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The reflectivity method with polar sampling

DEPARTMENT OF MATHEMATICS DUKE UNIVERSITY, DURHAM, NORTH CAROLINA 27706
AMOCO PRODUCTION COMPANY, P.O. BOX 3385, TULSA, OKLAHOMA 74102

Abstract

A modification to the reflectivity method that results in more accurate and efficiently computed theoretical seismograms is introduced. The reflectivity method involves an explosive point source and a radially symmetric earth, and in the temporal frequency domain the displacement field and the complex plane wave reflectivity are, to within a phase factor, Hankel transform pairs in the polar coordinate variables radial offset and wavenumber. This motivates formulation of the time-transformed displacement field into a Fourier-Bessel series over the reflectivity function, and replacement of the traditional method for sampling the plane-wave reflectivity with the proper polar sampling scheme, based on the finite Fourier transform representation for a band-limited signal. Several numerical examples are discussed.