Multiscale Deep Learning Reparameterized Full Waveform Inversion With the Adjoint Method

The application of deep learning techniques to full waveform inversion (FWI) theory represents a significant research direction. Leveraging the nonlinear representations offered by deep learning and conducting practical FWI are paramount. This article utilizes the classic adjoint method in FWI to compute the gradients of model parameters, employing deep learning to represent model parameters and optimize network training. The focus is on achieving high-precision FWI through multiscale deep learning optimization. Specifically, deep neural networks are used to represent model parameter information and compute gradients of model parameters on high-performance platforms. The gradients of the network parameters are automatically obtained through backpropagation, with deep learning optimization tools updating the network parameters and, consequently, the model parameters. To enhance inversion accuracy, a multiscale learning strategy is introduced, where deep networks optimize the learning of model parameter information at each scale, ensuring effective representation of inversion parameter information across multiple scales. Experimental results demonstrate that deep learning reparameterization methods possess broad-spectrum modeling capabilities. The multiscale deep learning strategy significantly improves inversion accuracy, and the reparameterization method of deep learning shows potential for high-precision modeling under conditions of sparse and noisy observational data. Furthermore, the application of field data underscores the reliability of the proposed method.