Deep-learning (DL) technology has emerged as a new approach for seismic data interpolation. DL-based methods can automatically learn the mapping between regularly subsampled and complete data from a large training data set. Subsequently, the trained network can be used to directly interpolate new data. Therefore, compared with traditional methods, DL-based methods reduce the manual workload and render the interpolation process efficient and automatic by avoiding the selection of hyperparameters. However, two limitations of DL-based approaches exist. First, the generalization performance of the neural network is inadequate when processing new data with a different structure compared to the training data. Second, the interpretation of the trained networks is very difficult. To overcome these limitations, we have combined the deep neural network and classic prediction-error filter (PEF) methods, proposing a novel seismic data dealiased interpolation framework called prediction-error filters network (PEFNet). The PEFNet designs convolutional neural networks to learn the relationship between the subsampled data and the PEFs. Thus, the filters estimated by the trained network are used for the recovery of missing traces. The learning of filters enables the network to better extract the local dip of seismic data and has a good generalization ability. In addition, PEFNet has the same interpretability as traditional PEF-based methods. The applicability and the effectiveness of our method are demonstrated here by synthetic and field data examples.

Although reverse time migration (RTM) is a powerful imaging method, it uses only the adjoint of the wave-propagation operator and produces only a blurred image. Through linearized inversion, least-squares RTM (LSRTM) reduces migration artifacts, balances the amplitudes, and improves the resolution of the imaging results. Compared to data-domain LSRTM, image-domain LSRTM (ID-LSRTM) is a more practical choice because it typically requires one round of RTM and subsequently solves the deblurring problem of the conventional RTM image involving the Hessian matrix. The Hessian matrix can be effectively replaced by a set of point-spread functions (PSFs). PSFs are traditionally obtained through one round of demigration-migration; hence, the traditional PSF estimation has a computational cost that is twice that of the RTM. We have deduced an analytic expression of the Hessian/PSF by using an asymptotic Green’s function and derived an efficient estimation strategy for the Hessian/PSF. The proposed method significantly reduces the computational cost and allows more flexible spatial sampling of PSFs without interference. Based on the explicitly calculated PSFs, ID-LSRTM can be achieved by solving an optimization problem with combined total-variation and curvelet-domain L1 regularizations. The total computational cost of the proposed LSRTM is approximately the same as that of the conventional RTM. Numerical examples of synthetic and field data find that the proposed LSRTM significantly improves image quality while being highly efficient.

Existing deep learning-based seismic data denoising methods mainly involve supervised learning, in which a denoising network is trained using a large amount of noisy input/clean label pairs. However, the scarcity of high-quality clean labels in practice, limits the applicability of these methods. Recently, the blind spot (BS) strategy in the field of image processing has attracted extensive attention. Under the assumption that the noise is statistically independent, and the true signal exhibits some correlation, BS strategy allows us to estimate a denoiser from the noisy data itself. In this paper, we study the application of the BS strategy to the random noise attenuation of seismic data, and propose an unsupervised blind spot network (BSnet) method. Specifically, considering the characteristics of the random noise, we improve the commonly used Unet network and design two types of randomly mask operators to deal with Gaussian white noise and band-pass noise respectively. Synthetic and real data experiments validate the effectiveness of the proposed method.

Acoustic impedance (AI) is a key parameter frequently used for characterizing reservoirs in the oil and gas industry. The absolute AI can be divided into background and high-wavenumber components, which are related to the background velocity and migrated reflectivity, respectively. The relative AI derived from the migrated images is commonly used, but it is generally limited by the wavenumber range of the migrated image. Owing to the advantage of deep learning methods in determining the relationships among data sets, a learning-based AI inversion method that fuses the background model and the migrated reflectivity is proposed to determine the absolute AI. We first acquire learning labels using a synthetic model, and the initial parameters of a convolutional neural network are obtained by training the mapping from the known background AI and the reflectivity to the labels. We then establish a transfer learning scheme to refine the mapping network parameters using the target data. Finally, the target field data are processed using the refined network. The Marmousi model is used as the label for pretraining, and the synthetic Sigsbee2A model and field data are used for validation. Numerical tests demonstrate the effectiveness of the proposed method for absolute AI fusion, and the transfer learning scheme performs well to constrain the inverted AI that has decent consistency with the background model and reflectivity of the target data.