Application of the $χ^2$ principle and unbiased predictive risk estimator for determining the regularization parameter in 3D focusing gravity inversion
For geophysicists performing gravity inversion, this provides a more effective way to choose regularization parameters, improving model accuracy and convergence speed.
The paper applies the χ² principle and unbiased predictive risk estimator to determine optimal regularization parameters in 3D focusing gravity inversion, achieving smaller reconstruction errors and fewer iterations compared to the Morozov discrepancy principle in synthetic and real-world tests.
The $χ^2$ 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.