Study Of 3D Resistivity Modeling And Inversion Using Unstructured Grids And Their Applications

The direct current (DC) resistivity methods is widely used in the geophysical explorations, which is based on the difference in the resistivities of rocks and minerals underground. Apparent resistivity is the common observed data from the DC resistivity methods. In the old days, an ordinary way to explain the observed data is to compare it with the analytical solution of the theoretical models. But the more complex the real structure is, the harder for people to find the analytical solution through the theory. With the development of computer technology, the 3D resistivity modeling is able to construct arbitrary structure of rocks and minerals underground. The modeling is usually based on finite difference method or finite element method. The numerical solution of the 3D resistivity modeling is helpful to explain the observed data. When using structured grids in the 3D resistivity modeling, the accuracy is limited by the quantity of the nodes in the grids. As a new technology, the unstructured grids can improve the accuracy of the 3D resistivity modeling with a small quantity of the nodes. Because the unstructured grids can be build up by tetrahedrons, it is more flexible than the structured grids when constructing the complex structure.Surface topographies have a great influence for the DC resistivity methods, which cannot be avoided in actual explorations.3D resistivity modeling is available in recent years, especially for arbitrary topography and complicated subsurface structure 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 grids. Therefore,3D resistivity inversion incorporating topography based on unstructured grids is necessary.We use finite element method based on unstructured grids for 3D resistivity modeling in order to simulate arbitrary topography and complicated subsurface structure. The numerical solutions of our modeling for sphere model and board model show high accuracy in comparison with analytical solutions. On the basis of 3D resistivity modeling, we implement an inexact Gauss-Newton inversion on arbitrary surface topography.Advanced detection in tunnel with DC resistivity methods is important to ensure the safety of the underground work. When using pole-dipole array to measure the resistivity in the tunnel, the apparent resistivity curve shows the influence around the tunnel. As the position of the minimum value in the apparent resistivity curve seems to have a relationship with the distance of the low resistivity anomaly in front of the tunnel, several prediction models have been developed by resistivity modeling or experimental measurements in recent year. However, only simple subsurface structure is considered so far. We are not sure whether the developed prediction models are accurate and reliable for the actual complicate subsurface structure. Moreover, anisotropic resistivity effect should be considered for advanced detection in tunnel. We use finite element method based on unstructured grids for 3D anisotropic resistivity modeling in tunnel. A linear equation to predict the distance of the low resistivity anomaly in front of the tunnel is developed. Then we use parallel Monte Carlo method for the design of huge number of random models and 3D resistivity modeling of these random models. The statistics results of the prediction for advanced detection in tunnel are analyzed to evaluate accuracy and reliability for different prediction models, illustrating our linear equation is more accurate and reliable for the advanced detection in tunnel. Finally we focus anisotropic resistivity effect and suggest that the available prediction models for the advanced detection in tunnel are completely unreliable especially when the background resistivity is anisotropic, resulting in safety problem.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. 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 structure. 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 grids, in which the topography is directly incorporated into the inversion algorithm, obtains the true high resistivity structure under a mountain ridge. The 3D resistivity 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 noise. The 3D resistivity inversion for synthetic data with higher Gaussian noise is presented finally. Good result shows the 3D resistivity inversion algorithm in this study is very robust.After all the synthetic examples, our 3D resistivity inversion is used to explain observed data from the actual explorations. As a result, our 3D resistivity inversion shows the underground structure well, the anomalies are shown clearly. With the success of the real mineral exploration, our resistivity inversion in this paper promotes a key step towards the 3D field interpretation.