Spatial uncertainty constraints reduce overfitting for potential field geophysical inversion

Summary Understanding the internal structure of the Earth is achieved using geophysical data and inversion is a powerful mathematical technique used by resource explorers to do so. Inherent ambiguity means that an infinite number of petrophysical models exist that can explain the geophysical data, so constraints such as geological models and petrophysical data have been employed to reduce the solution space. The constraints, like the data, are subject to noise and error, resulting in uncertainty propagating to the final model because inversion is designed to use the algorithm and constraints to find the single ‘best’ solution. Current practice assumes the best solution is found by optimising for the lowest misfit between the data and model; however, if the data is uncertain, the model fit to that data is likewise uncertain and potentially misrepresentative. Optimising misfit also means that inversion is subject to overfitting. Overfitting occurs when a model achieves the lowest misfit values by inadvertently fitting to data noise. Overfitting inversion occurs when the model has too many free parameters with no constraints, resulting in near-surface anomalies that can be mistakenly identified as legitimate targets for exploration rather than model artefacts. This contribution describes the use of spatial uncertainty calculated from geophysical data, providing free parameter constraints to reduce overfitting for geophysical inversion. The spatial uncertainty estimate is taken from a geostatistical model calculated using Integrated Nested Laplacian Approximation (INLA). A region in the East Kimberley, northern Western Australia, is subject to gravity inversion using Tomofast-x, an open-source inversion platform. Inversion is conducted using different configurations. Inversion is run without spatial uncertainty constraints, as is current practice, and then with spatial uncertainty constraints to test their effect on the resulting petrophysical model. The geostatistical model offers different percentiles from the geophysical model representing the extrema of estimated gravimetry values in the 10th and 90th percentiles. Inversions are run using these ‘extrema’ alongside the current practice of using the 50th percentile (or ‘mean’) gravity models as the observed field. Examination of inversion using and not using spatial uncertainty constraints shows that overfitting can be reduced. Using the extrema percentiles as the observed field has lesser benefits to reduce overfitting.