Seismic Data Reconstruction Research Articles

Nonconvex Log-Sum Function-Based Majorization–Minimization Framework for Seismic Data Reconstruction

Because of the fact that complete seismic data can have a low rank in the frequency-space (f-x) domain, rank-reduction methods are classical techniques used for seismic data reconstruction. Models that employ nuclear-norm minimization signify convex relaxation methods in traditional rank minimization problems. However, the results obtained after solving the nuclear-norm minimization problem are usually suboptimal because the nuclear norm indicates a loose approximation of the rank function. To overcome the limitations of the nuclear norm, we propose a new method of seismic data reconstruction based on the log-sum function minimization, which is closer to the rank function than the convex nuclear norm. However, the problem based on the log-sum function is nonconvex. Consequently, a majorization–minimization framework has been adopted to solve the associated minimization problem. Numerical experiments performed using synthetic and real data demonstrate that the quality of reconstruction derived from our proposed algorithm is better than that of the singular value thresholding algorithm and the weighted nuclear norm method.

Reflection waveform inversion based on full-band seismic data reconstruction for salt structure inversion

SUMMARYSalt structures are high potential targets for oil and gas exploration. However, large-scale salt domes with irregular surfaces pose significant challenges for velocity model building. For full waveform inversion, in the absence of a high-fidelity initial model, the success of the inversion depends on low-frequency seismic data, which are scarce in the exploration data sets. This paper presents a new idea to solve the problem of salt structure velocity modelling. First, we propose an envelope-based full-band seismic data reconstruction algorithm. The smoothness of envelope is used to segment the events in seismic data, and the phase independence of envelope is used for the identification of the seismic event's arrival-time to obtain the apparent reflection sequences of the subsurface. Full-band seismic data are obtained by convolving the apparent reflection sequence with full-band source. Window averaging function and threshold strategy are used to ensure the accuracy of seismic event segmentation and the stability of the algorithm when dealing with noisy data. Then the multiscale reflection waveform inversion based on reconstructed data is proposed for salt structure velocity building. The numerical experiment results of the Sigbee2A model demonstrate the performance of the inversion algorithm in the case where the seismic data lack low-frequency components and contain noise. The limitations of the algorithm have also been analysed and studied.

Artificial Intelligence Improves Seismic-Image Reconstruction

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of the open-submission paper “Artificial Intelligence for Seismic-Image Reconstruction,” by Yogendra Narayan Pandey, SPE, and Govind Chada, Prabuddha, and Tejas Karmarkar, Oracle Cloud Infrastructure. The paper was not presented at an SPE conference and has not been peer-reviewed. Seismic imaging provides vital tools•for the exploration of potential hydrocarbon reserves and subsequent production-planning activities. The acquisition of high-resolution, regularly sampled seismic data may be hindered by physical or financial constraints, which lead to undersampled, sparse seismic data. However, if seismic data are available at a higher resolution and sampled evenly throughout the region of interest, the generated 3D models of petrophysical properties could be improved. Such improvements would show potential benefits through the successive steps of reservoir modeling and production•planning. Traditional Approaches Traditional methods used to overcome the previously mentioned data-quality issues can be divided broadly into three categories. Wave-equation-based methods. These methods use physics-based•wave-propagation equations, using•velocity models•to•reconstruct missing seismic traces. Domain-transform methods. These are data-driven methods that involve transformation of data•between different domains, such as time and frequency. Prediction-error filters. These methods use a filter that learns from the known seismic data and constructs missing seismic data. Given recent advances in the field of artificial intelligence (AI), it is worth examining whether AI methods also can be useful in the task of seismic-data•reconstruction. Generative Adversarial Networks (GANs) GANs are a recent addition to the field of solution techniques. A variant of GANs, conditional generative adversarial networks, was used to test the efficacy of GANs for seismic-data reconstruction. Fig. 1 shows a schematic of a GAN model for seismic-data reconstruction. To effectively reconstruct a seismic image, a large number of 2D seismic images are fed into the GAN during the training process. A GAN model consists of two main components: Generator. This is a deep convolutional neural network (CNN) that uses random noise as an input and generates an image by expanding the input through a series of deconvolutions. As shown in Fig.•1, the generator network is fed 2D seismic images, with a portion of these masked to replicate missing traces. The generator network tries to reconstruct these•masked portions of the 2D seismic images. Discriminator. This is also a deep CNN that is shown the images reconstructed by the generator network and the original seismic images from which some parts were masked. The discriminator’s job is to distinguish between the images reconstructed by the generator from the original seismic images. As training progresses, the generator network tries to create images that the discriminator will not be able to differentiate from the original seismic images. At the same time, the discriminator’s ability to distinguish the generated images from the original images continuously improves. As a result, the generator begins producing reconstructed seismic images, which look similar to the original ones.

