Inverting gravity data is an important geophysical method for imaging underground structures, but it naturally suffers from non-uniqueness. To produce solutions that make geological sense, some form of regularization is necessary. This paper presents an improved methodology for 3D gravity data inversion using higher-order total variation regularization techniques. Traditional first-order TV regularization has proved effective for blocky geological structures with sharp contrasts but often fails when the subsurface features are complex. We propose second and third-order TV regularization schemes that have the strengths of classical TV but provide much greater flexibility in handling more general geological contexts. The optimization problem including these higher-order regularization terms is solved by the reweighted regularized conjugate gradient algorithm, carefully addressing the parameters selection and focusing strategies. We demonstrate the effectiveness of our approach through synthetic examples, including a dipping dyke model and a multiple blocks scenario, where the higher-order TV methods give better performance for the reconstruction of subsurface structures compared to the minimum norm and first-order TV regularization. Then, the methodology was further validated using field data from the Thunderbird V-Ti-Fe deposit, Ontario, Canada, where the inversion of airborne gravity gradiometer data successfully revealed subsurface density distributions well-matched by the known geological and drilling data. The results illustrate that the higher-order TV regularization produces a more focused and geologically plausible model, especially in resolving complex structures at different levels. Current advances in inversion methodology are offering superior performance for applications in mineral exploration and geological studies.
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