2.5DC Resistivity Forward Modeling And Inversion By Finite-infinite Element Coupling Method

The finite element method (FEM) is widely used in geophysical forward modeling problem for its flexible simulation of arbitrary complex model. But the speed of forward modeling with FEM largely depends on the grid nodes. As is well known, fast forward modeling is the basis of inversion, so how reduce the grid nodes and obtain a result with high accuracy in a small mesh area is undoubtedly a valuable research topic.In the numerical simulation of stable current field, two boundary conditions were commonly used, one is mixed boundary condition and the other is quansic boundary condition. The first one could get a solution with higher precision in reasonable mesh area. However, the global system matrix which generated with this boundary condition is dependent on the position of source point, so the global system matrix need to regenerate and the equation need to resolve if the position of source point changes. The calculation with this boundary condition is time-consuming, especially for inversion. The system matrix calculated with second boundary condition is independent of the location of source point, but it needs a larger mesh area to reduce truncation error which would result to overmuch elements and nodes, then increase the storage of computer and the difficulty of equation solving.In order to solve the shortage of the above two boundary conditions, the infinite element boundary condition was proposed in this paper. It not only ensure that global system is independent of the position of source point, but also make sure that mesh area is almost as big as calculation area which avoid excessive elements and nodes. The core concept of infinite element boundary condition is extending the element to infinity in a certain direction with coordinate mapping, then make the potential rapid decay to zero through element integral. Thus, truncation boundary condition is unnecessary to consider. Series of simulation results show that the solution calculated with finite-infinite element couple method has a higher accuracy than the results calculated by tradition FEM with mixed boundary condition or quansic boundary condition, especially when the measure point is close to boundary. In addition, the global system matrix generated with infinite element boundary condition is independent to the position of source point, a fast and accurate forward modeling could achieve in small mesh area.Based on fast forward modeling, the2.5D DC resistivity least squares inversion was implemented with the finite-infinite element couple method. The numerical results show that the finite-infinite element couple method can reduce computational domain and calculation speed. Compared with quansic boundary condition, it can improve the convergence speed in a small area and reduce the time-consuming of inversion.