Application of the χ2 principle and unbiased predictive risk estimator for determining the regularization parameter in 3-D focusing gravity inversion

Saeed Vatankhah, Vahid E. Ardestani, Rosemary Renaut

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

The χ2 principle and the unbiased predictive risk estimator are used to determine optimal regularization parameters in the context of 3-D focusing gravity inversion with the minimum support stabilizer. At each iteration of the focusing inversion the minimum support stabilizer is determined and then the fidelity term is updated using the standard form transformation. Solution of the resulting Tikhonov functional is found efficiently using the singular value decomposition of the transformed model matrix, which also provides for efficient determination of the updated regularization parameter each step. Experimental 3-D simulations using synthetic data of a dipping dike and a cube anomaly demonstrate that both parameter estimation techniques outperform the Morozov discrepancy principle for determining the regularization parameter. Smaller relative errors of the reconstructed models are obtained with fewer iterations. Data acquired over the Gotvand dam site in the south-west of Iran are used to validate use of the methods for inversion of practical data and provide good estimates of anomalous structures within the subsurface.

Original languageEnglish (US)
Pages (from-to)265-277
Number of pages13
JournalGeophysical Journal International
Volume200
Issue number1
DOIs
StatePublished - Jan 1 2015

Keywords

  • Asia
  • Gravity anomalies and earth structure
  • Inverse theory
  • Numerical approximations and analysis
  • Tomography

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology

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