Random Voronoi Cells Based Parsimonious Inversion: Methodology and Application to Global S wave Arrival Time Data
Abstract
Tikhonov regularization is usually adopted to tackle the ill-posed geophysical inverse problems. Though subjectively stable results can be obtained by incorporating a-priori damping and smoothing terms, there is no consensus about how and to what degree the regularization terms affect the final results. In this study, we propose a new method to solve linearized geophysical inverse problems by projecting the original high dimension model spaces into different sets of low dimension subspaces. The subspaces are formed by piecewise constant functions on Voronoi cells, which are randomly distributed via a Poisson process. We then solve each low dimension normal equation with 'LSQR'. The final results can be retrieved by stacking, or a linear combination, of the projected images from different sets of Voronoi cells. The low dimension problems are well posed, and thus explicit regularization is not necessary. We evaluate the fidelity of our method with synthetic tests and apply the method to the ISC-EHB S wave arrival times. We compare the resultant global S wave model with models from other research groups. At last, we discuss the reliability of the model uncertainty, which is estimated from different sets of projected results. We test how different number of Voronoi cells, how stacking via subspace clustering or linear combination by solving another norm equation via total variation constraints, affect the final results.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2018
- Bibcode:
- 2018AGUFM.S31D0537F
- Keywords:
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- 7260 Theory;
- SEISMOLOGYDE: 7270 Tomography;
- SEISMOLOGYDE: 7290 Computational seismology;
- SEISMOLOGY