Surface-related multiple elimination remains one of the most robust primary estimation approaches for decades, in which the adaptive subtraction step is a non-trivial task. Due to imperfections in the made assumptions during prediction, the perfect adaptive subtraction is a highly non-linear and non-stationary process, which is suitable for the popular deep learning (DL)-based image processing. Different from the most straightforward DL-based adaptive subtraction (i.e., the full wavefield and the advanced estimated primary training pair), we propose to include both the original full wavefield and the initial globally estimated surface multiples as the two-channel input, and train a DL neural network (U-Net) on synthetic modeled primaries. In this way, the robust physics (i.e., the globally estimated multiples) is utilized, and the ground truth primary labels can be beneficial to the framework. Both synthetic and field examples are provided to demonstrate the current performance of our proposed framework.

An important imaging challenge is creating reliable seismic images without internal multiple crosstalk, especially in cases with strong overburden reflectivity. Several data-driven methods have been proposed to attenuate the internal multiple crosstalk, for which fully sampled data in the source and receiver side are usually required. To overcome this acquisition constraint, model-driven full-wavefield migration (FWM) can automatically include internal multiples and only needs dense sampling in either the source or receiver side. In addition, FWM can correct for transmission effects at the reflecting interfaces. Although FWM has been shown to work effectively in compensating for transmission effects and suppressing internal multiple crosstalk compared to conventional least-squares primary wavefield migration (PWM), it tends to generate relatively weaker internal multiples during modeling. Therefore, some leaked internal multiple crosstalk can still be observed in the FWM image, which tends to blend in the background and can be misinterpreted as real geology. Thus, we adopted a novel framework using local primary-and-multiple orthogonalization (LPMO) on the FWM image as a postprocessing step for leaked internal multiple crosstalk estimation and attenuation. Due to their opposite correlation with the FWM image, a positive-only LPMO weight can be used to estimate the leaked internal multiple crosstalk, whereas a negative-only LPMO weight indicates the transmission effects that need to be retained. Application to North Sea field data validates the performance of the proposed framework for removing the weak but misleading leaked internal multiple crosstalk in the FWM image. Therefore, with this new framework, FWM can provide a reliable solution to the long-standing issue of imaging primaries and internal multiples automatically, with proper primary restoration.

Three upcoming Martian missions will deploy a ground-penetrating radar (GPR) to reveal the fine-resolution subsurface structure and dielectric properties of materials beneath the surface. Numerical forward simulations of radar echo using a model of the near-surface structure at the landing site can provide a valuable reference for processing and interpretation of future radar data collected on Mars. In this study, based on the geological information of the Jezero crater, a detailed stratigraphic model of the near-surface structure is derived, which includes several key features, for example, the randomness of the medium, terrain, and cracks. To identify correctly the reflections of subsurface interfaces and fractures from the radar image, a v(z) f-k migration is carried out, the performance of which is evaluated using the GPR data obtained near Antarctic Zhongshan Station since the electrical properties of Antarctic glaciers and Martian materials are to some extent comparable. The results in this work show that compared with common migration algorithm, the v(z) f-k method not only improves the clarity of radar image but also provides the permittivity profiles to infer the composition of the substrate, leading to a better understanding of Martian near-surface geology.

Reliably separating primary and multiple reections in a shallow water environment (i.e., 50 m to 200 m water depth) still remains a challenge. The success of previously published closed-loop surface-related multiple estimation (CL-SRME) depends heavily on the data coverage, i.e., the near-offset reconstruction. Therefore, we propose the integrated framework of CL-SRME and full-wavefield migration (FWM). Multiples recorded in the data are capable of helping inll the acquisition imprint of the FWM image. With this image as a strong constraint, we are able to reconstruct the data at near-offsets, which is essential for better primary and multiple estimation during CL-SRME. FWM applied in a non-linear way can avoid the negative inuences from the missing data, and at the same time bring in more physics between primaries and multiples. The FWM image of the top part of the subsurface is also used to back-project the information from multiples to primaries with the physical constraint of all this information belongs to the same earth model, provided that a good description of the source wavefield and a reasonable velocity model are available. The proposed integrated framework first reconstructs near-offsets via the closed-loop imaging process of FWM and then feeds the complete reconstructed data to CL-SRME for better primary and multiple estimation. A good performance is demonstrated on both 2D synthetic and field data examples in a challenging shallow water environment.

