INVERSE THEORY APPLIED TO MULTI‐SOURCE CROSS‐HOLE TOMOGRAPHY.

TLDR

Frequency‑domain methods are well suited to wide‑aperture cross‑hole data, but combining them with wavenumber techniques requires linearization around homogeneous reference media. The study applies inverse techniques in the frequency‑space domain to eliminate the linearization and geometry restrictions of traditional diffraction tomography. A nonlinear finite‑difference approach is used, applying the finite‑difference wave equation directly in frequency space, factoring the equations in‑place on vector computers to compute wavefields for many source positions at low cost. Synthetic tests show that while diffraction tomography slightly outperforms a single iteration of nonlinear inversion under weak‑scatter conditions, it fails when background velocities increase with depth, whereas nonlinear inversion still produces useful images from a single frequency component and is effective for time‑lapse monitoring of injection fluids in tertiary hydrocarbon recovery.

Abstract

A bstract Frequency‐domain methods are well suited to the imaging of wide‐aperture cross‐hole data. However, although the combination of the frequency domain with the wavenumber domain has facilitated the development of rapid algorithms, such as diffraction tomography, this has also required linearization with respect to homogeneous reference media. This restriction, and association restrictions on source‐receiver geometries, are overcome by applying inverse techniques that operate in the frequency‐space domain. In order to incorporate the rigorous modelling technique of finite differences into the inverse procedure a nonlinear approach is used. To reduce computational costs the method of finite differences is applied directly to the frequency‐domain wave equation. The use of high speed, high capacity vector computers allow the resultant finite‐difference equations to be factored in‐place. In this way wavefields can be computed for additional source positions at minimal extra cost, allowing inversions to be generated using data from a very large number of source positions. Synthetic studies show that where weak scatter approximations are valid, diffraction tomography performs slightly better than a single iteration of non‐linear inversion. However, if the background velocities increase systematically with depth, diffraction tomography is ineffective whereas non‐linear inversion yields useful images from one frequency component of the data after a single iteration. Further synthetic studies indicate the efficacy of the method in the time‐lapse monitoring of injection fluids in tertiary hydrocarbon recovery projects.