Forward modeling and inversion based on deep learning by using an effective optimal nearly analytic discrete method

Abstract

In this paper, we implement forward modeling and inversion based on deep learning strategies by using an effective optimal nearly analytic discrete (ONAD) method. The forward modeling method combines the ONAD method with a recurrent neural network (RNN). RNN is a kind of neural network suitable for sequential data, which uses information from both the previous and current time to obtain the output information. ONAD is an effective forward modeling method and is similar to RNN in that it uses the previous wavefield to calculate the current wavefield. Therefore, we express ONAD method through RNN framework to advance the time iteration of the acoustic equation. This can simplify the programming by using RNN and convolution kernels. Next, based on the proposed forward modeling method, we use deep learning to study full waveform inversion (FWI) problems. Since the main purpose of inversion is to minimize the error between real data and synthetic data, so inversion is essentially an optimization problem. There are many new optimization ideas in the framework of deep learning, such as Adam optimizer and Nadam optimizer, which can achieve better effectiveness of inversion than traditional optimizers used in FWI. We carry out six numerical experiments. The first two show the forward modeling results, which indicate that the forward modeling method can effectively suppress the numerical dispersion. The other four experiments show the inversion results. We compare several optimizers used in deep learning, and find that Nadam optimizer can almost restore the true velocity model with faster convergence and great effectiveness based on the ONAD method combined with RNN. These numerical experiments highlight the effectiveness of forward modeling and inversion based on deep learning by using ONAD method.