Frequency-Dependent Fault Identification by Convolutional Neural Networks with Uncertainty Analysis

Frequency-dependent similarity has previously been used to preferentially detect faults with different vertical displacements at different dominant frequencies (e.g. Dewett and Henza, 2016; Johan and Castagna, 2017). By decomposing seismic data into multi-frequency dominated data, structural and stratigraphic delineation such as complex fault systems could be better interpreted in various scales. Similarities and differences are also highlighted. Low-frequency seismic data provides an effective broadband to suppress wavelet partials and improve the resolution of seismic data. Several authors have pointed out that low-frequency data offers a stronger penetration ability to restrict the influence of scattering and absorption on the reflected waves (e.g. Wu, et al., 2013; Sun et al., 2021). On the other hand, high-frequency seismic data could improve vertical resolution, leading to a better mapping of horizons and stratigraphic features that are key for a detailed geological characterization of the reservoirs. Convolutional Neural Networks (CNN) show a promising way to automatically identify fault attributes in seismic data by analyzing image segmentation and feature extraction with high accuracy. Wu et al. (2019) performed efficient image-to-image fault segmentation by using a supervised CNN architecture. By creating multiple synthetic seismic images and corresponding binary fault-labeled images, the authors successfully trained a fault segmentation network. Jiang and Norlund (2020, 2021) implemented a multi-channel CNN with a multi-scale aggregated module to combine pixel-level accuracy with global-level feature identification to improve prediction accuracy. However, those prediction images may still be disappointing due to strong noise existing in the data or the juxtaposition of relatively similar reflectors across a fault. Lyu et al. (2019) computed multiple spectral coherence to reduce the noise and improved the continuity of the faults. Quantifying uncertainty in seismic interpretation can be divided into regression settings, such as rock property analysis, or classification setting, such as semantic segmentation. There are two main types of uncertainty to evaluate a deep learning model. Aleatoric uncertainty captures noise inherent randomness of distribution in the machine learning prediction. The prototypical example of aleatoric uncertainty is coin flipping. The data generating process in this type of experiment has a stochastic component that cannot be reduced by any additional source of information. Conversely, epistemic uncertainty stands for uncertainty caused by a lack of knowledge to obtain a best model. It refers to the ignorance of the agent or decision maker, and hence to the epistemic state of the agent instead of any underlying random phenomenon. (Hullermeier and Waegeman, 2021). Kendall and Gal (2017) show the uncertainty observations in many different big data regimes to demonstrate the efficiency of uncertainty analysis in computer vision applications. Kwon et al (2020) implemented a Bayesian neural network and propose a natural way to quantify uncertainty in classification problems by decamping predictive uncertainty into two parts, aleatoric and epistemic uncertainty. In this paper, we performed spectral decomposition to decompose a group of training seismic data to different frequencies. We then fed each iso-frequency training data into a multi-channel, multi-scale CNN architecture to train a series of frequency-dependent ML models to evaluate the ability to enhance the fault identification process. We applied our technique to a real case study, revealing significant improvements on the prediction results using a multiple frequencies model compared to those predictions generated from a full-bandwidth ML model