Approximating Probabilistic Joint Inversion using Bayesian Spatial Ensemble Fusion

Bayesian posterior sampling is a flexible and general purpose method that can be used to quantify uncertainty in geophysical inversion results. It produces large ensembles of plausible subsurface models consistent with the data and some spatial prior. Unfortunately, it is computationally expensive and becomes impractical for high-dimensional models. This problem is exacerbated by the challenges of joint inversion using data from different geophysical methods, which may be sensitive to different petrophysical properties at different resolutions. To speed up and simplify both implementation and application, we introduce Bayesian spatial ensemble fusion.

The method is demonstrated here using airborne electromagnetic (both VTEM and Tempest) and magnetotelluric data from Cloncurry in the Mount Isa province of Queensland, Australia. 1D transdimensional inversion is applied to individual sites to quantify uncertainty locally, which produces ensembles of 1D layered resistivity models with variable numbers of layers. These local ensembles are then fused together to produce ensembles of more complex 2D models as an approximation to what laterally constrained probabilistic joint ensemble inversion would have produced.

There are several benefits to this approach: Different and existing software can be used by different specialists to create the input ensembles, which reduces the need for complex coordination and simplifies coding. Forward calculations are performed once and then stored to be recycled in many subsequent fusions. Many inversions of the same data, or different combinations thereof, can then be performed using different priors, constraints and geological interpretations, at very little additional cost. Thorough exploratory uncertainty analysis is thus made more practical as specialists can elicit and test different interpretations more quickly.