  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.
