【作者】 韩江涛；

【导师】 刘国兴；

【作者基本信息】 吉林大学 ， 地球探测与信息技术， 2009， 博士

【摘要】 起伏地表问题一直是三维电阻率法勘探中一项重要的研究课题,对其进行数值模拟研究关键问题有两点:其一、三维起伏地形及其它边界条件的精确描述;其二、三维复杂地电模型的精确描述。本文通过网格映射方案将起伏地表转换成水平地表解决第一问题;通过网格类算法的代表——有限差分法解决第二问题。根据网格映射原理,推导出坐标变换后稳定电流场的基本方程和边界条件,在变换后空间采用有限差分法数值模拟,最后将计算结果回归到原空间,实现了起伏地表条件下三维电阻率法正演问题。未知节点电位的求取最终归结到线性方程组Au = f的求解上,由于三维问题网格节点众多,如何节约存储空间和提高计算速度是其关键。在此,系数矩阵采用一维压缩存储方案,在线性方程组求解上比较了常规的共轭梯度法(CG)和基于LU分解的乔勒斯基共轭梯度法(ICCG),计算结果表明:后者计算速度比常规共轭梯度法快一倍,可以处理网格精细剖分的三维电阻率法数值模拟问题。通过编制程序,系统地研究了不同地形形态、不同地电条件、不同装置条件下的直流电场响应,得到了具有参考价值的结论;探讨了三维电阻率法在探测断层、接触带等常见地质单元时受地形影响的规律;对复杂地表条件,即起伏地形和浅部不均匀体组合存在时视电阻率异常特征进行分析,同时总结了消除二者影响后异常的分布规律。通过上述若干问题研究,为起伏地表三维电阻率法实际勘探工作提供理论依据。更多还原

