Precision analysis of supervised machine learning for predicting seismic recurrence in multi-faults system

Forward modeling (FM) approach has been successful in reproducing geodynamic phenomena with a wide range of time- and spatial-scales (e.g., subductions and seismicity). Researchers have put much effort on understanding the seismic recurrence periods. The FM with controlled arrangement of faults has been widely used to reproduce seismic recurrence behavior modulated by fault interactions. For instance, So and Capitanio (2017) demonstrated multi-faults model based on a simple elastoplastic rheology. On the other hand, an inverse modeling is also successful in predicting parameter from observations. Recently, a machine learning (ML) technique has been adopted to solve the inverse problem. In this study, we adopted a supervised ML- SVM(support vector machine) to classify the images. For the FM, we prepared the elastoplastic model domains (1000 km * 1000 km) with randomly distributed 10 faults (10 km * 10 km) within a circle (radius R = 60 - 300 km) centered at the domain. Then, the FM calculated the seismic recurrence period of each fault. Then, we got many pairs composed of i) spatial arrangement of faults (i..e., images) and ii) its corresponding averaged seismic recurrence periods of all faults within the circle (i.e., values). As preprocessing for the ML, we split the pairs into training and test datasets. Depending on values of R, we group the datasets into 3 to 6 classes (i.e., labeling). Next, we applied the ML algorithm to train the machine. The machine derived a label of the closest training image in response to a given image without the FM calculation. We found that the precision is 75-90% when numbers of classes are relatively small (i.e., 3-4), However, the precision is sharply reduced to 60% with the classes numbers > 5. We also tested different type of fault distribution. The one fault was pivoted at the center of circle and the other faults are randomly distributed within the circle. Then, we applied the same ML-SVM to predict the seismic recurrence period of the central fault. The results showed a similar trend of the precision depending on numbers of classes we found in the former tests. If the precision of ML is high enough to predict the recurrence time of arbitrarily selected fault distribution, it implies that the ML has a potential to predict the seismic recurrence behavior using the image of fault distribution from nature.