Abstract
SUMMARY 1-D reflectivity method in the frequency ray-parameter domain is the most popular method for computing synthetic seismograms. We explore an extension of this method to media consisting of homogeneous layers with curved interfaces. The 2-D extension of the method involves explicit evaluation of boundary conditions that results in a matrix formulation involving several matrix inversions in a coupled ray-parameter domain. First, we revisit this method by examining the intermediate results in the coupled shot-receiver ray-parameter domain for realistic models; numerous numerical artefacts are caused by matrix operations. Next we investigate an alternate asymptotic approach by examining a tangent plane or Kirchhoff formulation in the plane wave domain to replace the exact boundary condition evaluation. All other reflectivity operations such as the invariant imbedding or iterative computation of reflection, transmission, multiple and mode conversions can be readily applied even under this approximation. Our resulting algorithm computes noise free seismograms even with coarse sampling of the interfaces and ray parameters. Approximate calculation of reflection/transmission coefficients, however, does not include multiple interaction of a plane wave with an interface. We show examples of synthetic seismograms for a suite of realistic models. Our computations are performed in the coupled slowness domain and thus, multiple shot-receiver data can be synthesized rapidly. Intermediate results in the coupled slowness space provide important insight into understanding wave propagation in heterogeneous media.
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