Open AccessComputational recipes for electromagnetic inverse problems
Author(s) -
Egbert Gary D.,
Kelbert Anna
Publication year - 2012
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2011.05347.x
Subject(s) - jacobian matrix and determinant , magnetotellurics , inversion (geology) , inverse problem , computation , computer science , inverse theory , inverse , mathematics , algorithm , conjugate gradient method , geophysics , mathematical analysis , geology , geometry , physics , surface wave , seismology , telecommunications , quantum mechanics , tectonics , electrical resistivity and conductivity
SUMMARY The Jacobian of the non‐linear mapping from model parameters to observations is a key component in all gradient‐based inversion methods, including variants on Gauss–Newton and non‐linear conjugate gradients. Here, we develop a general mathematical framework for Jacobian computations arising in electromagnetic (EM) geophysical inverse problems. Our analysis, which is based on the discrete formulation of the forward problem, divides computations into components (data functionals, forward and adjoint solvers, model parameter mappings), and clarifies dependencies among these elements within realistic numerical inversion codes. To be concrete, we focus much of the specific discussion on 2‐D and 3‐D magnetotelluric (MT) inverse problems, but our analysis is applicable to a wide range of active and passive source EM methods. The general theory developed here provides the basis for development of a modular system of computer codes for inversion of EM geophysical data, which we summarize at the end of the paper.