电导率连续变化大地电磁无网格法数值模拟

摘要

针对地下空间目标体多为电性参数连续变化且分布形态复杂等特点,结合无网格法物性参数加载方便、计算精度较高、自适应分析便利等优势,基于径向基函数构造了连续导电模型下的形函数,推导了等价线性方程组,进行了电导率连续变化的二维大地电磁数值模拟,给出了形状参数最优值.通过电导率连续变化的水平层状模型验证了算法的正确性,计算结果均方根相对误差不超过0.36%,精度优于有限元法.讨论了电导率连续变化的水平模型与均匀分块模型的电磁响应差异,对连续变化的地堑模型和不同倾斜角度下油藏注水模型进行了数值模拟.研究表明:连续变化模型和均匀分块模型差异明显,在实际反演解释中采用连续变化模型有利于提高反演的精度;TM模式的观测方式对于异常体的倾斜分布具有更好的分辨能力;无网格法避免了复杂的模型输入和网格的生成,更适合计算电性参数连续变化和复杂分布的异常体响应,将成为复杂电性和分布形态下电磁探测高精度数值模拟新方法.%In view of the problem in which most target bodies are continuously changing and the distribution is complex in the actual geological structures,2-D magnetotelluric forward modeling is simulated combined with the advantage of meshfree method where parameter loading is convenient,calculation accuracy is high and adaptive analysis is convenient.The shape function of the continuous medium model is constructed by the radial basis function,the equivalent linear equations are derived and the corresponding program is compiled.The optimal values of the shape parameters are given by numerical experiments.The correctness of meshfree method is verified by a horizontal continuous variation layered model.The root mean square error of the calculation results is not more than 0.36%,and its accuracy is superior to the finite element method.The electromagnetic response of the horizontal layer with the continuous variation of electrical conductivity and the uniform block model is discussed,and a graben terrain model and a reservoir water flooding model whose conductivity is continuously variable are calculated,respectively.The conclusions are given: the electromagnetic responses between the continuous variation model and uniform block model are significantly different,the use of the continuous variation model is helpful to improve the accuracy of inversion in the actual interpretation,and the observation method of the TM mode has better resolution for the inclination distribution of anomalous body.The meshfree method does not need the complicated mesh generation,and it is more suitable to calculate the response of continuous variation and complex distribution models.Therefore,meshfree method is expected to be a new and robust method for the numerical simulation of complex medium and complex structures.