De‐aliased and de‐noise Cadzow filtering for seismic data reconstruction

ABSTRACTCadzow filtering is currently considered as one of the most effective approaches for seismic data reconstruction. The basic version of Cadzow filtering first reorders each frequency slice of the seismic data (to be reconstructed) to a block Hankel/Toeplitz matrix, and then implements a rank‐reduction operator, that is truncated singular value decomposition, to the Hankel/Toeplitz matrix. However, basic Cadzow filtering cannot deal with the problem of recovering regularly missing data (up‐sampling) in the case of strongly aliased energy, because the regularly missing data will mix with signals in the singular spectrum. To solve this problem, it has been proposed to precondition the reconstruction of high‐frequency components using information from the low‐frequency components which are less aliased. In this paper, we further extend the de‐aliased Cadzow filtering approach to reconstruct regularly sampled seismic traces from the noisy observed data by modifying the reinserting operation, in which the high‐frequency components are projected onto the sub‐space spanned by several singular vectors of the low‐frequency components. At each iteration, the filtered data are weighted to the original data as a feedback. The weighting factor is related to the background noise level and changes with iteration. The feasibility of the proposed technique is validated via two‐dimensional, three‐dimensional and five‐dimensional synthetic data examples, as well as two‐dimensional post‐stack and three‐dimensional pre‐stack field data examples. The results demonstrate that the proposed technique can effectively interpolate regularly sampled data and is robust in noisy environments.

Identification method and distribution of palaeovolcanoes in Mulei Depression in the Junggar Basin, Western China

The Mulei Depression is a secondary structural unit in the south‐eastern part of the Junggar Basin in the Central Asian Orogenic Belt. As in other parts of the Junggar Basin, it experienced large‐scale volcanic activity in the Carboniferous. However, due to the seismic data, quality of this area is poor, and the drilling data is less early, the Carboniferous volcanic activity is difficult to identify and explain. In the case of minimal well information available, we identify the volcanoes of the Upper Carboniferous Bashan Formation of the Mulei Depression and clarify its distribution characteristics. Through frequency decomposition and a reconstruction of seismic data, the seismic reflection characteristics of the ancient volcanic cone become prominent and easy to identify, and even the period of some stacked volcanic cones can be divided. According to the geological model put forward, the seismic reflection characteristics of the ancient volcanic cone and its surrounding volcanic rocks are clarified. The volcanic cones are characterized by mound‐clutter and weak‐blank amplitude reflection. The internal clutter mainly have resulted from rapid changes in lithology and complex secondary faults. Away from the crater direction, the energy of a seismic event is gradually enhanced, and the volcanic sediments from other sources will be superimposed above the previously formed volcanoes. It is found that the volcanic channel with a short‐axis continuous illusion is often developed at the bottom. The volcanic channel which can be identified in seismic mainly affects the development of large volcanoes. Finally, 27 volcanic cones and seven volcanic channels were identified via establishing the three‐dimensional (3D) model of the volcano and the amplitude of the root mean square of seismic data after reconstruction, as well as interpreting deep faults. The volcanic development in the Mulei Depression has the characteristics of an NE spread along deep faults and northern more than southern.

