Fault interpretation is influenced by inherent challenges, such as the degraded seismic image quality, and the inconsistency of individual interpretation. These limitations cause significant uncertainty in determining location of faults and how faults extend (Mustafa, 2024, Michie, 2021). In the natural image domain, the consensus of a large group of uncertain labels typically converges to the gold standard with the variance capturing the uncertainty (Zhou, 2023). However, faults delineated by different interpreters exhibit significant variation in quality thereby practically not converging to high-quality labels. Figure 1 (a) shows varying-quality faults of two F3 seismic inlines delineated by multiple interpreters with different background and an expert geophysicist from the CRACKS dataset (Prabhushankar, 2024). A few high-quality fault labels approximate the geophysicist’ delineation, while a larger set of lower quality labels are less reliable in delineating fault features. The variance w.r.t. the consensus is an inaccurate reference to the uncertainty of fault features. Thus, the varying-quality aspect needs to be explicitly considered when estimating fault delineation uncertainty.
In this work, we introduce a generative-based approach that estimates fault delineation uncertainty leveraging multi-quality annotations. A seismic image with multi-quality fault labels are mapped to different points in the neural network intermediate feature space. We show an example 2D feature plot that encodes varying-quality label-conditioned data in Figure 1 (b). These points form a distribution in the feature space and act as the anchors for estimating uncertainty through decoding their disagreements w.r.t. the expert label-conditioned features. During inference, sampling from the distribution can generate multiple fault disagreements and further aggregate to estimate uncertainty without requiring manual labels. In Figure 2, we show examples of our generated faults in comparison with the manual faults. Our approach possesses the advantage under scarce-labeled data, compared to the alternative generative modeling using only expert-labeled data. We conduct an empirical study of generating uncertain faults when sourcing varying number of interpreters with different background. Using ~4% labeled CRACKS volume, our approach achieves lower error of uncertain faults modeling, measured by BCD-based (Li, 2024) generalized energy distance (GED) (Zhang, 2023), than conditional generative modeling using only expert-labeled data when accumulating multiple interpreters as shown in Figure 3. Thus, with scarce-labeled data, multi-quality annotations can assist uncertain fault modeling better than generative modeling of only expert-labeled data.
