From Seismic Source Localisation to Facies Classification: A Fourier Neural Operator Framework for Petrophysical Subsurface Characterisation

Abstract

The identification of low-resistivity low-contrast (LRLC) reservoirs in interbedded sand-shale sequences remains one of the principal unsolved challenges in petrophysical log interpretation. Conventional resistivity-based evaluation systematically misclassifies thin hydrocarbon-bearing sandstone beds as shale or water-bearing zones because the vertical resolution of standard logging tools is insufficient to resolve laminations thinner than approximately three metres. This paper proposes a Fourier Neural Operator (FNO) framework for petrophysical facies classification that directly addresses this limitation. The approach is motivated by a formal analogy with FNO-based microseismic source localisation, in which the same operator learning architecture learns the mapping from sparse traveltime observations to a full subsurface field. Here, the FNO learns the operator mapping from multi-log petrophysical functions to a depth-continuous facies probability field. A physics-based synthetic dataset is generated using Archie's equation for clean sandstone resistivity and the Thomas–Stieber horizontal resistivity model for laminated shaly sand, with a uniform-filter tool-averaging operator applied to simulate sub-resolution blurring. Three facies are defined: C0 (shale), C1 (LRLC sandstone), and C2 (clean sandstone). The trained FNO achieves a macro-F1 score of 0.952 and a C1-specific F1 of 0.892, compared with 0.931 and 0.845 for a point-wise XGBoost baseline, respectively. Critically, the FNO maintains these scores across a fourfold range of depth-sampling intervals (0.25–1.00 m) without retraining, demonstrating the resolution invariance that is the defining property of neural operators. The results establish operator learning as a principled and practical framework for LRLC facies classification in petrophysical log analysis.