瞬变电磁法基于有限差分的2.5维反演方法研究

项目名称： 瞬变电磁法基于有限差分的2.5维反演方法研究

项目编号： No.41504060

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 天文学、地球科学

项目作者： 李展辉

作者单位： 北京大学

项目金额： 20万元

中文摘要： 瞬变电磁法是一种国内外在资源、环境等领域具有广泛应用的近地表电磁勘探方法。虽然已有数十年的发展历史，但是主流的资料反演方法一直停留在一维阶段。国外在三维反演上虽有一定研究，但是三维反演计算量依然过大，其在实际应用中受到很大限制。而2.5维反演的研究在国内外均比较少。但是瞬变电磁2.5维反演相对一维反演能明显提高结果可靠性，而相对三维反演则能很大程度减小计算量，更有利于其在实际数据反演中的应用，对于瞬变电磁的进一步发展具有重要意义。本项目将从这一点出发，研究瞬变电磁法的2.5维反演方法。首先研究基于有限差分的2.5维正演方法，包括时间域与频率域，比较分析时间域与频率域方法各自的优劣。然后选取合适的模型约束矩阵与正则化因子，并利用SVD求解Occam反演迭代方程组。最后针对实际数据的具体情况，例如测线长度、地形等因素，对反演方法进行优化改进，完成反演算法从理论研究到实际应用的转换。

中文关键词： 瞬变电磁；有限差分；2.5维正演；Occam反演

英文摘要： Transient electromagnetic method is a widely used near surface survey tool in varies areas such as mineral resources exploration and water detection. However, via decades of development, data interpretation method still remains mainly in 1D inversion. Though some three dimensional inversion methods have been developed internationally, the computation is still too massive, which limits its application to real data. 2.5D inversion also didn’t have much research for transient electromagnetic data in the past, though some 2.5D inversion methods have been developed for frequency domain electromagnetic data. 2.5D inversion can improve the interpretation accuracy greatly compared to 1D inversion and the computation is much less than 3D inversion, which can help its application to real data greatly. This project comes out from this point. First a 2.5D forward modeling method based on a finite difference method will be developed in both time domain and frequency domain, respectively, with the sensitivity matrix calculated using the adjoint equation method corresponding to the form of the forward method. Then a proper model roughness matrix and regularization factor will be selected, and the SVD will be used to solve the Occam’s inversion equations. Varies of synthetic data will be used to test the 2.5D inversion method. Then some real cases will be studied to further test the inversion method. The program will be further improved and optimized according to the characteristics of real data, such as the length of a survey line and the topography in the area.

英文关键词： Transient electromagnetic;Finite difference;2.5 dimensional forward modeling;Occam’s inversion