Expression of Concern: Multi-step damped multichannel singular spectrum analysis for simultaneous reconstruction and denoising of 3D seismic data

Expression of Concern: Multi-step damped multichannel singular spectrum analysis for simultaneous reconstruction and denoising of 3D seismic data

Expression of Concern: Adaptive rank-reduction method for seismic data reconstruction

Expression of Concern: Adaptive rank-reduction method for seismic data reconstruction

Gaussian beam reconstruction of seismic data

We have developed a new Gaussian beam reconstruction algorithm using time-domain Gaussian beam (TGB) method to decompose seismic data. The TGB is characterized by a particular arrival time, location, amplitude, orientation, curvature, and extent. TGB decomposition and reconstruction of seismic data are implemented by the plane-wave decomposition (PWD) theory. First, we evaluate the construction principle of TGB, and then we develop the PWD filter to decompose seismic data into local plane waves by estimated dip fields and curvature fields of the seismic records. Next, the local plane waves in terms of TGBs are used to reconstruct seismic data through iteratively minimizing the residual error. Afterward, Gaussian beam depth migration is performed on the reconstructed data. Finally, we analyze the reconstruction results under the circumstance of seismic data with randomly missing traces. Numerical tests indicate that for data with missing traces, the Gaussian beam method obtains better reconstruction performance than the traditional projection onto convex sets method with the same number of iterations. The combination of Gaussian beam seismic data reconstruction and migration extends the research field of Gaussian beam migration, which has an important theoretical and practical significance.

Five-dimensional seismic data reconstruction using the optimally damped rank-reduction method

Five-dimensional seismic data reconstruction using the optimally damped rank-reduction method

Irregularly Sampled Seismic Data Reconstruction Using Multiscale Multidirectional Adaptive Prediction-Error Filter

The interpolation based on prediction-error filter (PEF) is one of the most effective approaches recently proposed for seismic data reconstruction. However, the number of effective regression equations for estimating the filter coefficients will be much less when missing many seismic traces, which makes the estimated filter coefficients inaccurate or even impossible to be estimated. To improve the accuracy of filter coefficients, in this paper, we design a multiscale and multidirectional PEF, in which the number of effective regression equations can be increased much more, and use it to seismic data reconstruction. First, we estimate the adaptive different directional PEFs using the known data in different scales. The known data can be regularly sampled with randomly or regularly missing, or even both of them. Then, we interpolate missing seismic traces using estimated PEF and the sparse known traces. The regularization in least-squares inversion controls the adaptivity of multiscale multidirectional PEF. The use of more effective regression equations in inversion makes the filter coefficients more accurate. In addition, the multiscale filter can conveniently deal with the case of the simultaneous existence of randomly and regularly missing, while the conventional methods have to be treated separately for randomly and regularly missing. The applicability and effectiveness of the proposed method are examined by synthetic and field data examples.

Five-dimensional seismic data reconstruction using the optimally damped rank-reduction method

Five-dimensional seismic data reconstruction using the optimally damped rank-reduction method

Computational efficient multidimensional singular spectrum analysis for prestack seismic data reconstruction

We have evaluated a fast and memory efficient implementation of the multidimensional singular spectrum analysis (MSSA) method for seismic data reconstruction. The new algorithm makes use of random projections and the structure of Hankel matrices to avoid the construction of large Hankel trajectory matrices. Through tests with synthetic and real data examples, we find that the presented algorithm significantly decreases the computational costs of MSSA seismic data recovery without compromising its accuracy.

Robust tensor-completion algorithm for 5D seismic-data reconstruction

Multidimensional seismic data reconstruction has emerged as a primary topic of research in the field of seismic data processing. Although there exists a large number of algorithms for multidimensional seismic data reconstruction, they often adopt the [Formula: see text] norm to measure the discrepancy between observed and reconstructed data. Strictly speaking, these algorithms assume well-behaved noise that ideally follows a Gaussian distribution. When erratic noise contaminates the seismic traces, a 5D reconstruction must adopt a robust criterion to measure the difference between observed and reconstructed data. We develop a new formulation to the parallel matrix factorization tensor completion method and adapt it for coping with erratic noise. We use synthetic and field-data examples to examine our robust reconstruction technique.

Reconstruction of missing seismic traces based on sparse dictionary learning and the optimization of measurement matrices

Due to limitations arising under complicated geological conditions and field collection environments, we often cannot collect complete and regular field seismic data. To solve that problem, the reconstruction of seismic data has been widely studied. In this paper, we propose a reconstruction algorithm for seismic data with missing traces based on sparse dictionary learning and measurement matrix optimization. The algorithm views the seismic data as a matrix. It first uses the neighboring channel to fill in the missing trace and then uses the transposed matrix and applies the K-singular value decomposition (K-SVD) algorithm by columns to train the sample, obtaining an over-complete dictionary that can be used to develop an optimal sparse representation of seismic data. In the process of seismic data reconstruction, we first transpose the seismic data with missing traces, adopt the regularized orthogonal matching pursuit (ROMP) algorithm to obtain optimum estimations of the data in each column and then transpose the matrix to obtain the reconstructed seismic data. To further increase the quality of seismic data reconstructions, the algorithm presented in this paper also introduces the Equiangular Tight Frame (ETF) method to optimize the measurement matrix. The experiments indicate that this paper's algorithm can achieve high-quality reconstructions of seismic data.

