Weighted cross-gradient function for joint inversion with the application to regional 3-D gravity and magnetic anomalies

In the absence of quantitative relationships, a cross-gradient function can be used to correlate unknown physical properties in a joint inversion of geophysical data sets. It introduces a structural correlation between properties. A commonly used, inexact approach adds a weighted cross-gradient term as a penalty to the cost function being minimized during inversion. This weighting factor needs to be tuned to balance the regularization and cross-gradient terms. In this paper we propose nonlinear weighting for the cross-gradient function which addresses the very different magnitudes of the cross-gradient and regularization terms. This approach also couples the weighting factors for the regularization and correlation terms reducing the number of tuning parameters. The approach is investigated for a synthetic case. Results are also shown for the 3-D joint inversion of high-resolution magnetic and gravity anomaly data from Southern Queensland in Australia with over 30 million cells.

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