A critical problem in inversion of geophysical data is developing a stable inverse problem solution that can simultaneously resolve complicated geological structures. The traditional way to obtain a stable solution is based on maximum smoothness criteria. This approach, however, provides smoothed unfocused images of real geoelectrical structures. Recently, a new approach to reconstruction of images has been developed based on a total variational stabilizing functional. However, in geophysical applications it still produces distorted images. In this paper we develop a new technique to solve this problem which we call focusing inversion images. It is based on specially selected stabilizing functionals, called minimum gradient support (MGS) functionals, which minimize the area where strong model parameter variations and discontinuity occur. We demonstrate that the MGS functional, in combination with the penalization function, helps to generate clearer and more focused images for geological structures than conventional maximum smoothness or total variation functionals. The method has been successfully tested on synthetic models and applied to real gravity data.

We develop a method of 3-D magnetic anomaly inversion based on traditional Tikhonov regularization theory. We use a minimum support stabilizing functional to generate a sharp, focused inverse image. An iterative inversion process is constructed in the space of weighted model parameters that accelerates the convergence and robustness of the method. The weighting functions are selected based on sensitivity analysis. To speed up the computations and to decrease the size of memory required, we use a compression technique based on cubic interpolation. Our method is designed for inversion of total magnetic anomalies, assuming the anomalous field is caused by induced magnetization only. The method is applied to synthetic data for typical models of magnetic anomalies and is tested on real airborne data provided by ExxonMobil Upstream Research Company.

We develop a new method for interpretation of tensor gravity field component data, based on regularized focusing inversion. The focusing inversion makes its possible to reconstruct a sharper image of the geological target than conventional maximum smoothness inversion. This new technique can be efficiently applied for the interpretation of gravity gradiometer data, which are sensitive to local density anomalies. The numerical modeling and inversion results show that the resolution of the gravity method can be improved significantly if we use tensor gravity data for interpretation. We also apply our method for inversion of the gradient gravity data collected by BHP Billiton over the Cannington Ag-Pb-Zn orebody in Queensland, Australia. The comparison with the drilling results demonstrates a remarkable correlation between the density anomaly reconstructed by the gravity gradient data and the true structure of the orebody. This result indicates that the emerging new geophysical technology of the airborne gravity gradient observations can improve significantly the practical effectiveness of the gravity method in mineral exploration.

It is often argued that 3D inversion of entire airborne electromagnetic (AEM) surveys is impractical, and that 1D methods provide the only viable option for quantitative interpretation. However, real geological formations are 3D by nature and 3D inversion is required to produce accurate images of the subsurface. To that end, we show that it is practical to invert entire AEM surveys to 3D conductivity models with hundreds of thousands if not millions of elements. The key to solving a 3D AEM inversion problem is the application of a moving footprint approach. We have exploited the fact that the area of the footprint of an AEM system is significantly smaller than the area of an AEM survey, and developed a robust 3D inversion method that uses a moving footprint. Our implementation is based on the 3D integral equation method for computing data and sensitivities, and uses the re-weighted regularised conjugate gradient method for minimising the objective functional. We demonstrate our methodology with the 3D inversion of AEM data acquired for salinity mapping over the Bookpurnong Irrigation District in South Australia. We have inverted 146 line km of RESOLVE data for a 3D conductivity model with ~310 000 elements in 45 min using just five processors of a multi-processor workstation.

We present a new formulation of the integral equation (IE) method for three-dimensional (3D) electromagnetic (EM) modeling in complex structures with inhomogeneous background conductivity (IBC). This method overcomes the standard limitation of the conventional IE method related to the use of a horizontally layered background only. The new 3D IE EM modeling method still employs the Green's functions for a horizontally layered 1D model. However, the new method allows us to use an inhomogeneous background with the IE method. We also introduce an approach for accuracy control of the IBC IE method. This new approach provides us with the ability to improve the accuracy of computations by applying the IBC technique iteratively. This approach seems to be extremely useful in computing EM data for multiple geologic models with some common geoelectrical features, like terrain, bathymetry, or other known structures. It may find wide application in an inverse problem solution, where we have to keep some known geologic structures unchanged during the iterative inversion. The method was carefully tested for modeling the EM field for complex structures with a known variable background conductivity. The effectiveness of this approach is illustrated by modeling marine controlled-source electromagnetic (MCSEM) data in the area of Gemini Prospect, Gulf of Mexico.