A novel approach to the model appraisal and resolution analysis of regularized geophysical inversion

Abstract

The existing techniques for appraisal of geophysical inverse images are based on calculating the model resolution and the model covariance matrices. In some applications, however, it becomes desirable to evaluate the upper bounds of the variations in the solution of the inverse problem. It is possible to use the Cauchy inequality for the regularized least-squares inversion to quantify the ability of an experiment to discriminate between two similar models in the presence of noise in the data. We present a new method for resolution analysis based on evaluating the spatial distribution of the upper bounds of the model variations and introduce a new characteristic of geophysical inversion, resolution density, as an inverse of these upper bounds. We derive an efficient numerical technique to compute the resolution density based on the spectral Lanczos decomposition method (SLDM). The methodology was tested on 3D synthetic linear and nonlinear electromagnetic (EM) data inversions, and also to interpret the helicopter-borne EM data collected by INCO Exploration in the Voisey’s Bay area of Canada.

Object-based model verification by a genetic algorithm approach: Application in archeological targets

“…Friedel, 2003;Günther, 2004;Zhdanov and Tolstaya, 2006). However, the parameter appraisal may need statistical analysis in genetic algorithms.…”

Metalliferous mining geophysics — State of the art after a decade in the new millennium

“…Schultz and Ruppel (2005) developed robust and convergent regularized, least-squares inversion algorithms for application in conductive terrains. Zhdanov and Tolstaya (2006) presented a new method for resolution analysis that is based on evaluating the spatial distribution of the upper bounds of the model variations, and they introduced a new characteristic of geophysical inversion -resolution density -as an inverse of those upper bounds. Pujol (2007) presented in a unified way the Levenberg-Marquardt damped least-squares method, which often is used in geophysical inversion.…”

Improved adaptive regularization for simulated annealing inversion of Transient Electromagnetic

“…When →0, the misfit functional plays a major role, while when →∞, the stabilizing functional is in a dominant position, and the inversion model is not at all data-driven. In literature, the initial regularization parameter is determined by the ratio of the misfit functional and the stabilizing functional of the initial model, and the attenuation coefficient is selected empirically according to the commonly used conventional adaptive regularization method 16,23 . This usually works well in linear inversion.…”

“…The key operations of these methods are changing the regularization parameters during inversion iterations. Applications of these adaptive regularization methods in linear inversion problems have been widely discussed [16][17][18] . However, there are only very few discussions of using this in stochastic inversions.…”