchon, M., Bouin, M. P., Karabulut, H., Toksöz, M. N., Dietrich, M., & Rosakis, A. J. (00). How fast is rupture during an earthquake? New insights from the Turkey earthquakes. Geophysical Research Letters, (), -. Bydlon, S. A., & Dunham, E. M. (0). Rupture dynamics and ground motions from earthquakes in D heterogeneous media. Geophysical Research Letters, (), 0-0. Dolan, S. S., & Bean, C. J. (). Some remarks on the estimation of fractal scaling parameters from borehole wire line logs. Geophysical Research Letters, (0), -. Dunham, E. M., & Archuleta, R. J. (00). Evidence for a supershear transient during the 00 Denali fault earthquake. Bulletin of the Seismological Society of America, (B), S-S. Dunham, E. M., & Archuleta, R. J. (00). Near source ground motion from steady state dynamic rupture pulses. Geophysical Research Letters, (). Dunham, E. M., & Bhat, H. S. (00). Attenuation of radiated ground motion and stresses from threedimensional supershear ruptures. Journal of Geophysical Research: Solid Earth, (B). Ellsworth, W. L., Celebi, M., Evans, J. R., Jensen, E. G., Kayen, R., Metz, M. C.,... & Stephens, C. D. (00). Near-field ground motion of the 00 Denali Fault, Alaska, earthquake recorded at Pump Station 0. Earthquake Spectra, 0(), -. Ely, G. P., Day, S. M., & Minster, J. B. (00). A support-operator method for viscoelastic wave modelling in -D heterogeneous media., (), -. Frankel, A., & Clayton, R. W. (). Finite difference simulations of seismic scattering: Implications for the propagation of short period seismic waves in the crust and models of crustal heterogeneity. Journal of Geophysical Research: Solid Earth, (B), -.

24 Page of Frenje, L., & Juhlin, C. (000). Scattering attenuation: -D and -D finite difference simulations vs. theory. Journal of applied geophysics, (), -. Graves, R. W., & Pitarka, A. (00). Broadband ground-motion simulation using a hybrid approach. Bulletin of the Seismological Society of America, 00(A), 0-. Guatteri, M., Mai, P. M., Beroza, G. C., & Boatwright, J. (00). Strong ground-motion prediction from stochastic-dynamic source models. Bulletin of the Seismological Society of America, (), 0-. Hartzell, S., Harmsen, S., & Frankel, A. (00). Effects of D random correlated velocity perturbations on predicted ground motions. Bulletin of the Seismological Society of America, 00(), -. Heaton, T. H. (0). Evidence for and implications of self-healing pulses of slip in earthquake rupture. Physics of the Earth and Planetary Interiors, (), -0. Imperatori, W., and Mai P. M. (0). Broad-band near-field ground motion simulations in -dimensional scattering media, Geophys. J. Int., no.,. Madariaga, R. (). High-frequency radiation from crack (stress drop) models of earthquake faulting., (), -. Mai, P. M., & Beroza, G. C. (00). A spatial random field model to characterize complexity in earthquake slip. Journal of Geophysical Research: Solid Earth, 0(B). Mai, P. M., & Thingbaijam, K. K. S. (0). SRCMOD: An online database of finite fault rupture models. Seismological Research Letters, (), -. Oglesby, D. D., & Day, S. M. (00). Stochastic fault stress: Implications for fault dynamics and ground motion. Bulletin of the Seismological Society of America, (), Oglesby, D. D., & Mai, P. M. (0). Fault geometry, rupture dynamics and ground motion from potential earthquakes on the North Anatolian Fault under the Sea of Marmara. Geophysical Journal International, (), 0-0.

25 Page of Olson, A. H., & Apsel, R. J. (). Finite faults and inverse theory with applications to the Imperial Valley earthquake. Bulletin of the Seismological Society of America, (A), Pitarka, A., & Ichinose, G. (00). Simulating forward and backward scattering in viscoelastic D media with random velocity variations and basin structure. US Geol. Surv. Tech. Rep. Ritter, J. R., Shapiro, S. A., & Schechinger, B. (). Scattering parameters of the lithosphere below the Massif Central, France, from teleseismic wavefield records., (), -. Rothert, E., & Ritter, J. R. (000). Small scale heterogeneities below the Gräfenberg array, Germany from seismic wavefield fluctuations of Hindu Kush events., 0(), -. Schmedes, J., Archuleta, R. J., & Lavallée, D. (00). Correlation of earthquake source parameters inferred from dynamic rupture simulations. Journal of Geophysical Research, (B), B00. Takemura, S., Furumura, T., & Saito, T. (00). Distortion of the apparent S-wave radiation pattern in the high-frequency wavefield: Tottori-Ken Seibu, Japan, earthquake of 000. Geophysical Journal International, (), 0-. Tinti, E., Fukuyama, E., Piatanesi, A., & Cocco, M. (00). A kinematic source-time function compatible with earthquake dynamics. Bulletin of the Seismological Society of America, (), -. Vallée, M., & Dunham, E. M. (0). Observation of far field Mach waves generated by the 00 Kokoxili supershear earthquake. Geophysical Research Letters, (). Walker, K. T., & Shearer, P. M. (00). Illuminating the near sonic rupture velocities of the intracontinental Kokoxili Mw. and Denali fault Mw. strike slip earthquakes with global P wave back projection imaging. Journal of Geophysical Research: Solid Earth, (B). Wang, D., & Mori, J. (0). The 00 Qinghai, China, earthquake: A moderate earthquake with supershear rupture. Bulletin of the Seismological Society of America, 0(), 0-0.

