Study Of3D Arbitrary Anisotropic Resistivity Modeling And Interpretation Using Unstructured Finite Element Methods

Electrical prospecting basing on isotropic theory generally achieves great success. It is widely applied in exploration of ore and hydrocarbon. It is also popular in near surface detection in hydrology, engineering, environment and crust, upper mantle detection. However, the underground anisotropy really exists and large errors will be produced if anisotropic structure is considered as isotropic. Isotropic resistivity is expressed as a scalar while anisotropic resistivity depends on directions and it is expressed as a tensor. Actually, isotropic resistivity is a special case of anisotropic resistivity. Two quantities should be used to express resistivity in transverse isotropic (VTI) media, just as laminating materials (e.g. sedimentary rock) and areas with horizontal fractures. In dipping laminated rocks and fracture areas, the resistivity is tilted transverse isotropic (TTI), whose resistivity should be expressed as three quantities. There are six independent quantities for arbitrary anisotropic resistivity. In hydrocarbon exploration and reservoir evaluation, the electrical anisotropy of superposed layers and fractured areas greatly influences the accuracy of evaluation of saturation. Besides, electrical anisotropy is especially important for earthquake monitoring and forecast because the anisotropy of resistivity reflects the stress of crust rocks and micro-fractures distribution in geo-electromagnetic monitoring. Owing to the complication of anisotropic theory, the interpretation of geo-electrical data is mainly focused on isotropic models at home and abroad. The research of anisotropic resistivity is just in preliminary step, which is mainly concerning the analytical solution and application of anisotropic half-space and1D model. However, these are far from actual applications because the real underground is generally3D and much more complex.There is almost no analytical solution in3D anisotropic resistivity media. It’s necessary to simulate anisotropic resistivity using numerical methods such as finite element (FE) method. Subsequently, mesh generation is very important which directly influences the efficiency and accuracy of3D FE modeling. We systematically discuss the influence of regular hexahedral grid, asymmetric tetrahedral grid (TS grid) and symmetric tetrahedral grid (TF grid) on3D FE modeling in this paper. It is found that artificial anisotropy exists when using TS grid which confuses us when analyzing anisotropic characteristics. We finish the3D arbitrary anisotropic resistivity modeling using unstructured finite element methods in the first time. Numerical code shows high accuracy and avoids artificial anisotropy. Besides, the unstructured grid also allows element quality controlling, local refinement and complex geometry simulation, which greatly improve the efficiency of3D FE modeling. For almost the same accuracy, both memory requirement and calculation time of3D unstructured FE modeling nearly reduce by one order in comparison to the modeling on regular grid.3D unstructured finite element simulations for typical TTI media reveal the serious distortion of results in two orthogonal directions. The excellent parameter of P2invariant used in isotropic media is found to be really efficient for3D complicated model, however, it shows limited accuracy while used in3D anisotropic media. Our3D FE simulation for a synthetic anisotropic model of energy exploration in hot-dry-rock area illustrates that the anisotropy of resistivity is able to reflect the fracture system by hydraulic pressure, showing significant potential in resource and energy explorations and exploitations.The resistivity imagings mainly focus on isotropic media at present. Two dimensional resistivity inversion has already been applied in real exploration and three dimensional resistivity inversion becomes fruitful as well. However, anisotropic resistivity inversion, especially two and three dimensional inversion is hardly seen because the forward modeling is not well solved so far. Basing on3D arbitrary anisotropic resistivity FE modeling, we can use the2D or3D isotropic inversion method to data set from2D or3D anisotropic model in order to measure the effect of anisotropy. Our results show the anisotropy may lead to great deviation in inverted model while the state-of-art2D and3D inversion methods faced on isotropic media are employed.