Plane‐wave destruction filters originate from a local plane‐wave model for characterizing seismic data. These filters can be thought of as a time–distance (T‐X) analog of frequency‐distance (F‐X) prediction‐error filters and as an alternative to T‐X prediction‐error filters. The filters are constructed with the help of an implicit finite‐difference scheme for the local plane‐wave equation. Several synthetic and real data examples show that finite‐difference plane‐wave destruction filters perform well in applications such as fault detection, data interpolation, and noise attenuation.

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Applications of plane-wave destruction filters

We present a rank reduction algorithm that permits simultaneous reconstruction and random noise attenuation of seismic records. We based our technique on multichannel singular spectrum analysis (MSSA). The technique entails organizing spatial data at a given temporal frequency into a block Hankel matrix that in ideal conditions is a matrix of rank k , where k is the number of plane waves in the window of analysis. Additive noise and missing samples will increase the rank of the block Hankel matrix of the data. Consequently, rank reduction is proposed as a means to attenuate noise and recover missing traces. We present an iterative algorithm that resembles seismic data reconstruction with the method of projection onto convex sets. In addition, we propose to adopt a randomized singular value decomposition to accelerate the rank reduction stage of the algorithm. We apply MSSA reconstruction to synthetic examples and a field data set. Synthetic examples were used to assess the performance of the method in two...

Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis

‘Subduction erosion’ has been invoked to explain material missing from some continents along convergent margins1. It has been suggested that this form of tectonic erosion removes continental material at the front of the margin or along the underside of the upper (continental) plate2,3,4. Frontal erosion is interpreted from disrupted topography at the base of a slope and is most evident in the wake of subducting seamounts5,6. In contrast, structures resulting from erosion at the base of a continental plate are seldom recognized in seismic reflection images because such images typically have poor resolution at distances greater than ∼ 5 km from the trench axis. Basal erosion from seamounts and ridges has been inferred7,8, but few large subducted bodies—let alone the eroded base of the upper plate—are imaged convincingly. From seismic images we identify here two mechanisms of basal erosion: erosion by seamount tunnelling and removal of large rock lenses of a distending upper plate. Seismic cross-sections from Costa Rica to Nicaragua indicate that erosion may extend along much of the Middle America convergent margin.

Subduction erosion along the Middle America convergent margin

SUMMARY Seismic data recovery from data with missing traces on otherwise regular acquisition grids forms a crucial step in the seismic processing flow. For instance, unsuccessful recovery leads to imaging artefacts and to erroneous predictions for the multiples, adversely affecting the performance of multiple elimination. A non-parametric transform-based recovery method is presented that exploits the compression of seismic data volumes by recently developed curvelet frames. The elements of this transform are multidimensional and directional and locally resemble wave fronts present in the data, which leads to a compressible representation for seismic data. This compression enables us to formulate a new curvelet-based seismic data recovery algorithm through sparsity-promoting inversion. The concept of sparsity-promoting inversion is in itself not new to geophysics. However, the recent insights from the field of ‘compressed sensing’ are new since they clearly identify the three main ingredients that go into a successful formulation of a recovery problem, namely a sparsifying transform, a sampling strategy that subdues coherent aliases and a sparsity-promoting program that recovers the largest entries of the curvelet-domain vector while explaining the measurements. These concepts are illustrated with a stylized experiment that stresses the importance of the degree of compression by the sparsifying transform. With these findings, a curvelet-based recovery algorithms is developed, which recovers seismic wavefields from seismic data volumes with large percentages of traces missing. During this construction, we benefit from the main three ingredients of compressive sampling, namely the curvelet compression of seismic data, the existence of a favourable sampling scheme and the formulation of a large-scale sparsity-promoting solver based on a cooling method. The recovery performs well on synthetic as well as real data by virtue of the sparsifying property of curvelets. Our results are applicable to other areas such as global seismology.

/pdf/non-parametric-seismic-data-recovery-with-curvelet-frames-3bf5izdudw.pdf

Non-parametric seismic data recovery with curvelet frames

Seismic data regularization, which spatially transforms irregularly sampled acquired data to regularly sampled data, is a long-standing problem in seismic data processing. Data regularization can be implemented using Fourier theory by using a method that estimates the spatial frequency content on an irregularly sampled grid. The data can then be reconstructed on any desired grid. Difficulties arise from the nonorthogonality of the global Fourier basis functions on an irregular grid, which results in the problem of “spectral leakage”: energy from one Fourier coefficient leaks onto others. We investigate the nonorthogonality of the Fourier basis on an irregularly sampled grid and propose a technique called “antileakage Fourier transform” to overcome the spectral leakage. In the antileakage Fourier transform, we first solve for the most energetic Fourier coefficient, assuming that it causes the most severe leakage. To attenuate all aliases and the leakage of this component onto other Fourier coefficients, the data component corresponding to this most energetic Fourier coefficient is subtracted from the original input on the irregular grid. We then use this new input to solve for the next Fourier coefficient, repeating the procedure until all Fourier coefficients are estimated. This procedure is equivalent to “reorthogonalizing” the global Fourier basis on an irregularly sampled grid. We demonstrate the robustness and effectiveness of this technique with successful applications to both synthetic and real data examples.

