Spatial error constraints reduce overfitting for potential field geophysical inversion

Abstract. Geophysical inversion is an important tool for characterising the structure of the Earth. The utility of geophysical inversion has led to widespread adoption by resource explorers, and used to adapt gravity, magnetic, seismic and electrical datasets into petrophysical models that can be used for targeting. However, 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. This is because inversion is designed to use the algorithm and constraints to find the ‘best’ solution by optimising the lowest misfit between the data and model. If the data is uncertain, the model fit to that data is likewise uncertain, and misrepresentative. Optimising misfit also means that inversion is subject to overfitting. Overfitting is when the lowest misfit values are attained by fitting the model to data noise. Overfitting inversion can create anomalies in the near-surface that can be mistakenly identified as legitimate targets for exploration rather than possible model artefacts. This contribution describes the use of spatial error constraints calculated from geophysical data to reduce overfitting for geophysical inversion. The spatial error estimate is derived 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 using different percentiles from the geophysical model explores whether the extrema of gravimetry values should be considered to explore the model space. Examination of inversion using and not using spatial error constraints shows that overfitting reduction can be achieved while using different percentiles as the observed field has lesser benefits.