Estimation of velocity and borehole receiver location via full waveform inversion of vertical seismic profile data

Abstract

ABSTRACTBecause a vertical seismic profile (VSP) survey includes the installation of geophones into a borehole, the results of data processing are influenced by the deviation error of the borehole trajectory. In particular, when full waveform inversion (FWI) is applied to VSP data, receiver location errors distort the results of velocity inversion. Under this circumstance, we attempt to estimate the exact locations of receivers and resolve the distortion of the inverted velocity model by adding receiver locations to the inversion parameters. This makes the FWI process a multi-parametric inverse problem. In this case, it is desirable to invert each parameter group alternatively. Because receiver coordinates depend on borehole trajectory, the inverse problem is regularised by adding a term measuring the curvature of the borehole trajectory gradient to obtain a physically meaningful solution. In addition, we propose a grid search method to improve the estimation of receiver coordinates. In the case of VSP data, the inversion of receiver coordinates using the grid search method is more efficient and robust than using a local descent method. Through numerical examples, we verify that the proposed inversion algorithm can improve FWI results and mitigate velocity distortion. We also demonstrate that the convergence of FWI can be improved by applying the grid search method to the estimation of receiver coordinates.