Low-Velocity Fault-Zone Guided Waves: Numerical Investigations of Trapping Efficiency

Recent observations have shown that shear waves trapped within lowvelocity fault zones may be the most sensitive measure of fault-zone structure (Li e t al. , 1994a, 1994b). Finite-difference simulations demonstrate the effects of several types of complexi ty on observations of fault-zone trapped waves. Overlying sediments with a thickness more than one or two fault-zone widths and fault-zone stepovers more than one or two fault widths disrupt the wave guide. Fault kinks and changes in fault-zone width with depth leave readily observable trapped waves. We also demonstrate the effects of decreased trapped wave excitation with increasing hypocentral offset f rom the fault and the effects of varying the contrast between the velocity in the fault zone and surrounding hard rock. Careful field studies may provide dramatic improvements in our knowledge of fault-zone structure. Introduction Major crustal faults are often marked by zones of lowered velocity with a width of a few hundred meters to a few kilometers (Healy and Peake, 1975; Feng and McEvilly, 1983; Mooney and Ginzburg, 1986; Li and Leary, 1990; Scholz, 1990; Michelini and McEvilly, 1991). These lowvelocity zones are thought to be caused by an unknown combination of fluid concentrated near faults, clay-rich fault gouge, increased porosity, and dilatant cracks (Sibson, 1977; Wang, 1984; Li et al., 1990). The strength of the low-velocity anomalies might vary over the earthquake cycle (Li et al., 1994a). Recently, fault-zone guided waves have been shown to reveal detailed information about the fine structure at the heart of fault zones and its lateral variation (Li et al., 1994a, 1994b). Since fault-zone trapped waves arise from constructive interference of multiple reflections at the boundaries between the low-velocity fault zone and highvelocity surrounding rocks, the feature of trapped waves (including amplitudes and frequency contents) are strongly dependent on the fault-zone geometry and physical properties. We can resolve fault-zone width from tens to several hundreds of meters using the records of fault-zone trapped waves. It is of interest to determine the factors that influence the propagation of these waves. The fine structure of fault zones is of great interest because the factors that control the initiation, propagation, and termination of rupture are not well understood (Aki, 1984; Scholz, 1990; Kanamori, 1994). Rupture models have been proposed that involved variations in fluid pressure over the *Present address: Department of Earth and Space Sciences, University of California, Los Angeles, Los Angeles, California 90095-1567. earthquake cycle (Sibson, 1973; Blanpied et al., 1992). Other studies predict that most earthquake energy is stored in areas with less-developed fault zones (Mooney and Ginzburg, 1986) or with higher-velocity rock outside the fault zone (Michael and Eberhart-Philips, 1991; Nicholson and Lees, 1992). Observations suggest that fault-zone complexity may segment fault zones (Lindh and Boore, 1974; Aki, 1979; Beck and Christensen, 1991) or control the timing of moment release in earthquakes (Campillo and Archuleta, 1993; Harris and Day, 1993; Li et al., 1994a, 1994b; Wald and Heaton, 1994). For all these models, knowledge of lateral variations or temporal variations in fault structure will help predict the behavior of future earthquakes, and such knowledge will help evaluate the models as well. Faults also sometimes mark the boundary between types of rocks with distinct seismic velocities, but the resulting refracted arrivals (McNally and McEvilly, 1977; Ben-Zion and Malin, 1991) are beyond the scope of this article. The Simulation Method We use finite-difference simulations below to investigate the effects of various possible fault structures as well as structures that might obscure the signature of faults. The finite-difference code is acoustic, fourth order in time, second order in space, and two-dimensional (Alterman and Karal, 1968; Vidale et al., 1985; Vidale, 1990). The SHwave equation is solved, and we are examining the component of S motion parallel to the strike of the fault. Windowing based on the precalculation of travel times by a 371 372 Y.-G. Li and J. E. Vidale finite-difference eikonal method (Vidale, 1988) reduces the computational requirements by a factor of 4. Each calculation uses a 600-by-600 element grid to simulate a vertical cross section that strikes perpendicular to the surface trace of the fault. The grid spacing is 20 m. The minimum velocity in the simulations is usually 2 km/sec, and we use a time step of 0.008 sec (Alford et al., 1974). We use at least eight grid points per wavelength to minimize grid dispersion (Alford et al., 1974). The fault zone is placed down the middle of the grid, far enough from the left and right edges that side reflections do not appear in the seismograms. The sources are shallow enough that bottom reflections also arrive later than the arrivals we analyze. The top surface, where the seismometers are located, is a free surface. The simulation is for a line source; to simulate a point source, we apply an approximate correction. Tile time series in each seismogram is differentiated with respect to time t and convolved with the time series 1/fi (Vidale et aI., 1985). An isotropic radiation pattern is used, although in earthquakes, the familiar P and S radiation patterns of a double couple are present (Aki and Richards, 1980). In elastic finitedifference modeling of strong motion records from the 1971 San Femando earthquake, Vidale and Helmberger (1987) have shown that despite the three-dimensional nature of the basins, the geometry may be approximated by a two-dimensional model with useful results. They, however, note that the amplitude attenuation due to geometrical spreading in the two-dimensional profile may vary somewhat due to threedimensional effects, even if the energy path is not laterally deflected. They also note that the simulations of the energy in nodal directions may be a problem. We note that in our previous work (Li et al., 1994b) the appropriate double-couple radiation patterns were included. In the present article, we illustrate an example of seismograms using the doublecouple source with the S radiation pattern (Fig. 9) and compare with seismograms using isotropic radiation pattern. Previous articles have used analytical methods to compute seismograms that result from layer-cake fault models (Li et al., 1987) or raytracing methods that are limited by the difficulty of finding ray paths in strongly heterogeneous structures (Cormier and Spudich, 1984). This study provides the next logical step by allowing arbitrary velocity variations in a two-dimensional cross section, with the limitation that no along-strike variation is allowed, and the source and receiver must be in the same cross section that is perpendicular to the fault. The computation of fault-zone trapped waves with 3D elastic structures has been demonstrated, but so far only propagation to a distance up to several wavelengths has been obtained with a Connection Machine (Igel et aL, 1991; Leary et aL, 1991). Simulation Results The Reference Model Our simulations are based on geometries similar to those inferred for major vertical strike-slip California faults (Li et al., 1994b). In the simulations, our reference model has an 8-km source depth, the fault-zone width is 200 m, and the source is placed against one edge of the low-velocity fault zone. The receiver array is centered on the surface fault trace. We set the wall rock shear-wave velocity to 3 km/sec and the fault zone velocity to 2 km/sec, so the velocity anomaly in the fault zone is about 40%. This structure most effectively traps 3to 10-Hz shear waves. The Perturbations to the Reference Model Table 1 lists the model parameters used in various fault structures, and maximum amplitudes of the seismograms generated with these fault models as well as the figure numbers in which seismograms are shown. Effect of Source Location Guided waves are most efficiently excited by a seismic source that is located within the wave guide. This is clear in Figure 1, which shows the ground motion for no wave guide (Fig. la) and for five source positions at various distances from the wave-guide center. The maximum amplitude of seismograms generated in each case is listed in Table 1. The sources in the center (Fig. lb) and on the edge of the fault zone (Fig. lc) produce large guided waves. The centered source location produces less high-frequency trapped energy because of the symmetric source radiation pattern and symmetric fault structure. There are no numerical problems with the edge of the fault zone. However, a real fault would contain attenuation and heterogeneity that may mask the differences between source locations within the fault zone. A source location 200 m, or one fault-zone width, outside the fault zone (Fig. ld) still produces visible trapped waves that appear within a few hundred meters of the fault trace. However, their amplitude is about a factor of 3 weaker than for source locations inside the fault zone. A source 400 m outside the fault (Fig. le) excites only the longest-period guided waves. A source 1000 m outside the fault (Fig. if) produces no guided waves, although some reflections and shadowing from the sides of the fault zone are still visible. Effect of Fault-Zone Width and Velocity Contrast The amount of reduction of velocity in the fault zone determines the amount of dispersion in the guided wave. A 20% velocity reduction (Fig. 2a) results in a more compact guided wave than a 50% velocity reduction (Fig. 2b). The frequency content of the guided wave also depends on the velocity within the fault zone, since lower-velocity material within a fixed width fault zone causes longer-period resonance, but this effect is weak. The width of the low-velocity fault, however, controls the frequency of the guided waves. An 80-m-wide fault zone shows a clear shift toward higher-frequency guided waves (Fig. 2c) compared with the reference model of a 200-mwide fault zone (Fig. 2b). Low-Velocity Fault-Zone Guided Waves: Numerical Investigations of Trapping Efficiency 373 Table 1 Perturbations in Model Parameters and Maximum Amplitudes Reference Model Parameters: Fault-zone thickness: 200 m Fault-zone velocity: 2.0 km/sec Wall rock velocity: 3.0 km/sec Source depth: 8.0 kin Number of receivers: 31 Receiver space: 40 m Array length: 1.2 km Array position: centered on the surface fault trace Source Position: (offsets from the center of the fault zone) Source offset (m): 0 0 100 300 50