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有限单元法在直流电阻率法勘探中的研究及应用

The Study and Application of Finite Element Method in DC Resistivity Prospecting

【作者】 钟升明

【导师】 江玉乐;

【作者基本信息】 成都理工大学 , 地球探测与信息技术, 2010, 硕士

【摘要】 随着找矿程度的不断深入,浅部易于发现和利用的矿产日趋减少,对寻找深部有色金属矿藏的快速预测定位方法的研究已成为当今整个地质界的最重要研究课题之一。直流电阻率法是矿产资源勘查及水文地质和环境地质调查中,十分有效和应用相当广泛的一种物探方法。近年来,其应用领域不断拓宽,观测空间从地表发展到地下、水下。直流电阻率法正朝着高密度、高精度方向发展。与此同时,勘探地区地形越来越复杂,对直流电阻率法的资料处理解释也提出了新的要求。而长期以来,起伏地形条件下的地电异常的处理与解释是电法勘探中的一个难题,这一方面是由于问题本身比较复杂,另一方面是由于同时期的科技发展水平达不到。在数值模拟方法中,有限单元法因具有精度高、解题过程比较规范、能自动满足内部边界条件、适合于复杂地形的物性分布问题等优点而得以应用研究。本文从二维电性介质点源有限单元模拟出发,介绍了地电二维点源有限单元法原理,有限单元法中边界条件的选取、单元剖分、插值及单元合成,系数矩阵的形成,以及解方程的方法。然后重点对于多种地形(山脊、山谷、山脊与山谷组合)进行了大量的模拟计算,并对计算结果进行了较系统全面的分析和论证,总结出了起伏地形情况下的电阻率法剖面异常分布规律,较好地消除了地形在电阻率法剖面异常中的影响,确保了后期电性资料的地质、地球物理解释效果。最后借用他人对实际电性资料的应用结果,验证了该方法技术的有效性,说明了用有限单元法研究起伏复杂地形下电阻率剖面异常,对克服起伏地形的影响有一定的实际意义和应用前景。

【Abstract】 With the deepening level of prospecting, the shallow mineral easy to find and use has been dwindling, so the study for the methods of quick prediction location to search for deep non-ferrous metal deposits has become one of the most important topics in the entire geological community today. In the mineral exploration and hydro- geological and environmental geology survey, DC resistivity method is an effective and widely applied geophysical method.In recent years, DC resistivity method has been expanding constantly in the application field, with its observation space from surface to underground and underwater. DC resistivity method has developed in the direction of high-density and high-precision. At the same time, Topography of the area for exploration becomes more and more complex, which also puts forward to new requirements to data processing and interpretation of DC resistivity method.However, for a long time, the earth resistivity anomaly under the condition of rolling topography is a problem in electrical prospecting, which results from the complicated problem itself for one thing and the backward technological development in the same period for another thing. Among numerical simulation methods, finite element method is applied to research because of these advantages such as high precision, a fairly standard problem-solving process, satisfying the internal boundary conditions automatically, suitable for the physical distribution issues of complex terrain, and so on.Starting from finite element simulation of two-dimensional electric media for point source, this paper introduces the theory of two-dimensional finite element method for point source in section, selection of boundary conditions, cell triangulation, interpolation and unit synthesis of finite element method, and simulated calculation using high-density measurement on surface and well resistivity measurement to two-dimensional geoelectric model. Besides, data mapping has been done with data analysed qualitatively and quantitatively.This paper studys futher the resistivity profile anomaly under the undulating terrain, simulates forward resistivity profiles of a variety of typical geoelectric models and analyses the calculated results. And then it is summarized that the regularities of distribution about the resistivity profile anomaly under the undulating terrain, with the false anomaly eliminated successfully.Finally,the paper shows summarily that it is effective to research the resistivity profile anomaly with finite element method in terms of overcoming the effect of the complicated undulating terrain.

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