三维频率域可控源电磁反演研究

3D frequency-domain CSEM inversion

对于三维可控源电磁,反演计算效率、张量测量、旁侧效应以及阴影效应是目前研究的热点.本文正演采用基于库仑规范条件的耦合势有限体积算法,反演采用有限内存BFGS(L-BFGS)算法.合成数据反演结果表明:(1)有限内存BFGS法比非线性共轭梯度法,在反演计算效率上具有一定的优势,更适合求解大规模三维可控源电磁反演问题.(2)张量可控源电磁法相对于标量可控源电磁法,前者在模型分辨率上优于后者.(3)在某个区域无法布置测网的情况下,我们可利用旁侧效应在异常体周围布置测网进行三维反演,从而获得真实异常体的信息.同时,为避免阴影效应,我们应在测网外增加可控源电磁控制点,使得三维反演的数据更加完备.

Recently,the frequency domain controlled-source electromagnetic method is playing an increasingly important role in oil and gas exploration,aviation near-surface survey and search for concealed metallic deposits.For three-dimensional controlled-source electromagnetic（3D-CSEM）inversion,the computation efficiency of inversion,tensor measurement,lateral effect and shadow effect are focused topics in recent research of this technology.In order to improve the 3Dinversion speed,if the frequency is lower or resistivity is higher in the control equation in 3Delectromagnetic forward modeling,directly dispersing the Maxwell＇s equations finally forms the large-scale complex coefficients sparse system of linear equations.The condition number of this system is large,which makes it difficult to converge when solving the equation.This work establishes a set of 3Dfinite volume algorithms based on the coupling potential to solve the problem of low number of induction.At present most linear inversion methods are based on linear search methods.How to choose the search direction is the core of the inversion method,and different search directions can yield different solutions.This paper adopts L-BFGS algorithm for inversion.To verify the correctness of 3Dnumerical solution and the effectiveness of the grid design,we use a 3Dprogram to calculate apparent resistivity and phase responses of a layered model,and make comparisons with the 1Danalytical solution.According to the inversion results of synthetic data,this paper analyzes the nonlinear conjugate gradient method and limited memory quasi-Newton method,compares the tensor of the controlled source electromagnetic method and the scalar controlled source electromagnetic method,and also analyzes the influence of the lateral effect and shadow effect.This paper presents comparison of the L-BFGS and NLCG algorithms.Firstly,we find that the execution efficiency of the L-BFGS algorithm is higher than NLCG algorithm in 3Dinversion,and the L-BFGS algorithm is more suitable for dealing with 3Dinversion of large amount of data.Secondly,comparing the 3D inversion results of the tensor observations and the scalar observations of survey data,we note that the former has a better effect than the latter in delineating the abnormal body and reflecting the true resistivity values.Finally,in the area in which survey network cannot be deployed,we can use the lateral effect for 3Dinversion.At the same time,in order to avoid the shadow effect in the field exploration,we should use 3D inversion to deal with the real data,and add the control points of CSEM outside the survey grid.On the basis of this work,adopting the way of encryption grid can improve the calculation accuracy.However,this will bring about more unknown parameters,and make inversion more singular.The next step,we may consider to separate the grid of forward modeling from inversion,so that the stability of the 3Dinversion can be improved.