Joint gravity and magnetic inversion with trans-dimensional alpha shapes and autoregressive noise models

Abstract

Typical geophysical inverse problems are ill-posed and non-unique which causes challenges for interpretation. To address these issues, deterministic inversion methods often apply constraints to parameter values, which control the effective number of parameters. However, such approaches can inhibit inference on complex structural boundaries. Bayesian trans-dimensional (trans-D) parametrizations for Earth structure partition space based on data information with the ability to adapt the parametrization locally to data information. Therefore, trans-D approaches can avoid under- or over-parametrizing regions of the model. Nonetheless, these parametrizations depend on the choice of partitioning types, such as Voronoi nodes or wavelet decomposition. In addition, trade-offs exist between spatial resolution and correlated data errors. We present a hierarchical model that treats both spatial and data noise parametrizations as trans-D to better incorporate trade-offs between noise and structure into uncertainty quantification. This includes a hierarchical spatial partitioning based on linear and nearest-neighbor interpolations and alpha shapes. The alpha shapes provide advantages for the inversion of potential field data by permitting flexibility in the shapes of structures of interest. The trans-D autoregressive noise model quantifies the impact of correlated noise on geophysical parameter estimates. We compare these methods with nested Voronoi partitioning and show differences in uncertainties, data fit, and parsimony of the parametrizations. Studies on simulated data show well-resolved structures and successful decorrelation of data residuals while requiring few parameters. The inversion of field data infers basement and salt broadly consistent with previous studies, but results show additional details that are consistent with independent geological knowledge.