Rosemary Renaut, Arizona State University
Authors: Rosemary Renaut, Matthias Chung and Saeed Vatankhah
2023 AWM Research Symposium
Computational Inverse Problems and Uncertainty Quantification [Organized by Julianne Chung, Rosemary Renaut, and Malena Sabate-Landman]

Geophysics data from subsurface geometries give rise to magnetic and gravity potential fields that are measured only above, or at the surface, of the region to be recovered. The aim in the inversion is to reconstruct the subsurface structures in terms of magnetic susceptibility or density, respectively. The inversion problem is highly under determined; there are significantly fewer measurements than desired voxel values in the subsurface. These problems are highly susceptible to the noise in the data and are typically large scale. In this presentation I will present the results of inverting simulated and practical data sets using a new variable projection augmented Lagrange algorithm. The new algorithm is robust and provides comparable results as compared to the use of the standard iteratively reweighted approximation for finding the L1 regularized solution. Further, the algorithm is easily adapted to the case of missing data, and imposition of variable constraints on the parameters. Results for the inversion of kimberlite data will be used to illustrate the performance of the TV regularized algorithm.

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