In wave equation modeling, wavefields propagating over time can be regarded as feedforward in a recurrent neural network. Therefore, the seismic inversion problem based on partial differential wave equations can be addressed using automatic differentiation in the state-of-art deep learning frameworks, eliminating the need for explicit backpropagating the residual wavefield. However, one challenge that arises in the context of automatic differentiation is the significant memory usage due to the necessity of storing the hidden states of the RNN (i.e., wavefields in seismic modeling) during forward computation for constructing the computational graph and computing the derivatives during backpropagation. This memory overhead can become a bottleneck, particularly when dealing with large-scale inversion problems. To mitigate this issue, we propose an effective boundary saving strategy that allows for the reconstruction of the computational graph during the backpropagation process. Instead of storing all the intermediate wavefields at each time step, we selectively save the necessary information at the boundaries, thereby significantly reducing the memory footprint. This approach enables us to maintain the convenience and efficiency of automatic differentiation computations while minimizing the memory requirements. Both 2D and 3D numerical experiments validate the accurate reconstruction of wavefields with minimal loss in precision, while the computational graph is simultaneously reconstructed. Consequently, the gradients can also be calculated correctly by automatic differentiation with minimal CPU/GPU memory occupation.

The supervised neural network-based method provides an effective way for seismic data denoising. The noise level of seismic erratic noise, i.e., outlier, varies from traces, time windows, and shot gathers. The networks with popular structures may damage reflections because the network cannot learn the exact location of the noises. In order to accommodate the characteristics of erratic noise, we propose using an attention-based network that focuses more on noisy regions. The network outputs an attention map, which shows the spatial distribution probability of erratic noise and a raw noise that may have leakage reflections. To train the network with two kinds of outputs, we use two different loss functions to optimize the network. The erratic noises in the specified area can be extracted by multiplying the attention map and the raw noise, and the reflections in areas without noise are preserved. For generating the training set, we proposed a shuffled noise strategy, which starts from the inaccurate denoised data with the conventional method. Only the noisy data are available in the whole denoising workflow. The network can learn the noise features effectively with the shuffle noise strategy and can achieve better denoising effect than that based on the conventional method. In addition, the denoising capability of the network can be controlled manually by filtering the attention map with probability, and the denoising effect can be further improved through recovering the leaked signals. Synthetic and field data examples show that the proposed method has potential for field erratic noise attenuation.

The determination of the P- and S-wave propagation directions is crucial for wavefield decomposition, polarity reversal correction, and noise suppression in elastic reverse time migration (RTM). Compared with the conventional decoupled elastic wave equation, the first-order velocity-dilatation-rotation equations enable more accurate computation of propagation directions for P and S waves. Moreover, compared with the Poynting vector, the optical flow vector signifies the wavefield propagation directions more accurately. To effectively enhance the accuracy of elastic wave imaging, we develop an elastic RTM based on first-order velocity-dilatation-rotation equations using the optical flow vector. Numerical tests illustrate that our method, with or without noise, can better eliminate migration artifacts and improve the imaging accuracy of the elastic RTM than conventional methods, achieving more accurate wavefield decomposition and superior S-wave polarity reversal correction.

The high-amplitude shear wave in the z-component of ocean-bottom node (OBN) data challenges conventional seismic data imaging and interpretation. The process of shear-wave attenuation from the z-component data can be regarded as a coherent noise reduction problem. However, conventional noise attenuation methods, such as filtering or matching and subtraction, are time-consuming or have limited accuracy for field data processing. Unlike conventional methods with indirect feature recognition, pretrained neural networks provide end-to-end denoising frameworks by directly predicting and subtracting the shear-wave-free data from the original z-component data. Here, we have developed a deep learning-based method to address the shear-wave leakage problem and adopted a training set generation strategy based on the field data. Denoised z-component data are not needed to train the network. The generation of the training set and the extraction of noise features are based on the data of the x- and p-components. A residual learning strategy is introduced to extract the noise from the field data other than those in the training set. Synthetic examples confirm the excellent performance of our training set generation strategy. Field 4C OBN examples show that our method can attenuate shear-wave noise without harming the signals and, therefore, can be integrated into multicomponent field data processing.

This paper introduces the fourth-order absorbing boundary condition (ABC) into staggered-grid finite difference forward modeling of the first-order st