26 Page of Yue, H., Lay, T., Freymueller, J. T., Ding, K., Rivera, L., Ruppert, N. A., & Koper, K. D. (0). Supershear rupture of the January 0 Craig, Alaska (Mw.) earthquake. Journal of Geophysical Research: Solid Earth, (), 0-.

27 Page of List of Tables Table : Eight source models generated from combinations of uniform and heterogeneous rupture parameters. Model Reference D Tr Vr U DTrVr U U U H D H U U H Tr U H U H Vr U U H H DTr H H U H DVr H U H H TrVr U H H H DTrVr H H H Table : Six D earth models generated from combinations of correlation lengths and standard deviations with fixed Hurst exponent. Model Reference Correlation length a (km) Standard deviation σ (%) Hurst exponent H M.0 0. M.0 0. M M M M

28 Page of List of Figures Figure : (a) Slip heterogeneities and supershear rupture speed variations (white contours depict rupture time in seconds) used for analyzing effects on Mach wave coherence. The rise time variations are fully correlated with slip, and range from.0 s -. s. The black star marks the hypocenter. (b) Moment rate functions for sources with all parameters being heterogeneous (red H DTrVr) and the uniform source model (black U DTrVr). (c) Receiver geometry for ground-motion analysis (blue dots) as well as waveform comparison (black triangles, s to s). The red and black dashed lines show the theoretically estimated Mach boundaries for rupture speeds. Vs (heterogeneous sources) and. Vs (uniform source). The solid black line depicts the fault trace, the black star marks the epicenter.

29 Page of Figure : Ground acceleration (m/s ) for fault parallel (FP), fault normal (FN), and vertical (Ver) components, comparing source model H Tr to the reference source U DTrVr at five stations (s - s, Figure - c). Theoretical arrivals from the epicenter of P- and S-waves (black bars) are also shown. Waveforms are aligned according to the theoretical P-wave arrival, and normalized with respect to the absolute maximum of the two sources for a given component (indicated in upper left corner). The S-Mach-wave and Rayleigh-Mach-wave are also marked.

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31 Page 0 of Figure : Snapshots of the ground-acceleration wavefield, for the three components (FP, FN and Ver) computed using the reference source U DTrVr and source model H Tr. The S-Mach-wave (green dashed line) and Rayleigh-Mach-wave (magenta dashed line) are marked to show their planar nature and orientation with respect to the fault. The Mach waves travel large distances from the fault without any attenuation. Note the smaller amplitudes for H Tr compared to the reference source. 0

32 Page of Figure : PGA GMrot as a function of distance for eight rupture models depicts the effects of rupture heterogeneity on ground motions generated from supershear ruptures. The mean (circles) and standard deviation (bars) of PGA GMrot are computed using stations at a given fault-perpendicular distance. The median (solid line) and -sigma bounds (dashed lines) of PGA GMrot from BA00 are shown for comparison. Notice how heterogeneity in rise time (H Tr orange symbol) lead to lower mean PGA GMrot compared to reference source.

33 Page of Figure : Average Fourier amplitude (AFA) spectra as a function of frequency for the FP and FN components of ground motion for eight source models at different fault perpendicular distances (, 0, 0 km). The AFA from model H Tr is lower than for U DTrVr, while for H DVr and H DTrVr, the AFA are higher than the uniform reference model.

34 Page of Figure : Surface slices of shear-wave speed for the six realizations of D random Earth models, using combinations of three correlation lengths (.0 km,.0 km, 0. km) and two standard deviations (%, 0%) for fixed Hurst exponent (H = 0.). The solid black line depicts the fault trace; the black star marks the epicenter.

35 Page of Figure : Ground acceleration (m/s ) for FP, FN and Ver components, comparing two heterogeneous media M and M with the homogeneous medium at five stations (s - s, Figure -c). Theoretical P- and S-wave arrival times (for the homogeneous medium) are shown for reference. Waveforms are aligned according to theoretical P-wave arrival time, and normalized with respect to absolute maximum of motion within the three media for a given component (indicated in upper left corner).