Seismic Inversion Based on Acoustic Wave Equations Using Physics-Informed Neural Network

Seismic inversion is a significant tool for exploring the structure and characteristics of the underground. However, the conventional inversion strategy strongly depends on the initial model. In this work, we employ the physics-informed neural network (PINN) to estimate the velocity and density fields based on acoustic wave equations. In contrast to the traditional purely data-driven machine learning approaches, PINNs leverage both available data and the physical laws that govern the observed data during the training stage. In this work, the first-order acoustic wave equations are embedded in the loss function as a regularization term for training the neural networks. In addition to the limited amount of measurements about the state variables available at the surface being used as the observational data, the well logging data is also used as the direct observational data about the model parameters. The numerical results from several benchmark problems demonstrate that given noise-free or noisy data, the proposed inversion strategy is not only capable of predicting the seismograms, but also estimating the velocity and density fields accurately. Finally, we remark that although the absorbing boundary conditions are not imposed in the proposed method, the reflected waves do not appear from the artificial boundary in the predicted seismograms.