In this paper we first give a brief summary of the formulation of elastic-wave complex-screen (ECS) method recently developed by R.S. Wu (1993) using elastic Rayleigh integrals and elastic Born scattering theory, then discuss the implementation of the ECS method and present some numerical results. The wavenumber domain formulation of elastic wave scattering and propagation leads to a compact solution to the one-way propagation and scattering problems in 3D heterogeneous media. It is shown that wide-angle scattering in heterogeneous elastic media cannot be fonnulated as passage through regular phase-screens, since the interaction between the incident wavefield and the heterogeneities is not local in both the space do~ain and .the wavenumber domain. This more generally valid fonnulanon is called the "thin-slab" formulation. After applying the small-angle approximation, the thin-slab effect degenerates to that of a elastic complex-screen. The computation speed of the complex screen method can be 2 to 3 orders of magnitude faster than the thin-slab method for large 3D problems. Compared with the scalar phase-screen, the elastic complex-screen has the following features: 1). For P-P scattering and S-S in-plane scattering, the elastic complexscreen can be equated to two separate scalar phase-screens for P and S waves respectively. The phase distortions are determined by the P and S wave velocity perturbations respectively. 2). For P-S and S-P conversions, the screen becomes complex; both conversions are determined by the shear wave velocity perturbation and the shear modulus perturbation. For Poisson solids the S wave velocity perturbation plays a major role. A comparison with the work of FM91 is also made and shows that the ECS method can correctly treat the conversion between P and S waves when the former fails. Comparison with 3D finite difference calculations has been made for two special cases. One is the case of pure P-velocity perturbation, the other is for pure Svelocity perturbation, The scattered field from such spheres calculated by 3D ECS and 3D finite difference generally show good agreement.


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