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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]

We propose a new framework for incorporating petrophysical and geological information into voxel-based geophysical inversion. By developing the geophysical inverse problem from a probabilistic perspective, we redesign the objective function and the iteration steps as a suite of cyclic optimization problems in which three separate MAP optimization problems are solved using geophysical, petrophysical and geological data, respectively. By quantitatively linking these data into a single framework, we recover a final inverted model that reproduces the observed, or desired, petrophysical and geological features while fitting the geophysical data. To achieve our goal we replace the Gaussian prior, used in the Tikhonov inversion approach, by a Gaussian mixture model. After each geophysical model update, the mixture parameters (means, variances and proportions) are determined by the geophysical model and the expected characteristics of the lithologies through another optimization process using the expectation–maximization algorithm. We then classify the model cells into rock units according to the petrophysical and geological information. These two additional steps over the petrophysical and geological data result in a dynamic update of the reference model and associated weights and guide the inversion towards reproducing the expected petrophysical and geological characteristics. The resulting geophysical objective function does not require extra terms to include the additional petrophysical and geological information; this is an important distinction between our work and previous frameworks that carry out joint geophysical and petrophysical data inversion. We highlight different capabilities of our methodology by inverting magnetotelluric and direct-current resistivity data in 1-D and 2-D, respectively. Finally, we apply our framework to inverting airborne frequency domain data, acquired in Australia, for the detection and characterization of saline contamination of freshwater. [ABSTRACT FROM AUTHOR]

The variation of temperature in the crust is difficult to quantify due to the sparsity of surface heat flow observations and lack of measurements on the thermal properties of rocks at depth. We examine the degree to which the thermal structure of the crust can be constrained from the Curie depth and surface heat flow data in Southeastern Australia. We cast the inverse problem of heat conduction within a Bayesian framework and derive its adjoint so that we can efficiently find the optimal model that best reproduces the data and prior information on the thermal properties of the crust. Efficiency gains obtained from the adjoint method facilitate a detailed exploration of thermal structure in SE Australia, where we predict high temperatures within Precambrian rocks of 650 °C due to relatively high rates of heat production (0.9–1.4 μW m−3). In contrast, temperatures within dominantly Phanerozoic crust reach only 520 °C at the Moho due to the low rates of heat production in Cambrian mafic volcanics. A combination of the Curie depth and heat flow data is required to constrain the uncertainty of lower crustal temperatures to ±73 °C. We also show that parts of the crust are unconstrained if either data set is omitted from the inversion. [ABSTRACT FROM AUTHOR]