An efficient symplectic stereo-modeling method for seismic inversion by using deep learning technique

Abstract

AbstractThis paper proposes an efficient symplectic stereo-modeling (SSTEM) method for full waveform inversion (FWI) by using a deep learning technique. To solve the 2D acoustic equation, the SSTEM method uses a third-order optimal symplectic partitioned Runge–Kutta approach as a time-stepping method. An eighth-order stereo-modeling operator is used for spatial discretization. The SSTEM method is then expressed with a recurrent neural network (RNN). This is realized mainly because the time advancing format of the SSTEM method is similar to that of RNN, and they both use the information from the previous time step to obtain information from the current time step. With SSTEM as the forward modeling method, FWI is implemented using Tensorflow. The well-known adaptive moment estimation (Adam) optimizer and Nesterov adaptive moment estimation (Nadam) optimizer with mini-batch are used. The applicability of the developed code is also verified on GPUs. The numerical results show that the SSTEM method is more efficient and produces less numerical dispersion than the conventional finite-difference (FD) method when the same sampling rate in a wavelength is used. We compare several loss functions. The mean square (MSE) error and absolute (ABS) error loss functions are first tested. Another loss function that adds a physical differential operator to the original loss function is then considered. The FWI results show that this loss function has some improvements. Finally, we implement FWI on the complex Marmousi and SEG/EAGE models, and the inversion results demonstrate that the proposed method is suitable for seismic imaging in complex media.