Antileakage Fourier transform for seismic data regularization

Seismic surveys generally have irregular areas where data cannot be acquired. These data should often be interpolated. A projection onto convex sets (POCS) algorithm using Fourier transforms allows interpolation of irregularly populated grids of seismic data with a simple iterative method that produces high-quality results. The original 2D image restoration method, the Gerchberg-Saxton algorithm, is extended easily to higher dimensions, and the 3D version of the process used here produces much better interpolations than typical 2D methods. The only parameter that makes a substantial difference in the results is the number of iterations used, and this number can be overestimated without degrading the quality of the results. This simplicity is a significant advantage because it relieves the user of extensive parameter testing. Although the cost of the algorithm is several times the cost of typical 2D methods, the method is easily parallelized and still completely practical.

3D interpolation of irregular data with a POCS algorithm

Attenuating random noise with a prediction filter in the time-space domain generally produces results similar to those of predictions done in the frequency-space domain. However, in the presence of moderate- to high-amplitude noise, time-space or t-x prediction passes less random noise than does frequency-space, or f-x prediction. The f-x prediction may also produce false events in the presence of parallel events where t-x prediction does not. These advantages of t-x prediction are the result of its ability to control the length of the prediction filter in time. An f-x prediction produces an effective t-x domain filter that is as long in time as the input data. Gulunay's f-x domain prediction tends to bias the predictions toward the traces nearest the output trace, allowing somewhat more noise to be passed, but this bias may be overcome by modifying the system of equations used to calculate the filter. The 3-D extension to the 2-D t-x and f-x prediction techniques allows improved noise attenuation because more samples are used in the predictions, and the requirement that events be strictly linear is relaxed.

Lateral prediction for noise attenuation by t-x and f-x techniques

This paper demonstrates a method of producing pre-stack gathers from blended acquisition data that are as noise-free as gathers from conventional acquisition. Filtering out the interference from the overlapping shots and stacking the data are fairly effective in attenuating the interference from blended shots. However high-quality separation of the interference from the pre-stack data would make the data more suitable for amplitude dependent analysis, such as that for amplitude-versus-offset, time-lapse measurements, and fracture detection. The method presented here produces seismic records in which the interference is attenuated to the point that it is well below the background noise. This high quality attenuation is achieved by using a sparse inversion process that solves a modified version of Berkhout's matrix system, allowing the source responses to be separated for high quality amplitude measurements. The success of this source separation step in the data processing of blended acquisition means we can produce results with a quality that is comparable to that of conventional acquisition. Furthermore, this method improves the data quality while retaining the lower cost and higher productivity of ISSTM acquisition when compared with conventional acquisition.

High Quality Separation of Simultaneous Sources by Sparse Inversion

Seismic surveys are often constrained by the time needed to activate all the required sources so the source signals do not interfere with each other. Simultaneous source seismic acquisition, also referred to as blended acquisition, is an effective method for reducing the cost and improving the quality of seismic surveys by eliminating the requirement that the sources do not interfere with each other. Independent simultaneous shooting is a unique form of blended acquisition in which sources operate independently of each other and the receiver recording is continuous. This acquisition method is particularly efficient and robust in obtaining high-density source grids for land and marine surveys. Processing the simultaneous source data depends on the randomness of the shot times to create a situation where the signal is coherent, and the interference is random in common-receiver gathers. Although the older and simpler method of separating interfering shots with random noise attenuation works well when...

Independent simultaneous source acquisition and processing

Coherent noise may be removed from seismic data by first making an approximate model of the noise, then producing an even better estimation of the noise by adaptively matching the modeled noise to the data. This modified model of the noise may then be subtracted from the data, eliminating most coherent noise. The success of this approach depends both on how well the initial model matches the true noise and the success of the adaptive matching in modifying the initial noise prediction to match the true noise. The adaptive matching step is complicated by the presence of the signal and other noise in the data. In this article, the noise of interest is surface-related multiples, although other types of coherent noise may be removed with this approach.

Ray Abma

Papers

3D interpolation of irregular data with a POCS algorithm

Lateral prediction for noise attenuation by t-x and f-x techniques

High Quality Separation of Simultaneous Sources by Sparse Inversion

Independent simultaneous source acquisition and processing

Comparisons of adaptive subtraction methods for multiple attenuation