Accurate removal of surface-related multiples remains a challenge in shallow-water cases. One reason is that the success of surface-related multiple estimation (SRME)-related algorithms is sensitive to the quality of the near-offset reconstruction. When it comes to a larger missing gap and a shallower water bottom, the state-of-the-art near-offset gap construction method - the parabolic Radon transform - fails to provide reliable recovery of the shallow reflections due to the limited information from the data and highly curved events at near offsets with strong lateral amplitude variations. Therefore, we have developed a novel workflow that first deploys a deep-learning-based reconstruction of the shallow reflections and then uses the reconstructed data as the input for the subsequent surface multiple removal. In particular, we use a convolutional neural network architecture - U-net that was developed from convolutional autoencoders with extra direct skip connections between different levels of encoders and the corresponding decoders. Instead of using field data directly in network training, the training set is carefully synthesized based on the prior water-layer information of the field data; thus, a fully sampled field data set, which is difficult to obtain, is not needed for training in our workflow. An inversion-based approach - closed-loop SRME - is used for the surface multiple removal, in which the primaries are directly estimated via full-waveform inversion in a data-driven manner. Finally, the effectiveness of our workflow is determined based on 2D North Sea field data in a shallow-water scenario (92.5 m water depth) with a relatively large minimum offset (150 m).

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The local signal-to-noise orthogonalization algorithm has been widely used in the community of seismic processing and imaging. It helps orthogonalize the signal-and-noise components in an elegant way so that the noise does not contain the signal leakage in seismic denoising. The traditional local signal-to-noise orthogonalization is based on solving a highly underdetermined, ill-posed inverse problem with local smoothness constraint. Due to the inversion nature, the local orthogonalization method requires a large number of iterations and thus is computationally demanding in large-scale applications. Here, we proposed a much accelerated signal-and-noise orthogonalization method, where we design an efficient way for calculating the orthogonalization weight. When new samples are involved in the calculation, we calculate the orthogonalization weight of the new samples by connecting them with the calculated weights of the previous samples. The orthogonalization weight needs to be smoothed and scaled after all samples have been processed to make the resulted orthogonalization weight smooth across the seismic data and match the amplitude level of the initially suppressed noise. In this way, we avoid iterations when calculating the orthogonalization weight. We apply the proposed method to several synthetic and field data examples, have a benchmark comparison with state-of-the-art algorithms, and demonstrate its much accelerated efficiency compared with the traditional local signal-and-noise orthogonalization.

Surface-related multiple elimination (SRME) is a solid and effective approach for primary estimation. However, due to the imperfections in data and method multiple energy leakage is commonly seen in the results of SRME-predicted primaries. Assuming that the primaries and multiples do not correlate locally in the time-space domain, we are able to extract the leaked multiples from the initially estimated primaries using multi-domain local primary-and-multiple orthogonalization. The proposed framework consists of two steps: an initial primary/multiple estimation step and a multiple-leakage extraction step. The initial step corresponds to SRME, which produces the initial estimated primary and multiple models. The second step is based on multi-domain local primary-and-multiple orthogonalization to retrieve the leaked multiples. Multi-domain indicates that we first extract the leaked multiples in shot domain, and then the residual can be further extracted in common-offset domain. Thus, we can obtain a better primary output which has much less leaked multiple energy. We demonstrate a good performance of our proposed framework on both synthetic and field data, where it repairs the leakage of standard global adaptive subtraction.

