Finite - Difference Seismograms for Sh Waves

The accuracy of the fi!lite-difference method for generating synthetic seismograms of SH wave propagation in cylindrically symmetric media is discussed. The finite-difference method has the advantage that arbitrary density and velocity fields in the medium may be specified. A point source is generated by a simple transformation of a line source. The accuracy of the finite-difference seismograms in flatand dipping-layered media is confirmed by comparison with the generalized ray method. A source radiation pattern is inserted by introducing a "nearfield" which has permanent displacement near the source. Strong motion synthetics are constructed with this new method for the 1968 Borrego Mountain earthquake as recorded at El Centro. Good fits to the data are achieved using the laterally varying model determined by a detailed refraction survey and the source parameters determined by teleseismic waveform modeling. Shallow faulting is no longer necessary to explain the long-period surfacewave development. INTRODUCTION The understanding of earthquake-generated motions has improved significantly in recent years. This progress is due in large part to the refinement of methods for generating synthetic seismograms to compare with an ever-growing collection of observations. Synthetic seismograms are generally used in iterative forward modeling schemes where the source and medium parameters are perturbed until a best match with the data is obtained. This technique has proven to be powerful for determining subtle features of both the source and the medium. The technique is limited, however, by the range of earth structure that can be modeled. Traditionally, the medium models have been a stack of homogeneous layers, which is inadequate for laterally heterogeneous structures such as ocean-continent transition zones and basin structures. In this paper, we relax some of these limitations by allowing dipping structure and introducing a procedure whereby two-dimensional finite-difference (FD) calculations can be mapped into synthetic seismograms with the proper point source shear dislocation characteristics. This procedure has the advantage of allowing for arbitrary density and velocity fields in two dimensions. In this paper, only SH waves (horizontally polarized shear waves) are treated but the method may be extended to P-SVwaves. In the first section, a procedure for mapping line source responses (the source used by the FD method) to point source responses with a radiation pattern is given. The similarity of the generalized ray theory (GRT) expressions for strike-slip and dip-slip types of sources leads to the identification of the vertical radiation patterns required for the line-source FD source. In the next section, FD seismograms generated using these radiation patterns are seen to agree well with GRT seismograms. In the last section, this technique is applied to model the seismogram recorded at El Centro for the 1968 Borrego mountain event. SOURCE REPRESENTATION The source representation described in this section is the first, to our knowledge, that allows the use of two-dimensional FD or finite-element programs to create 1765 1766 JOHN VIDALE, DONALD HELMBERGER, AND ROBERT CLAYTON point source synthetic seismograms that may be compared with data for both amplitude and waveform. This source is derived by matching previously known first-term asymptotic solutions (e.g., Heimberger, 1983) with the "pseudo-nearfield" terms necessary to produce radiation patterns with two-dimensional codes. The SH displacement in a horizontally layered medium from a buried point dislocation source can be conveniently expressed as a sum of generalized rays (Heimberger and Malone, 1975) M0 d [d D ( t) 2 ] v(t) = 4 -d -d·* ~ Aj+3(6, i\, o) Vj(t) 1rpo t t j=l (1)