Summary
Our last year studies attempted to clarify the properties and utility of seismic waves generated by laterally heterogeneous fault zones with coherent material interfaces. Toward that end, we derived from the 2D analytical solution of Ben-Zion and Aki [1990] an explicit version for a case with two vertical fault zone (FZ) layers. Using this solution, we examined the dependency of seismic FZ trapped waves on basic media properties and source-receiver geometry. The analysis indicates that seismic FZ waves are highly sensitive to a large number of parameters, and that the wavefield is far more complex than has been assumed in recent observational studies. The results also show that the zone connecting sources generating FZ waves and observation points with appreciable wave amplitude can be over an order of magnitude larger than the FZ width, in contrast to assertions made in other works on the subject. These results are discussed below in more detail.
Fields radiated by Laterally heterogeneous fault zone structures
To provide a better understanding of seismic radiation from laterally heterogeneous fault zone (FZ) structures, we used a generalized version of the 2D analytical solution of Ben-Zion and Aki [1990] for the scalar wave equation in a model of two vertical layers between two quarter-spaces. The solution accounts for body waves and a variety of seismic FZ waves, including head waves, internal FZ reflections, and trapped waves. The results (Figure 1) show that realistic FZ layers can have significant effects on the wavefield at normal distances from the fault of about 10 times the FZ width and more. In particular, the various FZ waves can lead to large motion amplification near the FZ proper. These conclusions are also evident from the synthetic seismograms in the different panels of Figures 6 - 8 of Ben-Zion and Aki [1990].
Our last year studies focused specifically on the dependency of the waves on media velocities, media attenuation coefficients, layers widths, and source-receiver geometry. In general, the interference patterns controlling seismic FZ waves change with the number of internal reflections in the low velocity structure. This number increases with propagation distance along the structure (r) and it decreases with FZ width (W). Thus the primary length scale governing the waves is the ratio of propagation distance along the structure divided by FZ width. This is illustrated in Figure 2, where we show time histories and amplitude spectra of velocity seismograms for various ratios of r /W. The receiver is at the free surface (z = 0) in the center of medium 2 modeling the FZ (x = 0.5W2). The quality factor of the FZ layer is Q2 = 100 and the other media parameters are the same as in Figure 1. In Figure 2 left, r is kept constant at 5 km and W varies, while in Figure 2 right, W = 50 m and r changes. The results demonstrate the importance of accounting properly for the evolution of seismic FZ waves with propagation distance along the fault. As discussed above and by Igel et al. [1997], there is a strong trade-off between r and W. Waveforms in a structure with a given width associated with different source-receiver configurations, and hence different values of r, can exhibit changes similar to those associated with fixed r and corresponding variations of FZ widths.
The critical angle of reflection within a low velocity layer increases with the impedance contrast between the layer and the bounding media. Hence the number of internal FZ reflections increases (for given length scales) with the velocity contrast. The relative lateral position of the source within the low velocity layer modifies the length scales associated with internal reflections and influences the resulting interference pattern. Low values of Q affect considerably the dominant period and overall duration of the waves. We thus find that there are significant trade-offs between propagation distance along the structure, FZ width, velocity contrast, source location within the FZ, and Q. The calculations demonstrate that the wavefield depends strongly not only on receiver distance from the FZ, but also on receiver depth below the free surface. Figures illustrating these effects are given in a paper submitted to J. Geophys. Res. [Ben-Zion, 1997]. The calculations indicate that previous observational works based on modeling of a few selective waveforms are subjected to significant uncertainties and should be regarded as very preliminary analyses.
Figure 3 gives displacement and velocity seismograms in a 4-media model characterized by b1 = 3.0 km/s, Q1 = 1000; b2 = 2.5 km/s, Q2 = 100, W2 = 500 m; b3 = 2.0 km/s, Q3 = 30, W3 = 50 m; b4 = 3.2 km/s, Q4 = 1000. The receiver is in the center of the core FZ layer (medium 3 here), and sources are located in the adjacent transition zone (medium 2). The media properties in this case are compatible with the structure assumed to characterize the San Andrea fault in central California. The results show that sources everywhere in the adjacent layer, at distances up to 10 times the FZ width (top 9 traces), produce trapped waves amplitudes similar to that generated by a source in the FZ proper (bottom trace). From Figures 1 and 3, it is clear that the FZ may be over an order of magnitude narrower than the width of the zone connecting sources and receivers associated with trapped waves. These calculations raise doubts on the validity of estimates of the width, continuity and other fault zone properties, based on inspection of the zone of sources and receivers associated with FZ trapped waves.
