Several methods of evaluating high-frequency seismic wavefields generated by earthquake sources in laterally varying, 2-D and 3-D, layered structures are discussed. They are based on the standard ray theory, on the paraxial ray approximation and on the summation of Gaussian beams. High-frequency expressions for the Green tensor for a general 3-D laterally varying layered structure are derived and used in evaluating seismic wavefields generated by point sources as well as finite extent faulting sources. Numerical examples of ray synthetic seismograms generated by buried double-couple point sources situated in a 2-D model of the Earth's crust are presented.
Special attention is devoted to faulting sources of finite extent with arbitrary spatial variations of rupture velocity and slip velocity intensity factor over a curved fault. Inserting Gaussian beams and/or paraxial ray approximations into the representation theorem leads to expressions which may be evaluated in several ways. For situations in which the involved parameters vary smoothly along the fault, the "narrow-beam" approach may be used. Within the region, on the fault, illuminated by a beam, the variation of parameters may be substituted by their Taylor expansion and the expressions resulting from the representation theorem may be evaluated easily. If any of the involved parameters do not change smoothly along the fault, the "broad-beam" approach may be used, in which the slip function is expanded into Gaussian envelope functions. Several other modifications and/or combinations of these approaches are proposed. None of the mentioned algorithms requires a two-point ray tracing. Moreover, synthetic ground motions generated by different faulting models may, under certain circumstances, be computed using the same system of rays; without repeating the relatively time-consuming ray tracing. This makes proposed algorithms more effective and, perhaps, even faster than the isochrone method. Numerical examples are presented, in which the Gaussian beam synthetic ground-velocity seismograms, evaluated for a rather complex faulting model, are compared with those calculated by the isochrone method and by the finite-element/discrete wave-number method, based on the complete Green tensor. The comparisons indicate that the Gaussian beam method yields sufficiently accurate results.
Seismic waves, finite extent faulting sources, summation of Guaussian beams, paraxial ray approximation, laterally inhomogeneous structures.
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