Amplitude-preserving data processing is an important and challenging topic in many scientific fields. The amplitude-variation details in seismic data are especially important because the amplitude variation is directly related with the subsurface wave impedance and fluid characteristics. We propose a novel seismic noise attenuation approach that is based on local plane-wave assumption of seismic events and the amplitude preserving capability of the orthogonal polynomial transform (OPT). The OPT is a way for representing spatially correlative seismic data as a superposition of polynomial basis functions, by which the random noise is distinguished from the useful energy by the high orthogonal polynomial coefficients. The seismic energy is the most correlative along the structural direction and thus the OPT is optimally performed in a flattened gather. We introduce in detail the flattening operator for creating the flattened dimension, where the OPT can be applied subsequently. The flattening operator is created by deriving a plane-wave trace continuation relation following the plane-wave equation. We demonstrate that both plane-wave trace continuation and OPT can well preserve the strong amplitude variation existing in seismic data. In order to obtain a robust slope estimation performance in the presence of noise, a robust slope estimation approach is introduced to substitute the traditional method. A group of synthetic, pre-stack and post-stack field seismic data are used to demonstrate the potential of the proposed framework in realistic applications.

We propose a new low-rank based noise attenuation method using an efficient algorithm for tracking subspaces from highly corrupted seismic observations. The subspace tracking algorithm requires only basic linear algebraic manipulations. The algorithm is derived by analysing incremental gradient descent on the Grassmannian manifold of subspaces. When the multidimensional seismic data are mapped to a low-rank space, the subspace tracking algorithm can be directly applied to the input low-rank matrix to estimate the useful signals. Since the subspace tracking algorithm is an online algorithm, it is more robust to random noise than traditional truncated singular value decomposition (TSVD) based subspace tracking algorithm. Compared with the state-of-The-Art algorithms, the proposed denoising method can obtain better performance. More specifically, the proposed method outperforms the TSVD-based singular spectrum analysis method in causing less residual noise and also in saving half of the computational cost. Several synthetic and field data examples with different levels of complexities demonstrate the effectiveness and robustness of the presented algorithm in rejecting different types of noise including random noise, spiky noise, blending noise, and coherent noise.

Five-dimensional (5D) seismic data reconstruction becomes more appealing in recent years because it takes advantage of five physical dimensions of the seismic data and can reconstruct data with large gap. The low-rank approximation approach is one of the most effective methods for reconstructing 5D dataset. However, the main disadvantage of the low-rank approximation method is its low computational efficiency because of many singular value decompositions (SVD) of the block Hankel/Toeplitz matrix in the frequency domain. In this paper, we develop an SVD-free low-rank approximation method for efficient and effective reconstruction and denoising of the seismic data that contain four spatial dimensions. Our SVD-free rank constraint model is based on an alternating minimization strategy, which updates one variable each time while fixing the other two. For each update, we only need to solve a linear least-squares problem with much less expensive QR factorization. The SVD-based and SVD-free low-rank approximation methods in the singular spectrum analysis (SSA) framework are compared in detail, regarding the reconstruction performance and computational cost. The comparison shows that the SVD-free low-rank approximation method can obtain similar reconstruction performance as the SVD-based method but with a large computational speedup.

Accurate multiple removal remains an important step in seismic data processing sequences. Most multiple removal methods, such as surface-related multiple elimination (SRME), consist of a multiple prediction step and an adaptive subtraction step. Due to imperfect circumstances (e.g., coarse data sampling) or built-in assumptions (e.g., 2D method versus 3D data), multiple leakage is commonly observed in the results. More aggressive adaptive multiple subtraction can reduce the leakage problem, for example, by using small local windows and a long filter length, but at the risk of severely damaging the primaries due to overfitting. In contrast, conservative adaptive subtraction with large or global windows and a short filter length can preserve most primary energy while tending to have more multiple leakage because of underfitting. Assuming that the primaries and multiples do not correlate locally in the time-space domain, our solution to this problem is to extract the leaked multiples from the initially estimated primaries using local primary-and-multiple orthogonalization (LPMO) rather than restoring the damaged primaries. Our framework consists of two steps: an initial primary estimation step and a multiple leakage extraction step. The initial step corresponds to conservative SRME (or an equivalent method) that produces the initially estimated primary and multiple models. The second step is based on LPMO to retrieve the leaked multiples from the estimated primaries via a time- and space-varying weight function that is estimated from the local correlation of predicted multiples and residual multiples in the estimated primaries with the help of shaping regularization. In this way, we can obtain a better primary model that has much less leaked multiple energy and less primary damage at the same time. We find good performance of our framework via two synthetic data examples and one field data example.

