Imperial College London
Wavefield reconstruction inversion (WRI) method is a PDE-constrained optimization method that aims to mitigate the cycle-skipping issue in full-waveform inversion (FWI). WRI was proposed to implement in the frequency domain, as the size of wavefield at a certain frequency is the same as the model size. However, it will be very expensive to reconstruct the wavefield for a large model, especially for 3D problems. In addition, conventional numerical methods cannot invert for a frequency-domain wavefield with irregular topography. A recently introduced framework called physics-informed neural network (PINN) is used to predict PDE solutions by setting the physical equation as a cost function. PINN has shown its effectiveness in solving the Helmholtz wave equation specifically for the scattered wavefield. By including the recorded data at the sensors' locations as a constraint, PINN can predict a wavefield which simultaneously fits the recorded data and the Helmholtz wave equation with a given initial model. With the predicted wavefields, we can build another independent PINN aiming at inverting for the velocity. In this new PINN, we still use spatial coordinates as the input data, and use the predicted wavefields and background homogeneous velocity as complimentary variables to define the cost function. After a fully connected 8-layer deep neural network is trained, we are able to predict the velocity in the domain of interests. We demonstrate the validity of the proposed method on a layered model, and the results show that PINN can reconstruct the scattered wavefield and invert for a reasonable velocity model even with a single source and a single frequency.