Elastic wave equation traveltime and waveform inversion of crosswell data

Abstract

A method is presented for reconstructing P‐ and S‐velocity distributions from elastic traveltimes and waveforms. The input data consist of crosswell hydrophone records generated by a piezoelectric borehole source. Borehole effects are partially accounted for by using a low‐frequency Green's function to simulate the pressure generated in the fluid‐filled receiver well. The tube waves in the borehole are ignored, on the assumption that they can be removed from the field data by median filtering. In addition, the source‐radiation pattern is partially taken into account by inverting for the equivalent stress components acting on the earth at the source location. The elastic wave equation traveltime and waveform inversion (WTW) method is applied to both synthetic crosswell data and the McElroy field crosswell data. As predicted by theory, results show that elastic WTW tomograms provide a sharper interface image than delineated in the traveltime tomograms. The spatial resolution of the McElroy traveltime tomogram is about 20 m compared to about 3 m and 1.5 m, respectively, for the associated P‐ and S‐velocity WTW tomograms. From these tomograms, detailed porosity maps of the interwell geology are constructed. There is a very good correlation between the P‐velocity tomograms and the P‐velocity log profiles, and there is a good correlation between the smooth parts of the S‐velocity tomogram and the S‐velocity logs. Unfortunately, the high‐wavenumber parts of the S‐velocity tomograms do not correlate well with the high‐wavenumber parts of the S‐velocity logs. We believe this problem is partly caused by not taking into account attenuation effects in the WTW algorithm.