Reliably estimating primary reflections in a shallow-water scenario remains a challenge. Therefore, we introduce the integration of closed-loop surface-related multiple estimation (CL-SRME) and full wavefield migration (FWM). Multiples present in the seismic data can help infill the acquisition imprint of the FWM image. With the image as constraint, we are capable of reconstructing the data at smaller offsets, which is crucial for CL-SRME. Therefore, in the proposed framework, we use the image to back-project the information from multiples to primaries with the physical constraint of all information belonging to the same earth model. We utilize a cascaded approach, which first involves reconstructing incomplete data via FWM and then uses the fully-sampled reconstructed data as the desired input for CL-SRME. Applications to both synthetic and field data demonstrate the good performance of the proposed framework in a shallow-water scenario.

Surface-related multiple elimination (SRME) is a solid and effective approach for primary estimation. However, due to the imperfections in data and method (e.g. coarsely-sampled dataset and balancing effect of adaptive subtraction) multiple energy leakage is commonly seen in the results of SRME-predicted primaries. Assuming that the primaries and multiples do not correlate locally in the time-space domain, we are able to extract the leaked multiples from the initially estimated primaries using local primary-and-multiple orthogonalization. The proposed framework consists of two steps: an initial primary/multiple estimation step and a multiple-leakage extraction step. The initial step corresponds to SRME, which produces the initial estimated primary and multiple models. The second step is based on local primary-and-multiple orthogonalization to retrieve the leaked multiples, which can be seen as a remedy for correcting the initial estimated primary and multiple models. Thus, we can obtain a better primary output which has much less leaked multiple energy. We demonstrate a good performance of our proposed framework on both synthetic and field data, where it repairs the leakage of standard adaptive subtraction.

Strong noise is one of the toughest problems in the controlled-source electromagnetic (CSEM) method, which highly affects the quality of recorded data. The three main types of noise existing in CSEM data are periodic noise, Gaussian white noise, and nonperiodic noise, among which the nonperiodic noise is thought to be the most difficult to remove. We have developed a novel and effective method for removing such nonperiodic noise by formulating an inverse problem that is based on inverse discrete Fourier transform and several time windows in which only Gaussian white noise exists. These critical locations, which we call reconstruction locations, can be found by taking advantage of the continuous wavelet transform (CWT) and the temporal derivative of the scalogram generated by CWT. The coefficients of the nonperiodic noise are first estimated using the new least-squares method, and then they are subtracted from the coefficients of the raw data to produce denoised data. Together with the nonperiodic noise, we also remove Gaussian noise using the proposed method. We validate the methodology using real-world CSEM data.

We propose a new low-rank based noise attenuation method using an efficient algorithm for tracking subspaces from highly corrupted seismic observations. The subspace tracking algorithm requires only basic linear algebraic manipulations. The algorithm is derived by analysing incremental gradient descent on the Grassmannian manifold of subspaces. When the multidimensional seismic data are mapped to a low-rank space, the subspace tracking algorithm can be directly applied to the input low-rank matrix to estimate the useful signals. Since the subspace tracking algorithm is an online algorithm, it is more robust to random noise than traditional truncated singular value decomposition (TSVD) based subspace tracking algorithm. Compared with the state-of-the-art algorithms, the proposed denoising method can obtain better performance. More specifically, the proposed method outperforms the TSVDbased singular spectrum analysis method in causing less residual noise and also in saving half of the computational cost. Several synthetic and field data examples with different levels of complexities demonstrate the effectiveness and robustness of the presented algorithm in rejecting different types of noise including random noise, spiky noise, blending noise, and coherent noise.