When linear inversion fails:Neural-network optimization for sparse-ray travel-time tomography of a volcanic edifice

In this study,we present an artificial neural network(ANN)-based approach for travel-time tomography of a volcanic edifice under sparse-ray coverage.We employ ray tracing to simulate the propagation of seismic waves through the heterogeneous medium of a volcanic edifice,and an inverse modeling algorithm that uses an ANN to estimate the velocity structure from the“observed”travel-time data.The performance of the approach is evaluated through a 2-dimensional numerical study that simulates i)an active source seismic experiment with a few(explosive)sources placed on one side of the edifice and a dense line of receivers placed on the other side,and ii)earthquakes located inside the edifice with receivers placed on both sides of the edifice.The results are compared with those obtained from conventional damped linear inversion.The average Root Mean Square Error(RMSE)between the input and output models is approximately 0.03 km/s for the ANN inversions,whereas it is about 0.4 km/s for the linear inversions,demonstrating that the ANN-based approach outperforms the classical approach,particularly in situations with sparse ray coverage.Our study emphasizes the advantages of employing a relatively simple ANN architecture in conjunction with second-order optimizers to minimize the loss function.Compared to using first-order optimizers,our ANN architecture shows a~25%reduction in RMSE.The ANN-based approach is computationally efficient.We observed that even though the ANN is trained based on completely random velocity models,it is still capable of resolving previously unseen anomalous structures within the edifice with about 5%anomalous discrepancies,making it a potentially valuable tool for the detection of low velocity anomalies related to magmatic intrusions or mush.