Minimax method to obtain depth migration explicit filters in transversely isotropic media

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:89736

Uzcategui, O ^[1]

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1. Colorado School of Mines, Golden, CO (United States)

Explicit depth-extrapolation filters to propagate plane waves corresponding to the P and SV (quasi-P and quasi-SV propagation) modes for transversely isotropic (TI) media can be obtained using a minimax method. In this approach, the filters are calculated in such a way that the maximum error in the propagation region between the ideal and the actual response of the filter is minimum. To get stability in the evanescent region, the author minimizes the maximum error between a decaying exponential function with amplitude values less than unity and the filter response. A tradeoff between the maximum errors allowed in the propagation and evanescent regions is needed in order to get accurate and stable filters. The author has modified the computer code of McClellan et al. (1973), originally designed to obtain bandpass filters, to allow the computation of depth-extrapolation filters for isotropic media and transversely isotropic media with a vertical axis of symmetry (VTI). Uzcategui (1993) has shown that the accuracy in depth-extrapolation filters obtained using a least-squares method is better than that obtained by using a modified Taylor series method. Here, the author shows that the computational cost of the minimax method for obtaining the filters is far less than that of a least-squares method, while the accuracy of the resultant operators is similar in both methods.

• OSTI ID: 89736
• Report Number(s): CONF-941015--
• Country of Publication: United States
• Language: English

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