大倾角地形下视电阻率数值模拟

APPARENT RESISTIVITY NUMERICAL SIMULATION UNDER STEEP TERRAIN

为解决大角度起伏地形即陡峭地形(如河流阶地、冲沟、堤坝、山谷、山脊等)对实测视电阻率的影响问题,这里优化了三维有限元数值模拟中的单元积分形式,使之适合大倾角地形条件下对电阻率的数值模拟。为验证方法的正确性,采用保角变换计算了相近地形在均匀电流场情况下,陡峭地形引起的视电阻率变化特征。计算表明,对于缓倾斜地形,有限元数值模拟和保角变换结果比较一致;对于陡峭地形,两种方法计算的视电阻率形态一致,但视电阻率数值有一定差距,即有限元数值模拟的值要略小于保角变换的值。其原因是针对同一模型,两种方法逼近陡峭地形的程度不同,其中三维有限元所构造的模型更逼近实际模型,计算结果也更可靠一些,这对以后研究校正陡峭地形对视电阻率的影响具有理论和实际指导意义。

To solve the problems which has the impact on measured apparent resistivity caused by large-angle rugged terrain that is steep terrain(such as river terraces,gullies,dams,valleys,ridges,etc.),we optimize the 3-D finite element numerical simulation of integral unit in this paper,which is suitable for steep terrain conditions to the numerical simulation of resistivity.To verify the correctness of the method,conformal mapping was proposed on calculating the similar terrain of variation characteristics of apparent resistivity caused by steep terrain under uniform current field.Calculation shows that,the results of conformal mapping and finite element simulation are consistent well for the gently inclined terrain;for the steep terrain,the shapes of apparent resistivity curves calculated by two methods are the same,but there is a certain discrepancy on apparent resistivity values,that is to say,the value of finite element simulation is slightly less than conformal mapping for it has different degrees of approximation of the steep terrain by the two methods for a same model,in which the constructed of 3-D finite element model is closer to the actual mode and the results are more reliable which has theoretical and practical guiding significance on the study of correction of impact of the apparent resistivity caused by steep terrain in the future.