Faults representation and uncertainty quantification in three-dimensional implicit geological modeling with neural network

RWTH Publications (RWTH Aachen)

Abstract

The Earth’s subsurface resources are a crucial energy source and provide key minerals that support the development of advanced manufacturing. To understand the underground geological structures, geological modelling is an essential tool. Recently, implicit neural representations have provided a flexible, scalable framework for three-dimensional geological modelling. These networks are feature-based and resolution independent, making them effective for modelling geological structures from scattered interface points, geological units, and structural orientations. Despite these promising characteristics, modelling faults within implicit neural representations remains a significant challenge. Moreover, quantifying predictive uncertainty also remains an open issue. To address these research gaps, this thesis first presents a method for representing discontinuities in neural networks, in which discontinuity information is concatenated as additional features of the observation and query points at the network input. The method is then applied to fault modelling within an implicit neural representation-based geological modelling framework. Results are compared with those obtained using Boolean operations and discontinuous activation functions. The results demonstrate the presented method’s ability to generate a well-defined implicit scalar field while preserving sharp transitions at fault locations. Methods for modelling finite faults and fault networks are then introduced. The proposed method defines an ellipsoidal displacement zone to represent a finite fault, and the signed, normalized fault displacement trend within this zone is defined as a fault feature. By providing this fault feature as an additional input to the network, the modelling output preserves the geometric characteristics of fault terminations. Additionally, a truncation scheme is introduced to correctly generate fault feature fields, which allows an implicit neural representation-based geological modelling framework to model complex fault networks. Finally, a Hamiltonian Monte Carlo sampler is incorporated into an implicit neural representation-based geological modelling framework to quantify uncertainty arising from both network parameters and observational data. The proposed method explores the space of plausible geological model realizations and quantifies the uncertainty of predicted geological interfaces within a Bayesian neural network framework. It is then compared with the commonly used Monte Carlo dropout approach and applied to a faulted scenario. Besides, its computational efficiency on large datasets and networks is discussed. In summary, this thesis proposes a discontinuity-aware implicit neural representation framework for fault modelling, extends it to finite faults and complex fault networks over an ellipsoidal displacement zone and a truncation scheme, and integrates Hamiltonian Monte Carlo to quantify predictive uncertainty within a Bayesian neural network framework. These works enhance the modelling capacity and reliability of the implicit neural representation-based geological modelling framework.

Authors 1

1. Kaifeng Gao corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen