Time-lapse adaptive inversion on resistivity monitoring data with Lp norm regularization and cross-time weight

Abstract

Time-lapse electrical resistivity tomography (ERT) can describe the dynamic processes occurring underground and has been widely employed in the fields of hydrology, environmental management, and engineering. The time-lapse inversion method is based on the space- and time-dimension regularization technique as it considers complementary information about more than one time interval and reduces the potential causes of the geophysical data inversion of the artifact. However, the L2 norm inversions smear out the models and cannot distinguish between the resistivity interfaces. Moreover, the determination of the two optimal regularization parameters for time-lapse inversion remains challenging, and the fixed-time regularization parameter smooths out the low-sensitivity area and inhibits the real variation on the target body of the deep region. To overcome this problem, we propose a time-lapse ERT inversion method of adaptively imaging the time-lapse model and focusing on the resistivity variation on the time dimension. This method is based on the Lp norm regularization provided by the M-estimator and uses the adaptive regularization parameters based on the model roughness and data misfit. In addition, a cross-time matrix improving the sensitivity in the deep region of model space is added to the time regularization term. We present two synthetic examples and a field dataset to validate the method. Numerical simulation and field dataset inversion results revealed that the proposed time-lapse inversion strategy can avoid the excessive smoothness caused by the low sensitivity in the model deep region and can thus enhance the response from the true ground variation to improve the accuracy of the inversion results. Owing to the adaptive regularization parameters that can preserve the dynamic balance between the objective function components, the inversion iteration progress can remain stable and can maintain the trend toward convergence.