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246 Machine learning for subsurface characterization


            intensity factor, to predict the crack growth rate. Miller et al. [9] applied CNN to
            process 2D images acquired from rock fracturing simulation. The 2D fracture
            image is processed as a weighted graph so that the CNN learns the graph fea-
            tures that are most predictive of final fracture length distribution. CNN has been
            applied on a large dataset of labeled raw seismic waveforms to learn a compact
            representation that can discriminate seismic noise from earthquake signals [10].
            Also, CNN can process labeled seismic data to output probabilistic locations of
            earthquake sources [10]. Loutas et al. [11] applied nonhomogeneous hidden
            semi-Markov model (NHHSMM) to process AE data for predicting the fatigue
            life of composite material under laboratory fatigue in real time. In terms of
            unsupervised methods, studies have successfully applied clustering methods
            to group the acoustic emission data with different signatures into different
            groups (clusters) to facilitate the characterization of fracture modes [1, 12].
            Apart from analyzing the measured data, several researches have analyzed sim-
            ulated data to monitor and predict the fracture evolution process. Moore et al.
            [13] gathered simulated data from the finite-discrete element model to train
            ANN to predict whether two fractures will coalesce or not based on the param-
            eters of fracture orientations, distances between two fractures, and the minimum
            distance from one of the fractures to its nearest boundary, to name a few.
            Rovinelli et al. [14] applied Bayesian network on simulated data to identify
            relevant micromechanical and microstructural variables that influence the
            direction and rate of crack propagation [14].


            2 Objective
            Characterization of mechanical discontinuity (crack or fracture) is a challenging
            problem in material evaluation, geophysics, civil engineering, rock mechanics,
            and oil and gas industry, to name a few. The geometry of the embedded
            discontinuities is governed by the geomechanical properties and the stress
            distributions. Popular methods for the characterization of discontinuities
            include acoustic emission, ultrasonic imaging, and CT scanning. AE method
            reconstructs the fracture system by detecting the acoustic events during fracture
            propagation. CT scanning method is based on the X-ray absorption phenome-
            non, such that open fractures absorb relatively less compared with surrounding
            materials. The CT scanning process is a relatively time-consuming and high-
            cost characterization technique. Ultrasonic imaging is another way for fracture
            characterization under laboratory condition.
               Sonic wave propagation phenomenon is influenced by the mechanical dis-
            continuities (fractures or cracks) in the material. Discontinuity can be investi-
            gated by measuring the compressional wave and shear wave travel times. This
            study explores the feasibility of applying classification methods to process the
            compressional wavefront travel times for the noninvasive characterization of
            mechanical discontinuity in material. In this study, we perform three major
            tasks in chronological order: (1) create thousands of numerical models of
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