3-D DC Resistivity Anisotropic Responses Forward Modeling Based On Unstructured Adaptive Finite-element Method

Direct current resistivity method is widely used in geophysical experiments and exploration of energy and minerals.Because the direct current stable electric field is influenced greatly by the change of resistivity,so whether in numerical simulation experiments or engineering exploration,the direct current resistivity method has shown its good ability to distinguish the underground abnormal resistivity.Compared with the present geophysical prospecting methods,the instruments of direct current resistivity method is simple and costs lowly,which is both rather suitable for small-scale underground water and subterranean heat exploration and fit for the large-scale geological investigation.In addition,the arrays of direct current resistivity method is very simple and convenient to move,so you will enjoy a high efficiency when choosing this geophysical method.However,geophysical exploration has stepped up a new step in recent years,under which situation,high precision and high resolution in energy explorations have become a hot spot.Therefore,improving the simulation theory of the direct current resistivity method and carrying out three dimensional simulations which can better simulate and compute the actual complex geological conditions become the next research direction.So as to carry out the above research,this paper uses the adaptive finite element method to simulate the complex medium of arbitrary electric anisotropy and analyzes the characteristics of the anisotropic response,based on the unstructured grids.In order to further improve the present three dimensional direct current resistivity method forward modeling theory,this paper combines the current adaptive finite element method with the unstructured grids.Unstructured grids can simulate arbitrarily irregular interfaces,which can be used to solve the low precision problem caused by the traditional structural grid simulation.In addition,we propose a local mesh refinement strategy using the posteriori error estimation based on gradient recovery.First of all,we preliminarily estimate the posterior error of each element using the posterior error method based on gradient recovery,then we set different error thresholds in the source region,the anomaly body region and the other computing regions.At last,we compare the posterior error of each element with the thresholds set before.When the posterior error exceeds the threshold,we will calculate the refined volume of this element according to the adaptive mesh refinement strategy.When the posterior is smaller than the threshold,we will keep the volume of this element unchanged.After this evaluating,we will write the refined volume of every element in the mesh generation file and regenerate a new mesh by software Tetgen.This grids adaptive refinement strategy successfully solve the problem of excessive memory in simulation computing.It not only realizes a reasonable generation of mesh,but also reduces the computing time of the forward modelling by sparing the computer memory.Great errors are often made in the current geophysical exploration inversion by using the isotropic medium as the initial model,because the actual geologic field is electric anisotropic.Considering this problem,we focused on simulating the complex arbitrary electric anisotropic model in this paper.In order to represent the three dimensional electric anisotropy,we introduce a three dimensional conductivity tensor and the Euler rotation.The principal conductivity tensor can be converted into any complex electrical anisotropic tensor form by Euler rotation,which is brought into the algorithm to compute.In the study of model computing and analysis,we first simulate and analyze the single homogeneous anisotropic medium.And by analyzing many typical models,we conclude the response law of the apparent resistivity when the principal electrical conductivity tensor rotates around the axis.Then,we simulate and compute the complex situation of arbitrary anisotropic abnormal body surrounded by arbitrarily anisotropic host rocks.We focused on distinguishing the arbitrarily anisotropic surrounding rock and arbitrarily anisotropic abnormal body and recognizing each principal conductivity tensor and rotated direction.After this,we simulate and compute the electric anisotropic ocean model.We improve the traditional detection method,by designing a simple and efficient two-boat towed exploration method.First we demonstrate the precision of the deep sea exploration algorithm.And then simulate the complex model that a resistive abnormal body surrounded by three-axis electric anisotropic submarine sediments.The results show that the principal conductivity tensor and rotated direction of the electrical anisotropy of the sedimentary layer and the rough position of the abnormal body are well recognized,although the receiving data is influenced by the resistivity of the sea water.