Efficient Probabilistic Inversion of Airborne Electromagnetic Data Under Spatial Constraints
Wednesday, 17 December 2014
Airborne electromagnetic (AEM) surveys are frequently used to delineate geological interfaces in the subsurface, such as the base of regolith or boundaries of an aquifer. However, inversion of AEM data is inherently non-unique, and estimating the robustness of models is often as important as finding a valid model. An example of this is groundwater modelling, where geological model uncertainty is one of the main sources of risk. In a Bayesian framework, Markov chain Monte Carlo (McMC) algorithms have been successful in mapping uncertainty in 1D model space corresponding to each AEM fiducial. But full McMC sampling for laterally-correlated models is computationally expensive, and independent 1D samplers are often the only feasible alternative. In these laterally independent 1D models, abrupt transverse changes in model parameters can occur, making it difficult to derive spatially coherent interfaces. By comparison, classically regularized deterministic inversions can take spatial correlation between 1D models into account, but provide little useful information about model uncertainty. Here we introduce a Bayesian parametric bootstrap approach to invert for layer properties, interfaces and related uncertainties, using a 1D kernel but incorporating lateral correlation. These methods treat Bayesian prior information on model uncertainty and its spatial correlation as implied observations, then apply the classical parametric bootstrap. Numerical examples demonstrate that our Bayesianized bootstrap will explore model space adequately for non-pathological situations, while requiring many fewer forward problem solves than a comparable McMC algorithm. Recovered uncertainties for synthetic data and field data exhibit the expected patterns; for example, we observe the well-known increase in uncertainty in interface depths with increasing depth to the interface. We believe the Bayesian parametric bootstrap offers an attractive and satisfactory compromise between efficiency and exhaustive search of model space for the derivation of spatially coherent models.