Research On Forward And Inversion Of 2D Borehole-to-surface Resistivity Method Based On Undulating Terrain

In the practical application of borehole resistivity method,the existence of undulating topography affects the data interpretation and inversion imaging in later work.The forward and inversion research of two-dimensional well to ground resistivity method in rugged terrain can improve the theoretical results of well to ground resistivity method and the applicability of well to ground resistivity method.Based on the finite difference method,the effect of relief terrain,power point source depth and resistivity of abnormal body on the apparent resistivity response of surface is studied by a large number of model tests.In the research of forward numerical simulation,the correctness of the algorithm is verified by the difference between the analytical solution and the numerical solution of the design model.Then,the paper designs the valley topography,the peak topography,and the valley topography coexisting with the peak topography,and carries on the model test under the above undulating topography conditions.The model test results show that:(1)Under the condition of mountain topography,the overall amplitude of the apparent resistivity response curve of the surface is increased due to the influence of the topography,and the observed data are most affected by the topography at the projection position of the point source of power supply;under the condition of valley topography,the amplitude of the apparent resistivity response curve of the surface is increased due to the influence of the topography at the projection position of the anomalous body and decreased at the region on both sides of the valley.(2)Under the condition of undulating topography,the influence of the depth of power supply point source on the surface apparent resistivity response mainly depends on the relative distance between the power supply point source and the anomalous body,and the smaller the relative distance is,the greater the impact on the surface apparent resistivity response.(3)Under undulating terrain conditions,when the resistivity of the abnormal body is lower than that of the surrounding rock,the greater the difference between the resistivity of the abnormal body and the resistivity of the surrounding rock,the more obvious the apparent resistivity response of the surface changes;when the resistivity of the abnormal body is higher than that of the surrounding rock,The smaller the difference between the resistivity of the abnormal body and the resistivity of the surrounding rock,the more obvious the apparent resistivity change of the surface.(4)Under the condition that the valleys and peaks coexist,the surface apparent resistivity difference caused by the terrain is obviously affected by the source depth of power supply,but is little affected by the change of the resistivity of abnormal body.In the aspect of well surface resistivity inversion,the basic theory of well surface resistivity inversion is described at first,and then the 2D resistivity inversion under the condition of bipolar device of well surface model is realized based on the principle of minimum structure method.Then the theoretical model is designed and the inversion program is validated by comparing the theoretical model with the inversion result.Model test results show that the proposed algorithm can effectively delineate the range of abnormal bodies.