Extensions of our basic parameter space to 3D cases of P, SV and SH waves in FZ models with irregular geometries and non uniform material properties are given by Leary et al. [1991] and Igel et al. [1997]. Additional results for complex FZ structures can be found in Leary et al. [1993], Huang et al. [1995] and Li and Vidale [1996]. The various possible complications from 3D wavefields in irregular FZ structures not covered here, strengthen further the need for careful and thorough analysis.
Igel et al. [1997] found from 3D numerical calculations that correlated heterogeneities of FZ material properties (correlation length > FZ width) destroy the ability of the fault system to act as a wave guide for FZ trapped waves. In addition, horizontal surface layer with properties (width, velocity) similar to those of the FZ layer diffuses the trapped waves and inhibits the ability to obtain useful observations at the surface. On the other hand, small-scale random heterogeneities of material properties in the FZ and moderate geometrical perturbations have little effect on the amplitude and waveform of the trapped waves. The simulations of Igel et al. suggest that observed FZ trapped waves average out small FZ irregularities. It thus appears that the existence of FZ trapped waves at given locations implies that the FZ structure is fairly uniform for the recorded range of wavelengths, and hence can be modeled effectively for those wavelengths by average property, plane-layered media.
Our study of parameter trade-offs indicates that a proper quantitative analysis of observed seismic FZ waves should involve the simultaneous modeling of many waveforms. An efficient modeling procedure requires a computational scheme that can on one hand account for the various basic phases expected to exist near low velocity FZ structure, while being at the same time fast enough to be used as a forward modeling kernel in a systematic inversion of a large data set. The above considerations, our last year calculations, and the limited previous observational studies of Leary and Ben-Zion [1992] and Hough et al. [1994], suggest that the 2D analytical solution employed in this work may provide an appropriate basic tool for large scale modeling of observed seismic FZ waves.
The proposed continuing studies will attempt to develop a rigorous procedure for large scale inversion of seismic fault zone waveforms in terms of material and geometrical FZ parameters, and apply the inversion procedure to waveforms associated with the rupture zone of the 1992 Landers earthquake and other available data sets.
References
Ben-Zion, Y., Properties of seismic fault zone waves and their utility for imaging low velocity structures, submitted to J. Geophys. Res., 1997.
Ben-Zion, Y. and K. Aki, Seismic radiation from an SH line source in a laterally heterogeneous planar fault zone, Bull. Seismol. Soc. Amer., 80, 971-994, 1990.
Hough, S. E., Y. Ben-Zion and P. Leary, Fault-zone waves observed at the southern Joshua Tree earthquake rupture zone, Bull. Seismol. Soc. Amer., 84, 761-767, 1994.
Huang, B.-S., T.-L. Teng and Y. T. Yeh, Numerical modeling of fault-zone trapped waves: acoustic case, Bull. Seismol. Soc. Amer., 85, 1711-1717, 1995.
Igel, H., Y. Ben-Zion and P. Leary, Simulation of SH and P-SV wave propagation in fault zones, Geophys. J. Int., 128, 533-546, 1997.
Leary, P. and Y. Ben-Zion, A 200 m wide fault zone low velocity layer on the San Andreas fault at Parkfield: Results from analytic waveform fits to trapped wave groups, Seismological Research Letters, 63, 62, 1992.
Leary, P., H. Igel and Y. Ben-Zion, Observation and modeling of fault zone seismic trapped waves in aid of precise evaluation of precursory microearthquake locations and evaluation, Earthquake Prediction: State of the Art, Proceedings international Conference, Strasbourg, France, 15 -18 October 1991, 321-328, 1991.
Leary, P., H. Igel, P. Mora and D. Rodrigues, Finite-difference simulation of trapped wave propagation in fracture anisotropic low-velocity layer, Can. J. Expl. Geop., 29, 31-40, 1993.
Li, Y. G. and J. E. Vidale, Low-velocity fault-zone guided waves: numerical investigation of trapping efficiency, Bull. Seismol. Soc. Amer., 86, 371-378, 1996.
Publications Supported by this Proposal
Papers:
Ben-Zion, Y., Properties of seismic fault zone waves and their utility for imaging low velocity structures, submitted to J. Geophys. Res., 1997.
Abstracts:
Ben-Zion, Y., Utility Of Seismic Fault Zone Waves For Imaging Low Velocity Structures, SRL, 68, 329, 1997.
Michael, A and Y. Ben-Zion, Joint Inversion of Fault Zone Waveforms for Structure and Hypocentral Location, EOS Trans. Amer. Geophys. Union, 78, F455, 1997.
