Time-lapse velocity inversion through image-domain tomography

Abstract

Adjoint-state methods (ASMs) are effective for calculating the gradients of the functionals commonly found in geophysical inverse problems. The image-domain ASM formulation of the 3D seismic velocity estimation problem leads to an objective function related to imperfections in 3D migrated images, which sets up an inverse problem that can be solved through standard optimisation approaches. Even though more the kinematic image-domain approaches afford lower resolution than their data-domain counterparts (because they do not directly match modelled amplitudes with measured data), they remain a powerful tool for the early iterations of velocity model building owing to their greater immunity to errors in starting velocity models. For time-lapse (4D) seismic scenarios, we show that the ASM approach can be extended to multiple datasets and recover high-resolution estimates of subsurface velocity perturbations. We discuss an absolute 4D inversion strategy that uses the difference between two independent 3D inversions to estimate 4D perturbations. We then present a relative 4D inversion approach that incorporates baseline image constraints into the monitor inversion to accentuate where the baseline and monitor images are different, and then recovers the velocity perturbation that caused the 4D image discrepancy. Both techniques yield very good 4D velocity estimates on synthetic data; however, we argue that the relative approach is more robust and preferable to the absolute strategy in the presence of 4D field noise because it represents a less-demanding inversion goal.