Time-lapse gravity inversion with an active time constraint

Traditional methods used to invert gravity data are generally based on smoothness as a regularizer and the time-lapse inversion of gravity data is traditionally based on sequential inversion. A smooth density model can be in contradiction with the known geology of the target and sequential time-lapse inversion may lead to the presence of artefacts in the sequence of tomograms due to the propagation of errors from the initial dataset and its associated tomogram. We propose a deterministic time-lapse algorithm to invert a sequence of gravity data combining two features: an image focusing technique and the use of a time-dependent regularizer using an Active Time Constrained (ATC) approach. These two features are included directly in the objective function to minimize. The ATC inversion of time-lapse gravity data is efficient in filtering out noise-contaminated data as long as the noise is not correlated over time. Our approach can also be used to incorporate prior information regarding the density model we want to retrieve. The forward solver is based on a commercial finite element solver with a high flexibility in meshing irregular domains, a feature that is important to include realistic topography from digital elevation maps, for instance, and to describe the density distribution of geological structures with complex geometries. We benchmark the accuracy of the forward modelling code using an analytical expression and test the effectiveness of the focusing algorithm. We show the advantage of our approach in the case of the water flooding of an oil reservoir in order to detect and monitor the position of the oil-water encroachment front. We also test the model against synthetic data describing the evolution of a hydrothermal system feed by a magmatic source and the collapse of a mine. In all these cases, the approach we follow is successful in monitoring density changes.