Gravity and magnetic methods have been applied successfully to a wide variety of problems such as archaeological mapping, environmental clean up and mineral and petroleum exploration. Unfortunately, these methods have frequently been stigmatized as being nonunique and viewed with suspicion. The notion of non-uniqueness, however, stems mainly from the mathematical properties of potential fields and has little to do with realistic geologic scenarios. In reality, geologic units producing the gravity or magnetic data that we acquire in real-world problems do not have an arbitrary variability. Imposing simple restrictions on admissible solutions often leads to a definitive interpretation of potential field data. Practicing geophysicists have been implicitly doing it for decades, and now generalized inversion algorithms following a similar philosophy can do it too and perhaps do it better. In this presentation, I will first outline one basic approach to the 3D inversion of potentialfield data using Tikhonov regularization. This approach focuses on constructing physical property models or interfaces by minimizing a model objective function subject to fitting the observed data. Prior conception of geology and other independent information can be easily incorporated into the inversion so that geologically plausible models are produced. I will discuss aspects of numerical computation for large-scale problems and illustrate the effectiveness of the method by examples drawn from mineral and petroleum exploration.

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