Research and Application of a Cross-Gradient Constrained Time-Lapse Inversion Method for Direct Current Resistivity Monitoring

The direct current resistivity method holds advantages such as rapid, efficient, and automatic data acquisition. It is an important geophysical exploration technology for monitoring dynamic changes in subsurface geology. However, this method has such issues as volume effect and non-uniqueness in inversion. To meet the demand for high-resolution direct current resistivity inversion of dynamic geological models characterized by discontinuous changes, this study proposed a cross-gradient constrained time-lapse inversion method, thereby enhancing inversion imaging accuracy. A cross-gradient constraint term between models was incorporated into the objective function of time-lapse inversion to constrain the structural consistency and highlight local resistivity changes. This method avoided excessively smooth imaging as often caused by over-reliance on a reference model in time-lapse inversion, thereby significantly improving both the spatial resolution and quantitative accuracy of direct current resistivity monitoring inversion images. Numerical examples confirmed that the proposed method delivers higher inversion imaging accuracy in identifying dynamic resistivity changes, evidenced by a substantially lower normalized mean-square error (MSE). Furthermore, physical model experiments and a case study confirmed the stability of this method under actual monitoring conditions. The proposed method provides a more precise and effective inversion imaging technique for refined monitoring of dynamic changes in subsurface geologic bodies.