Application of the $\chi^2$ principle and unbiased predictive risk estimator for determining the regularization parameter in 3D focusing gravity inversion

TL;DR

This paper introduces the use of the $hi^2$ principle and unbiased predictive risk estimator to optimize regularization parameters in 3D focusing gravity inversion, improving accuracy and efficiency over traditional methods.

Contribution

It applies the $hi^2$ principle and predictive risk estimator to 3D gravity inversion, demonstrating superior performance in synthetic and real data scenarios.

Findings

Both methods outperform Morozov discrepancy principle.

Smaller errors with fewer iterations in synthetic tests.

Effective in practical data from Gotvand dam site.

Abstract

The $\chi^2$ principle and the unbiased predictive risk estimator are used to determine optimal regularization parameters in the context of 3D 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 3D 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.