Estimation of a point source wavelet in elastic media

Abstract

A new method of wavelet estimation in elastic or acoustic media is presented. The method is based on the simple procedure of weighted summation of seismic traces for all the distances of source‐receivers, with a horizontal offset r as a weight. The model treated consists of a homogeneous elastic (or acoustic) layer with the free surface above and a half‐space below. The Lamé parameters and the density of the half‐space can be any function of the depth. A P‐wave point source operates in the layer, and the vertical displacement field or the vertical particle velocity field (or the pressure in the acoustic case) is measured by two horizontal lines of receivers located at two depth levels in the same layer. To obtain the wavelet‐estimation algorithm, the Fourier‐Hankel transform of the field is used. It is shown that there are two possibilities of data measuring: (1) when both the lines of the receivers are below the source and (2) when one of the lines is above the source. Numerical examples show that the proposed method gives a correct estimate of the source wavelet.