We recognized that the envelope fluctuation and decay of seismic records carries ultra low-frequency (ULF, i.e., the frequency below the lowest frequency in the source spectrum) signals that can be used to estimate the long-wavelength velocity structure. We then developed envelope inversion for the recovery of low-wavenumber components of media (smooth background), so that the initial model dependence of waveform inversion can be reduced. We derived the misfit function and the corresponding gradient operator for envelope inversion. To understand the long-wavelength recovery by the envelope inversion, we developed a nonlinear seismic signal model, the modulation signal model, as the basis for retrieving the ULF data and studied the nonlinear scale separation by the envelope operator. To separate the envelope data from the wavefield data (envelope extraction), a demodulation operator (envelope operator) was applied to the waveform data. Numerical tests using synthetic data for the Marmousi model proved the validity and feasibility of the proposed approach. The final results of combined EI+WI (envelope-inversion for smooth background plus waveform-inversion for high-resolution velocity structure) indicated that it can deliver much improved results compared with regular full-waveform inversion (FWI) alone. Furthermore, to test the independence of the envelope to the source frequency band, we used a low-cut source wavelet (cut from 5 Hz below) to generate the synthetic data. The envelope inversion and the combined EI+WI showed no appreciable difference from the full-band source results. The proposed envelope inversion is also an efficient method with very little extra work compared with conventional FWI.

Seismic impedance inversion is essential to characterize hydrocarbon reservoir and detect fluids in field of geophysics. However, it is nonlinear and ill-posed due to unknown seismic wavelet, observed data band limitation and noise, but it also requires a forward operator that characterizes physical relation between measured data and model parameters. Deep learning methods have been successfully applied to solve geophysical inversion problems recently. It can obtain results with higher resolution compared to traditional inversion methods, but its performance often not fully explored for the lack of adequate labeled data (i.e., well logs) in training process. To alleviate this problem, we propose a semi-supervised learning workflow based on generative adversarial network (GAN) for acoustic impedance inversion. The workflow contains three networks: a generator, a discriminator and a forward model. The training of the generator and discriminator are guided by well logs and constrained by unlabeled data via the forward model. The benchmark models Marmousi2, SEAM and a field data are used to demonstrate the performance of our method. Results show that impedance predicted by the presented method, due to making use of both labeled and unlabeled data, are better consistent with ground truth than that of conventional deep learning methods.

Seismic fault interpretation is one of the key steps for seismic structure interpretation, which is a time-consuming task and strongly depends on the experience of the interpreter. Aiming to automate fault interpretation, we have considered it as an image segmentation issue and adopt a solution using a residual UNet (ResUNet), which introduces residual units to UNet. Using the ResUNet model, we develop a fault-versus-azimuth analysis based on offset vector tile data, which, as common-azimuth seismic data, provide more detailed and useful information for interpreting seismic faults. To avoid manual efforts for picking training labels and the inaccuracy introduced by different interpreters, we use synthetic seismic data with a random number of faults with different locations and throws as the training and validation data sets. ResUNet is finally trained using only synthetic data and tested on field data. Field data applications show that the proposed fault-detection algorithm using ResUNet can predict seismic faults more accurately than coherence- and UNet-based approaches. Moreover, geologic fault interpretation results computed using common-azimuth data exhibit higher lateral resolution than those computed using poststack seismic data.

Missing trace reconstruction is an essential step in the seismic data processing. Various interpolation methods have been proposed for handling this issue. In recent years, deep learning-based interpolation techniques, especially convolutional neural networks (CNNs), have been widely studied. Typically, these studies target regularly/randomly missing cases, leaving consecutively missing situations not handled properly. In this article, we propose a hybrid loss function $\text {SSIM}+L_{1}$ , based on structural similarity (SSIM) and $L_{1}$ norm, for network training and attention mechanism as a network component that explicitly utilizes global information. We further design a CNN equipped with the hybrid loss and attention mechanism for successively missing trace reconstruction. Experiments on synthetic and field data demonstrate that our network can reconstruct more reasonable results than networks without attention mechanism in large gap situation and $\text {SSIM}+L_{1}$ loss promotes interpolation results. We also discuss the setup of key hyperparameters of the network by a thorough ablation study.

Because deep-learning networks can “learn” the complex mapping function between labeled inputs and outputs, they have shown great potential in seismic inversion. Conventional deep-learning algorithms require a large amount of labeled data for sufficient training. However, in practice, the number of well logs is limited. To address this problem, we have adopted a closed-loop fully convolutional residual network (FCRN) combined with a transfer learning strategy for seismic inversion. This closed-loop FCRN consists of an inverse network and a forward network. The inverse network predicts the inversion target from seismic data, whereas the forward network calculates seismic data from the inversion target. The inverse network is initialized by pretraining on the Marmousi2 model and is fine-tuned with the limited labeled data around the wells through transfer learning, to suit the target seismic data. The forward network is initialized by training with the limited labeled data around the wells. In this way, the closed-loop network is well initialized to ensure relatively good convergence. Then, the misfit of the limited labeled data and the error between the true and the forward seismic data are used to regularize the training of the initialized closed-loop network. The inverse network of the optimized closed-loop network is used to obtain the final inversion results. Our workflow can be used for velocity, density, and impedance inversion from poststack seismic data. We take velocity inversion as an example to illustrate the effectiveness of the method. The experimental results show that closed-loop FCRN with transfer learning is superior to open-loop FCRN with better lateral continuity and velocity details. Closed-loop FCRN can effectively predict velocity with high accuracy on synthetic data, has good antinoise performance, and can also be effectively used for field data with spatial heterogeneity.