4-D Inversion of Resistivity Monitoring Data Using L1 Norm Minimization

Abstract

Inversion artifacts, one of the major problems which may lead a misinterpretation of geophysical monitoring data, can be reduced through incorporating the time domain regularization by defining both the subsurface model and the time-lapse data in the space-time domain. Applying this time regularization, however, may result in a model too smoothly varying in the time domain, and as a result, underestimate the real subsurface changes. To alleviate this problem and to find a way to accurately evaluate the ground truth, we developed a new inversion algorithm where we can flexibly adopt either L1 norm or L2 norm minimization of each of the three penalty values in the four dimensional inversion: data misfits, model roughness in the space domain and that in the time domain. Synthetic data experiments of crosshole resistivity monitoring were conducted using the developed algorithm. Further tested was the application to field resistivity monitoring data obtained for the assessment of the ground condition changes caused by a tunnel excavation. All these tests showed that the 4D inversion of minimizing the L1 norms of both the data misfit and the model roughness in the time domain produced the results which closely resemble the true ground condition changes.