3D Forward Modeling of Seepage Self-potential Using Finite-infinite Element Coupling Method

Abstract

The streaming potential in porous media is one of the main constituents of the self-potential. It has attracted special attention in environmental and engineering geophysics. Forward modeling of streaming potentials could be the foundation of corresponding data inversion and interpretation, and improving the application effect of the self-potential method. The traditional finite element method has a large subdivision area and computational quantity, and the artificial boundary condition is not suitable for complex models. The Helmholtz-Smoluchowski equation is introduced for evaluating the streaming potential. Then three new shape functions of the multidirectional mapping infinite elements are proposed and the finite-infinite element coupling method is deduced for reducing the subdivision scale and improving both the calculation efficiency and accuracy. The correctness and validity of the new coupled method are verified by a resistive model in homogeneous half-space. Besides, a seepage model with complex terrain and a landfill model with dynamic leakages are modeled using the improved coupled method. The results show that the accuracy of the improved coupled method is superior to the unimproved coupled method, and is better than the finite element method. Also, the coupled method has better adaptability to complex models and is suitable for the accurate simulation of dynamic multi-source seepage models.