Extending Sommerfeld integral based spherical wavefield computations beyond two layers

Arnim B. Haase*

ABSTRACT

Plane-wave theory is the commonly accepted approach to AVO-analysis/inversion but it is known to break down near critical angles and at large offsets. What is more, commonly employed linear approximations to Zoeppritz's equations make the assumption of small parameter changes across the interface. Large offsets are desirable, however, when estimating densities by AVO-inversion. Spherical-wave theory overcomes offset related and small parameter change problems, but does not account for reverberations and tuning when only one interface is considered. In order to bring AVO and VSP modelling closer to actual geology, an extension to multi-layer situations is introduced. Based on the Ewing-method, multi-layer boundary equations are developed and programmed. Computed plane-wave reflection and transmission coefficients are then applied in Sommerfeld integrals to obtain multi-layer spherical-wave responses. A three-layer P-wave example modelled with this technique shows the expected reverberations and spherical spreading.

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