Improvements to a Probabilistic Joint Inversion of Magnetic and Gravimetric Data
Benjamin Moyer, University of Maryland, College Park
Geophysical inversions are a powerful tool for characterizing subsurface structure. Inversions of magnetic and gravimetric data provide constraints on variations in subsurface susceptibility and bulk density contrasts, such as those that arise from economically vital ore bodies. However, these inversions suffer from strong non-uniqueness and confounding interpretations. A probabilistic method, generating an ensemble of well-fitting models from which inferences can be extracted, offers distinct advantages over traditional techniques. This, however, comes at tremendous computational cost.
To address these challenges, we have developed an advanced trans-dimensional Bayesian method for understanding multi-scale variations in magnetic susceptibility and bulk density. We exploit three techniques for improving memory usage and computational efficiency to extend this method to large-scale three-dimensional model domains.
We explore the advantages of low-rank matrix approximation, compared to other methods of matrix compression, including wavelet decomposition, to make larger problems tractable. We use a quasi-random sampling scheme to explore the model space more uniformly, reducing the number of iterations necessary to converge to a stable region of the model space. Finally, we choose a parameterization based upon deviations from a “background” geologic unit. This allows us to further compress a working copy of the sensitivity matrix losslessly, converting it from a dense matrix to a sparse matrix with a resultant speed-up of the vector-matrix multiplication and even less memory consumption.