Research On Forward And Inversion Of 2.5D Borehole-ground Resistivity Method Under Undulating Terrain

For traditional surface observation methods,the exploration accuracy will decrease as the depth of the target anomaly body increases.Nowadays,the minerals and energy that are easy to find has been unable to meet the needs of the rapid development of industrial production.In order to improve the exploration accuracy of deep minerals,the borehole-ground observation method has become a better choice.Compared with the traditional surface observation method,the borehole-ground observation method arranges the power supply electrode that is closer to the target anomaly body in the borehole,which improves the anomaly response intensity.This paper combines the borehole-ground observation method and the resistivity method to compile the 2.5D forward and inverse algorithm suitable for undulating terrain,and systematically studies the anomaly characteristics of the target anomaly body under undulating terrain.In the forward research,starting from the basic relations and boundary conditions of the stable current field,this paper complete the 2.5D forward modeling of the borehole-ground resistivity method by the finite element method.The establishment of the geoelectric model,unstructured meshing and mesh encryption are all completed by Gmsh,which improves the efficiency of meshing.The large sparse matrix obtained by the finite element method is compressed and stored in the CSR format,which saves computer memory.Compared the efficiency of solving linear equations with various solvers in the Eigen library,and chose the direct LLT factorization solver to solve the linear equations in the forward modeling.Finally,using C++ language compile the 2.5D forward algorithm of borehole-ground resistivity method and the parallel forward algorithm by MPI..Using the parallel forward algorithm,we study the anomaly characteristics of the target anomaly body under the sharp valley terrain or the gentle valley terrain,and the influence of the pole-pole on borehole-ground observation device and the pole-dipole on borehole-ground observation device on the forward modeling results.The anomaly response generated by the sharp valley terrain is more obvious and prominent than the flat valley terrain.It has a greater impact on the abnormal response of the anomaly body.The amplitude of the abnormal response observed by the pole-dipole on borehole-ground observation device is higher than that of the pole-pole on borehole-ground observation device,and the abnormal shape is more complicated.In the inversion research,the least square method and the regularization theory are used to establish the inversion objective function.This paper completes the 2.5D inversion calculation of the borehole-ground resistivity method by the linear conjugate gradient method.In the solution of the partial derivative matrix,we only calculate the product of the partial derivative matrix and the vector,avoiding the difficulty of directly solving and storing the partial derivative matrix,which saves computer memory and speeds up the calculation speed of the inversion.The maximum smoothing constraint item is selected as the model constraint,we completed the 2.5D borehole-ground resistivity inversion algorithm and the parallel inversion algorithm based on MPI.Using the parallel inversion algorithm,we study the influence of undulating terrain on the typical anomaly body inversion results and the inversion result difference of the multi-angle water-bearing collapse column.The valley terrain will have some impacts on the anomaly body inversion results,while the ridge terrain has basically no effect on the anomaly body inversion results.The angular deviation of the water-bearing collapse column model will shift the distribution information represented by the low-resistance area in the inversion results,and we can only judge the approximate location of the waterbearing collapse column.