3D frequency-domain CSEM inversion

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 3D inversion speed, if the frequency is lower or resistivity is higher in the control equation in 3D electromagnetic 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 3D finite 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 3D numerical solution and the effectiveness of the grid design, we use a 3D program to calculate apparent resistivity and phase responses of a layered model, and make comparisons with the 1D analytical 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 3D inversion, and the L-BFGS algorithm is more suitable for dealing with 3D inversion 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 3D inversion. 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 3D inversion can be improved.