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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. [ABSTRACT FROM AUTHOR]

Gravity gradient tensors (GGTs) are used to investigate the density of subsurface structures in the Earth's crust and can reduce ambiguity during data interpretation. However, costs and research area restrictions often prevent their application during surveys, thereby limiting their utility. To address this limitation, a matrix equation based on the Taylor series expansion that uses the gravity vector and its neighbours was formulated to obtain the GGTs. Higher-order derivatives of the gravity vector were utilized to constrain the calculation, which improved the accuracy of the transformation. Synthetic data were used to demonstrate that the proposed approach improved accuracy when the radial component of the gravity vector was transformed into GGTs. This approach was also applied to gravity data from the Otway Basin in Australia. Compared with the measured GGT, the results obtained using the proposed approach had a relative error of 0.46. [ABSTRACT FROM AUTHOR]

The equivalent source technique is a powerful and widely used method for processing gravity and magnetic data. Nevertheless, its major drawback is the large computational cost in terms of processing time and computer memory. We present two techniques for reducing the computational cost of equivalent source processing: block-averaging source locations and the gradient-boosted equivalent source algorithm. Through block-averaging, we reduce the number of source coefficients that must be estimated while retaining the minimum desired resolution in the final processed data. With the gradient-boosting method, we estimate the sources coefficients in small batches along overlapping windows, allowing us to reduce the computer memory requirements arbitrarily to conform to the constraints of the available hardware. We show that the combination of block-averaging and gradient-boosted equivalent sources is capable of producing accurate interpolations through tests against synthetic data. Moreover, we demonstrate the feasibility of our method by gridding a gravity data set covering Australia with over 1.7 million observations using a modest personal computer. [ABSTRACT FROM AUTHOR]