Two and Three-Dimensional Inversion of Magnetotelluric Data: Annual Performance Report, 15 January 1987

摘要

Structure in terms of norms of the derivative of the conductivity (sigma) or logsigma with respect to a function of depth are measured. Models that minimize these norms for chosen levels of chi-squared misfit are found, using an iterative linearized algorithm. In most cases, the models found are very likely the global minima of these norms, as they do not depend on the starting model. It is demonstrated that overfitting data requires extraneous structure. Some choices of the depth function result in systematic overfitting of high frequencies, a 'blue' fit, and extraneous shallow structure. Others result in systematic overfitting of low frequencies, a 'red' fit, and extraneous deep structure. A robust statistic is used to test for whiteness, and show how to make the fit acceptably white by varying the depth function that defines the norm. Using artificial data, it is shown that the optimum norm produces an inversion which does not introduce false structure and which approaches the true structure in a reasonable way as data errors decrease. For models of sigma (but not logsigma) linearization errors are often so small that models may be reasonably interpreted as the true conductivity averaged through known resolution functions. 18 refs., 13 figs., 3 tabs. (ERA citation 12:021268)