Vertical seismic profile waveform inversion

Abstract

Waveform inversion of vertical seismic profile (VSP) data is studied in this paper. In this study, finite-difference acoustic wave modelling in the frequency-domain is used for seismic forward modelling and a classical iterative Gauss-Newton algorithm is used for inversion. The inversion algorithm in the frequency-domain allows a multiscale approach in which individual frequency components from low to high are inverted. This reduces nonlinearity of the inverse problem and decreases the computational costs by converging to a favourable solution via a limited number of frequency components. Here, the algorithm is applied to synthetic and real VSP datasets. The synthetic model includes both smooth and sharp features. It is observed that although satisfactory results can be obtained without including the higher-frequency components, these are essential in preserving the edges of the sharp discontinuities in the velocity model. Seismic preconditioning was applied to the real VSP dataset prior to inversion to mitigate the effects of noise and unwanted wave modes. By comparing the results of inversion with the sonic log data, it is shown that waveform inversion is capable of capturing the small scale variations in the velocity model, whereas traveltime inversion fails to capture the true range of velocity variations.