Seismic data interpolation is a longstanding issue. Most current methods are only suitable for randomly missing cases. To deal with regularly missing cases, an antialiasing strategy should be included. However, seismic survey design using a random distribution of shots and receivers is always operationally challenging and impractical. We have used deep-learning-based approaches for seismic data antialiasing interpolation, which could extract deeper features of the training data in a nonlinear way by self-learning. It can also avoid linear events, sparsity, and low-rank assumptions of the traditional interpolation methods. Based on convolutional neural networks, eight-layers residual learning networks (ResNets) with a better back-propagation property for deep layers is designed for interpolation. Detailed training analysis is also performed. A set of simulated data is used to train the designed ResNets. The performance is assessed with several synthetic and field data. Numerical examples indicate that the trained ResNets can help to reconstruct regularly missing traces with high accuracy. The interpolated results in the time-space domain and the frequency-wavenumber ([Formula: see text]-[Formula: see text]) domain demonstrate the validity of the trained ResNets. Even though the accuracy decreases with the increase of the feature difference between the test and training data, the proposed method can still provide reasonable interpolation results. Finally, the trained ResNets is used to reconstruct dense data with halved trace intervals for synthetic and field data. The reconstructed dense data are more continuous along the spatial direction, and the spatial aliasing effects disappear in the [Formula: see text]-[Formula: see text] domain. The reconstructed dense data have the potential to improve the accuracy of subsequent seismic data processing and inversion.
Interpolation and random noise removal is a prerequisite for multichannel techniques because the irregularity and random noise in observed data can affect their performances. Projection Onto Convex Sets (POCS) method can better handle seismic data interpolation if the data's signal-to-noise ratio (SNR) is high, while it has difficulty in noisy situations because it inserts the noisy observed seismic data in each iteration. Weighted POCS method can weaken the noise effects, while the performance is affected by the choice of weight factors and is still unsatisfactory. Thus, a new weighted POCS method is derived through the Iterative Hard Threshold (IHT) view, and in order to eliminate random noise, a new adaptive method is proposed to achieve simultaneous seismic data interpolation and denoising based on dreamlet transform. Performances of the POCS method, the weighted POCS method and the proposed method are compared in simultaneous seismic data interpolation and denoising which demonstrate the validity of the proposed method. The recovered SNRs confirm that the proposed adaptive method is the most effective among the three methods. Numerical examples on synthetic and real data demonstrate the validity of the proposed adaptive method.
Accurate and efficient velocity estimation using Transmission matrix formalism based on the domain decomposition method View the table of contents for this issue, or go to the journal homepage for more 2017 Inverse Problems 33 035002
Seismic trace interpolation is an important technique because irregular or insufficient sampling data along the spatial direction may lead to inevitable errors in multiple suppression, imaging, and inversion. Many interpolation methods have been studied for irregularly sampled data. Inspired by the working idea of the autoencoder and convolutional neural network, we have performed seismic trace interpolation by using the convolutional autoencoder (CAE). The irregularly sampled data are taken as corrupted data. By using a training data set including pairs of the corrupted and complete data, CAE can automatically learn to extract features from the corrupted data and reconstruct the complete data from the extracted features. It can avoid some assumptions in the traditional trace interpolation method such as the linearity of events, low-rankness, or sparsity. In addition, once the CAE network training is completed, the corrupted seismic data can be interpolated immediately with very low computational cost. A CAE network composed of three convolutional layers and three deconvolutional layers is designed to explore the capabilities of CAE-based seismic trace interpolation for an irregularly sampled data set. To solve the problem of rare complete shot gathers in field data applications, the trained network on synthetic data is used as an initialization of the network training on field data, called the transfer learning strategy. Experiments on synthetic and field data sets indicate the validity and flexibility of the trained CAE. Compared with the curvelet-transform-based method, CAE can lead to comparable or better interpolation performances efficiently. The transfer learning strategy enhances the training efficiency on field data and improves the interpolation performance of CAE with limited training data.
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