Using homotopy to invert geophysical data.

Jegen, Marion , Everett, M. and Schultz, A. (2001) Using homotopy to invert geophysical data. Geophysics, 66 (6). pp. 1749-1760. DOI 10.1190/1.1487117.

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Homotopy is a powerful tool for solving nonlinear equations. It is used here to solve small‐dimensional geophysical inverse problems by locating the solutions of the governing normal equations. An Euler‐Newton numerical continuation scheme is used to map trajectories in model space that start from a prescribed solution to a trivial set of equations and terminate at a solution to the inverse problem. The trajectories often map out a continuum of equivalent solutions that are caused by model equivalences or overparameterization. This allows exploration of the solution space topology. The homotopy method, in this application, is relatively insensitive to the choice of starting model. Several examples based on synthetic controlled‐source electromagnetic (CSEM) responses are shown to illustrate the method. An inversion of actual CSEM data from the Canadian Shield is also provided.

Document Type: Article
Keywords: Electromagnetic methods, homotopy, geophysical data, CSEM data
Refereed: Yes
Open Access Journal?: No
DOI etc.: 10.1190/1.1487117
ISSN: 0016-8033
Date Deposited: 10 Dec 2012 17:10
Last Modified: 18 May 2017 10:13

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