Time-lapse image-domain velocity analysis using adjoint-state methods

Adjoint-state methods (ASMs) have proven successful for calculating the gradients of the functionals commonly found in geophysical inverse problems. The 3D image-domain formulation of the seismic velocity estimation problem uses imperfections in 3D migrated images to form an objective function, which is minimized using a combined ASM plus line-search approach. While image-domain methods are less sensitive than their data-domain counterparts because they are based largely on wavefield kinematics and not directly matching amplitudes, they are more robust to poorer starting models, which makes them attractive for the early stages of seismic velocity estimation. For time-lapse (4D) seismic scenarios, we show that the 3D ASM approach can be be extended to multiple datasets to offer high-quality estimates of productionand/or injection-induced subsurface change. We discuss two different penalty operators that lead to what we term absolute and relative inversion strategies. The absolute approach straightforwardly uses the difference of two independent 3D inversions to estimate a 4D slowness perturbation. The relative approach directly incorporates the baseline image into the penalty function to highlight where the baseline and monitor images are different and to mask where they are similar even if reflectors are imperfectly focused. Both these techniques yield good 4D slowness estimates for synthetic data; however, we assert 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.