Analysis of singular values in a 3D joint inversion problem of MMT and MCSEM data

Abstract

Abstract Single value decomposition (SVD) is a mathematical method of decomposing a matrix into three other matrices that have very important properties of the original matrix. One of these matrices provides us with the singular values of the original matrix. By analysing these singular values, we can determine whether an inverse problem has an ambiguous solution or whether the solution is stable. With this analysis we can also check whether the estimated solution gives an exact fit to the data, find out which combinations of parameters can be determined by observations and which cannot, and more. In this work, SVD was applied to assess the feasibility of a joint 3D inversion of marine magnetotelluric method (MMT) and marine controlled source electromagnetic method (MCSEM) data, as these methods should theoretically provide complementary information. The singular values were generated from the Hessian matrix of each method and from the joint implementation, and we compared them by considering the null space of each method. The analysis of the singular values proved to be an important step before the iterative inversion process, indicating the feasibility of the inversion without spending much time. However, we still need to spend the time to calculate the Jacobian and Hessian matrices.