Application of the Wiener‐Hopf technique to the calculation of the diffraction of a cylindrical wave by a soft half‐plane embedded in a fluid half‐space

Abstract

Wavelets currently are estimated directly from the data by statistical means or, for marine data, by direct measurement with deep hydrophones. The first method, based on statistical arguments, uses the convolution model of seismic traces as the starting point. In addition, it also assumes whiteness of the earth’s reflectivity series and the minimum‐phase character of the wavelet. The second method does not work very well for shallow seas because of interference with reflections by the seafloor. In a companion paper, an algorithm for the estimation of wavelets of marine sources has been presented. The algorithm starts from the reduced wave equation to describe the measured field and an auxiliary field. Physically, the auxiliary field, also known as the Green’s function, is the wavefield configuration of a line source and a soft half‐plane in a fluid half‐space. The calculation of this Green’s function is the subject of this paper.