3D DC Resistivity Inversion Using Weighted Regularized Conjugate Gradient Method

Resistivity method is an important branch in the geophysical exploration and plays a very important role in nation-building. Resistivity method has important application fields such as detection hidden danger in large engineering foundation, exploration of concealed mineral resources etc. However the applications of DC method still meet series of problems:3D problems, under complex terrain, strong interference, multiple targets and so on. In order to solve these problems, it is necessary to develop a3D resistivity inversion algorithm on undulate topography. This paper using weighted regularized conjugate gradient method to achieve the3D resistivity inversion algorithm on undulate topography on the base of triangular prism element subdivision finite element forward modeling algorithm.For3D forward modeling, this paper use triangular prism element as a subunit of the finite element algorithm, which can easily simulate any angle undulate terrain. The comparison of simulation result with the analytical solution in two-layer model to meet the error requirement. The computing speed is fast that it takes only6minutes at a time for18000nodes,155power supply points, five section and using dipole-dipole device. The computational accuracy and high speed laid the foundation for the inversion interpretation. For3D resistivity inversion algorithm on undulate topography, the weighted regularized conjugate gradient method is adopted to solve optimization problems. Due to the introduction of the weighted regularization thought, the inversion algorithm effectively solved the problem of the objective function divergent when doing iteration and ensured the stability of the inversion. Due to the calculation data of sensitivity matrix in3D inversion iteration will take up a lot of CPU time problem, this paper use the reciprocal theorem to calculate the sensitivity matrix, it take only one time to get the result, which greatly increasing the speed. On this basis, we analyze the sensitivity matrix and discuss the resolution of shallow and deep grid cell. In order to improve the resolution of deep structure, the ideas of changeable sensitivity matrix is proposed.The numerical tests on theoretical model analysis show that the deep resolution is enhanced and this algorithm still has the ability to resist noise, as a result prove its effectiveness. Using FORTRAN compiles the program3D inversion, comparing with the results of the traditional conjugate gradient method and fixed damping least squares method calculated results for simple low resistance body model, separately and analyzing the inversion of models with topography and without topography. The results show that the weighted regularized conjugate gradient inversion algorithm can both guarantee the stable inversion convergence, and could be suitable for undulate topography inversion at the same time, to achieve satisfactory results.