Uncertainty quantification of geophysical models constructed by surface geometry inversion using Markov chain Monte Carlo sampling

Conventional Occam-style, minimum-structure inversion methods typically do not recover models with distinct boundaries between different geological units. Consequently, the constructed geophysical model can be very different from the true geological model and difficult to interpret in the geological context. This can be especially problematic for geological models with very thin structures that have a large physical property contrast with the background model, and determining the location of which is critical to, e.g., an exploration program. We have developed a new inversion method called surface geometry inversion which can construct geophysical models with distinct interfaces. The algorithm parameterizes the interface between geological units with triangular facets of connected nodes (vertices) and then inverts for the coordinates of these nodes. The algorithm only focuses on the boundary interface of localized anomalies and assumes the background model is known. Consequently, it is useful to have an adequately developed geological model and sufficient physical property data on which to base a background model. After the inversion, a model comprised of the background model and the anomalous region is constructed. We then utilize Markov chain Monte Carlo sampling to obtain statistical information, namely, the mean and standard deviation of the nodal coordinates of the constructed model. The standard deviation of each node is then used as an indicator of model uncertainty. The uncertainty information is useful as it can help us obtain a better understanding about the geological model. When applied to mineral exploration, the uncertainty quantification can also be used to mitigate the risks in drilling activities. We present synthetic transient electromagnetic data inversion examples with thin graphitic fault models. We also present a real-data example where transient electromagnetic data are used to target thin graphitic faults for a uranium exploration project.