【Abstract】 Resistivity method is a group of exploration methods based on different stone conductivities between rocks (mining),solving a group of geological problems through the observation and research by the distribution of the artificial electric field underground. With the improving of the body awareness level and the complex of the exploration objectives, the development of resistivity method has also encountered some problems, such as complex terrain, abnormal response of multiple objects, the cognition of three-dimensional observation methods and so on. We also encounter some problems in practical production, the reserves of temporary mines is limited in our nation and nearly to bankrupt. So we need to explore more unconscious mines especially in northwest and southwest China. The topography in these areas is so complicated that it will be influenced by the topography if we develop resistivity method to detect mines in these places. However, due to the development of computer technology and mathematic theory, we gain a better use of numerical simulation. So it’s suitable to use numerical simulation method to study the 3-D resistivity method on the basis of irregular topography.The character of the simulated medium and boundary shape both causes impacts on the DC field and both of the impacts are essential. With the level of calculating technology and the development of the hardware, there is no problem on complicate medium simulating in DC field. This paper using the finite difference method, using the cube subdivision method when discrete grids, if the grids are subdivided slimly enough, we can also implement the simulation of the complicate medium; On the contrary, it’s hard to implement the numerical simulation of the irregular surface. The key of this problem is the boundary condition that depends on the normal and tangential directions of the boundary .Therefore, numerical simulation program must be precise to identify all nodes of normal and tangential direction. This paper uses a strategy of“grid mapping”to implement it. Tessmer and some other people have raised a method called the indirect method or methods of“grid mapping”to solve the irregular terrain problem, Hestholm transformed the“grid mapping”method and combined with the finite difference method, studying the numerical simulation of visco-elastic medium model in the condition of irregular surface. In this paper, we use the“Tessmer mapping”method dealing with the irregular problems and bring the terrain function into the control equation directly, cast light upon the control function that in the physical domain coordinate, deduce the current field control equation with terrain in orthogonal domain, when simulating the stability of current field. Combine with the finite difference method in computational domain so as to realize the forward calculation of three-dimensional resistivity method.Every processing method on the condition of irregular topography cannot characterize the boundary conditions completely, grid mapping method cannot either. The calculating of this method refers to the first and second partial directional derivative of topography. The extra differential coefficient results in the complicated formation of the basic functions. In spite that we can use this method to process any complicated topography, and can combine the method with any complicated medium models, it stills results in the instability in the process of mapping when the curvature of the topography is big or the curvature changes dramatically. So this method is suitable to process the terrain with small curvature and smooth surface such as hills or the terrain with small changed curvature and continuous curvature such as valleys.In the process of the numerical simulation to form the linear differential equations, it involves the storage of the coefficient and the calculate of the large-scale linear equations inevitably .In case of the node character of the discrete coefficient matrix is sparse matrix, this paper adopts one-dimensional compression storage program proposed by Wu Xiaoping, this program saves much storage space. In the comparison of the common conjugate gradient method and the conjugate gradient method based on LU decomposition on the stage of solving linear equations, the latter calculation has a double speed. A computer with a CPU which basic frequency is 1.9GHz, can calculate a supple point within about 10 seconds using a 3-D model with the size of 45×23×17.Analysis the influenced laws that caused by terrains qualitatively and quantitatively when using the 3-D resistivity method through the numerical simulation of some typical terrain models. The abnormal resistivity surveyed by medium gradient method is enantiomorphous to terrain; While pole-pole method is opposite because it’s abnormal resistivity is coherent with terrain; The abnormal resistivity surveyed by tri-electrodes method is coherent with terrain when the polar distance is small, abnormal resistivity is enantiomorphous to terrain when the polar distance is bigger. The symmetry four-electrode method is similar to the tri-electrodes method, the difference is that it has a lower influence compared to the tri-electrodes method, the pure terrain abnormity mainly distributes in the portrait; The abnormity surveyed by dipole-dipole method is coherent with terrain, and dipole-dipole method is greatly influenced by terrain, the pure terrain abnormity mainly distributes in the horizon. Analysis the influence quantitatively, here is an example of a valley which span is D in horizon: the pole-pole method has an low influence, when the polar distance AM=D/2,the influence is the biggest, when AM=D the influence is getting weak; As to tri-electrodes, when surveying at right below the valley that AO=2D,the influence is at it’s peak value, when surveying at the two foot sides that AO=D, the terrain has a biggest influence, if the polar distance is AB=D ,the terrain also has a biggest influence, it getting to weak when AB=2D;As to symmetry four-electrode method ,when surveying at right below the valley that AB=2D, terrain has a serious influence, when measuring at the foot sides of the valley AB=D, the terrain has a biggest influence, when AB=2D the influence becomes to incline; As to dipole-dipole method, when the polar distance is OO′=D, terrain has a serious influence, when OO′=2D, the influence becomes to incline; when there is a combination of few kinds of terrain, the influence law from pure terrain is similar to a single terrain, but the abnormity is much confused because of the inter influence between different terrains. So we have to pay more attention in the interpretation of the practical data.By numerical simulation analysis to some geology tectonics of some special models, such as slip fault with low resistivity, perpendicular contact, abnormal body near surface and so on, conclude some aberrance law of apparent resistivity abnormity in the condition of irregular terrain.(1)We can adopt a reasonable exploration device to gain a big abnormal response if the slip faults in the area has a low resistivity, have to point out that transverse section method has a better abnormal resistivity response compared to portrait section method. The transverse section method requires a low polar distance, if we can choose a right polar distance, we could gain a good surveying result.(2)Terrain effects can change the abnormity apparent resistivity laws if survey in the perpendicular contact, the areas that are influenced seriously are the foot sides of valleys or hills. The superimposes of different terrains destroy the original abnormity laws in the perpendicular contact. The influences on hills are bigger than valleys when both of the two terrains have the same angels.(3)We can eliminate the influence caused by complicated terrain (combination of irregular terrain and abnormal body) in a big degree using a correcting function, while due to the ignore of influence and the high-order term in the function, the correct results cannot coherent with the value of background completely. The abnormity laws form corrected data have a direct relationship with the surveying devices, the position of inflexion and the position of inhomogeneous body.Using the numerical simulation analysis above, we can provide theories and references to the practical survey when using 3-D resistivity method in the irregular topography.更多还原