High-precision seismic data reconstruction with multi-domain sparsity constraints based on curvelet and high-resolution Radon transforms

In recent years, the sparsity-promoting reconstruction method based on the compressed sensing theory has been rapidly developed and applied to seismic data reconstruction. Many achievements have been made toward providing high-quality reconstruction by using undersampled data. However, the problem of insufficient reconstruction in null traces still hinders us a lot in practical applications, especially for complex seismic data. Aiming to solve this problem, we made full use of the sparsity characteristics of seismic data in multiple sparse transform domains and jointly reconstructed seismic data to realize the complementary advantages of multiple sparse transforms; As such, we propose a high-precision seismic data recovery method with multi-domain sparsity constraints based on curvelet and high-resolution Radon transforms. Numerical examples by synthetic and real data showed that the new approach can achieve a better reconstruction result than the commonly used curvelet-based recovery method. Integrated with the curvelet transform to develop new recovery method, the high-resolution Radon transform has more advantages than the conventional Radon transform for overcoming the shortcomings associated with the insufficient reconstruction of high-amplitude events. At the same time, the method is also applicable for developing new reconstruction methods by combining other sparse transforms depending on the characteristics of seismic data. The reconstruction method with multi-domain sparsity constraints can easily be extended to three-dimensional situation.

Full waveform inversion based on morphological component analysis seismic data reconstruction

Seismic exploration is the most important and the most effective method of solving the petroleum exploration problem which uses seismic data to cognize the underground geological structure and orientate oil and gas traps. Full waveform inversion (FWI) could build precision velocity model of earth medium through the extraction of the full information content of the seismic data. The quality of seismic data has significant impact on the full waveform inversion. However, field seismic data acquisition is restricted by various conditions, the observation system is often irregular, seismic data may be missing. Irregularity or missing of seismic data will seriously affect the seismic processing and interpretation results. Seismic data reconstruction methods can be used to restore the missing data, then improve the quality of seismic data. In this paper, we utilize the morphological component analysis (MCA) method to reconstruct the seismic data. Then we combine this method with full waveform inversion to provide high quality seismic data which used as input for FWI. Experimental results show that not only can the MCA method rebuild seismic data accurately but also has the effect of denoising. Full waveform inversion based on MCA seismic data reconstruction can obtain higher precision subsurface velocity. We apply this method to the field seismic data, the quality of seismic data is improved, and can obtain better inversion results.

Reconstruction of seismic data with missing traces using normalized Gaussian weighted filter

Reconstruction of seismic data with missing traces using normalized Gaussian weighted filter

Crossline-direction reconstruction of multi-component seismic data with shearlet sparsity constraint

Crossline-direction reconstruction of multi-component seismic data with shearlet sparsity constraint

Adaptive rank-reduction method for seismic data reconstruction

Abstract Seismic data reconstruction plays an important role in the whole seismic data processing and imaging workflow, especially for those data that are acquired from severe field environment and are missing a large portion of the reflection signals. The rank-reduction method is considered to be a very effective method for interpolating data that are of small curvature, e.g. the post-stack data. However, when the data are more complicated, the rank-reduction method may fail to achieve acceptable performance. A useful strategy is to use local windows to process the data so that the data in each local window satisfy the plane-wave assumption of the rank-reduction method. However, the rank in each window requires a careful selection. Traditional methods select a global rank for all windows. We have proposed an automatic algorithm to select the rank in each processing window. The energy ratio between two consecutive singular values is chosen as the criterion to define the optimal rank. We apply this strategy to seismic data interpolation and use both synthetic and field data examples to demonstrate its potential in practical applications.

Retracted: Adaptive rank-reduction method for seismic data reconstruction

Retracted: Adaptive rank-reduction method for seismic data reconstruction