基于非结构网格的电阻率三维带地形反演

地表起伏地形在野外矿产资源勘察中不可避免, 其对直流电阻率法勘探影响巨大.近年来, 电阻率三维正演取得诸多进展, 特别是应用非结构网格我们能够进行任意复杂地形和几何模型的电阻率三维数值模拟, 但面向实际应用的起伏地形下电阻率三维反演依然困难.本文基于非结构化四面体网格, 并考虑到应用GPS/GNSS时, 区域地球物理调查中可非规则布设测网的实际特点, 实现了任意地形(平坦或起伏)条件下、任意布设的偶极-偶极视电阻率数据的不完全Gauss-Newton三维反演.合成数据的反演结果表明了方法的有效性, 可应用于复杂野外环境下的三维电法勘探.

3D resistivity inversion incorporating topography based on unstructured meshes

Surface topographies have a great influence for the direct current(DC)resistivity methods, which cannot be avoided in actual mineral explorations. 3D DC resistivity forward modeling is available in recent years, especially for arbitrary topography and complicated subsurface structures using unstructured grids. However, surface topography is still a challenge for 3D interpretation in realistic applications, which may cause significant error in the 3D resistivity inversion without topography. Additionally it is a hard work to lay measurement points on regular observation network in complex terrains and the corresponding data cannot be simulated on ordinary structured grid. Therefore, 3D resistivity inversion incorporating topography based on unstructured meshes is necessary.#br#We use unstructured finite element method for 3D resistivity forward modeling in order to simulate arbitrary topography and complicated subsurface structures. Our modeling result for a sphere model shows high accuracy in comparison with analytical solution. On the basis, we implement an inexact Gauss-Newton inversion for dipole-dipole configuration on arbitrary surface topography. With the development of GPS/GNSS technique, it is not necessary to lay measurement points on regular observation network exactly in the field survey. The inversion method developed in this paper can inverse the resistivity data from arbitrary dipole-dipole measurements, which is more convenient for 3D interpretation in realistic applications.#br#A random acquisition system for arbitrary dipole-dipole measurements is designed, including 16 dipoles as transmitted electrodes and 100 random diploes as receiver electrodes, i.e. 1600 random dipole-dipole apparent resistivities. Firstly, flat terrain models are used to verify our 3D resistivity inversion for the random dipole-dipole apparent resistivities data, obtaining the inverted model in good agreement with subsurface geoelectrical structures. Then a high resistivity model under a mountain ridge is simulated to show the significant influence from surface topography. The 3D resistivity inversion obtains a low resistivity structure if the topography is ignored, showing a wrong subsurface structure. Our 3D resistivity inversion incorporating topography based on unstructured meshes, in which the topography is directly incorporated into the inversion algorithm, obtains the true high resistivity structure under a mountain ridge. The 3D inversions for models with complicated topography also turn out to be very successful. All dipole-dipole apparent resistivities data for synthetic examples above are generated with 5% Gaussian errors. The 3D resistivity inversion for synthetic data with 10% Gaussian errors is presented finally. Good result shows the 3D resistivity inversion algorithm in this study is very robust.#br#It becomes simple and practicable for the location of measurement points in field geophysical survey using modern GPS/GNSS technique, providing favorable conditions for flexible and efficient 3D resistivity field measurements. In combination to 3D resistivity modeling using unstructured finite element method, we implement an inexact Gauss-Newton 3D resistivity inversion for the random dipole-dipole measurements on arbitrary surface topographies. Synthetic examples show our 3D inversion routines obtain good results for theoretical model and simulated realistic model with complicated topography. The 3D resistivity inversion for synthetic data with 10% Gaussian errors converges stably and the result is also reliable. The 3D resistivity inversion incorporating topography based on unstructured meshes in this paper promotes a key step towards the 3D field interpretation in realistic applications.