Adjacent Seismic Traces Research Articles

Dealiased seismic data interpolation by dynamic matching

Interpolation is a critical step in seismic data processing. Gaps in seismic traces can lead to severe spatial aliasing phenomena in the corresponding f- k spectra. The aliasing caused by regularly spaced gaps has similar f- k spectra as those of the actual data. Existing dealiasing interpolation algorithms generally assume that seismic events are linear and cannot handle nonstationary events. To address this shortcoming, we develop a novel dealiased seismic data interpolation approach using dynamic matching. First, we match two adjacent seismic traces using the local affine regional dynamic time-warping algorithm. Subsequently, we calculate the local slope between two seismic traces. Finally, we perform linear interpolation on the regularly missing seismic data using local slope information. Our approach is tested on synthetic and field seismic data sets. The interpolation results indicate that our approach has a better antialiasing ability and computational efficiency than the traditional Spitz and seislet-based approaches. In addition, this method can be applied to interpolate irregularly sampled seismic data and for simultaneous seismic data interpolation and denoising.

Research on seismic hydrocarbon prediction based on a self-attention semi-supervised model

Predictions of oil and gas reservoirs play an essential role in hydrocarbon reservoir exploration. Multi-attribute seismic data can provide abundant reservoir information. However, traditional reservoir prediction models only reflect the characteristics of local seismic channels, ignoring information on global geological spatial structures. Thus, a semi-supervised prediction model based on self-attention is proposed to extract reservoirs' oil and gas characteristics. With the high cost of labeled samples, neighborhood similarity measurement based on Grey Relation Analysis is applied to determine the homogeneity of adjacent seismic traces for the first time to obtain pseudo-labels while considering geological spatial structure. As a semi-supervised prediction model, a multilayer convolutional neural network with a multi-head self-attention mechanism is utilized, which can extract features from multiple dimensions and investigate global structural information. The experimental results demonstrate that the algorithm in this paper's reservoir oil and gas prediction is more accurate than that of conventional approaches and is consistent with real drilling data.

Fast pre-stack multi-channel inversion constrained by seismic reflection features

Classical multi-channel technology can significantly reduce the pre-stack seismic inversion uncertainty, especially for complex geology such as high dipping structures. However, due to the consideration of complex structure or reflection features, the existing multi-channel inversion methods have to adopt the highly time-consuming strategy of arranging seismic data trace-by-trace, limiting its wide application in pre-stack inversion. A fast pre-stack multi-channel inversion constrained by seismic reflection features has been proposed to address this issue. The key to our method is to re-characterize the reflection features to directly constrain the pre-stack inversion through a Hadamard product operator without rearranging the seismic data. The seismic reflection features can reflect the distribution of the stratum reflection interface, and we obtained them from the post-stack profile by searching the shortest local Euclidean distance between adjacent seismic traces. Instead of directly constructing a large-size reflection features constraint operator advocated by the conventional methods, through decomposing the reflection features along the vertical and horizontal direction at a particular sampling point, we have constructed a computationally well-behaved constraint operator represented by the vertical and horizontal partial derivatives. Based on the Alternating Direction Method of Multipliers (ADMM) optimization, we have derived a fast algorithm for solving the objective function, including Hadamard product operators. Compared with the conventional reflection features constrained inversion, the proposed method is more efficient and accurate, proved on the Overthrust model and a field data set.

Structure-adapted Multichannel Matching Pursuit for Seismic Trace Decomposition

While the single-channel matching pursuit decomposes a seismic trace into a series of wavelets, the multichannel matching pursuit examines the lateral coherence of the seismic traces as a constraint to improve the lateral continuity of the decomposition. However, the presence of structures in the subsurface negatively affects the performance of the multichannel matching pursuit. We proposed a structure-adapted matching pursuit method that combines with a dynamic time-warping (DTW) algorithm to estimate the similarity between adjacent seismic traces and extract an optimal wavelet along the dip plane. This structure-adapted implementation would significantly speed up the convergence of the decomposition process. We modified the DTW algorithm by combining the Euclidean distance of the seismic trace and the first-order temporal derivative of the seismic trace. We also updated the amplitudes of all extracted wavelets simultaneously based on the least-squares principle. This DTW-based, structure-adapted, least-squares, multichannel matching pursuit method would improve the robustness and accuracy of seismic trace decomposition.

Multiscale Coherence Attribute and Its Application on Seismic Discontinuity Description

Geologic structure characterization is a key step for seismic structure interpretation, such as fluvial channels, faults, and fractures. The coherence attribute is a widely used tool for describing seismic discontinuities, which is usually calculated based on the similarity and dissimilarity of the adjacent seismic traces. However, accurately extracting coherence attribute is a difficult task in field data applications because seismic signal is one of the typical nonstationary, non-Gaussian, and wideband signals. To describe seismic discontinuities at different scales, we propose a workflow to extract the multiscale coherence (MSC) attribute. We first decompose seismic data into several band-limited intrinsic mode functions (IMFs) with different dominant frequencies via the multichannel variational mode decomposition (MVMD). Afterward, we develop a Cauchy kernel correlation-based coherence algorithm to extract the coherence attributes at different scales based on the decomposed IMFs. Finally, we can compute the MSC attribute by utilizing the calculated coherence attributes. Field data applications demonstrate that the proposed MSC attribute characterizes seismic discontinuities, such as faults and fluvial channels, more accurately and more clearly than the traditional coherence attribute and the 1-D variational mode decomposition (VMD)-based coherence attribute.

Unsupervised Deep Learning for Random Noise Attenuation of Seismic Data

Random noise attenuation is an essential step to improve the signal-to-noise ratio (SNR) of seismic data. Deep learning for seismic data denoising is dominated by supervised methods that require noise-free data as training targets. It is usually time-consuming and laborious to obtain such clean seismic data, and the effectiveness of the noise attenuation is difficult to be guaranteed. Therefore, we propose a novel unsupervised learning method that learns from noisy data. The method is based on two salient features of seismic data: 1) valid signals of adjacent seismic traces that are spatially correlated and 2) random noise that is spatially independent and unpredictable. An end-to-end deep convolutional neural network (CNN) was constructed to solve the denoising task. Adjacent traces of seismic data, which contain similar seismic phases and interface features, were used as the inputs and labels of the training set. The mapping of spatial correlation can be learned by the CNN so that valid signals from raw seismic data are predicted, while random noise is suppressed for unpredictability. Synthetic and field data were applied to the proposed CNN denoising model. The experimental results demonstrate the effectiveness of random noise attenuation while preserving amplitude compared with two commonly used state-of-the-art denoising methods.

Seismic geologic structure characterization using a high-order spectrum-coherence attribute

Characterization of seismic geologic structures, such as describing fluvial channels and geologic faults, is significant for seismic reservoir prediction. The coherence algorithm is one of the widely used techniques for describing discontinuous seismic geologic structures. However, precise coherence attributes between adjacent seismic traces are difficult to compute due to the nonstationary and non-Gaussian property of seismic data. To describe seismic geologic structures accurately, we define a high-order spectrum-coherence (HOSC) attribute. First, we have developed a time-frequency (TF) analysis method to compute a constant-frequency seismic volume with high TF resolution, i.e., the second-order synchrosqueezing wave packet transform. Then, we developed a coherence approach by combining the mutual information (MI) calculation and coherence algorithm based on the eigenvalue computation (C3). To improve computational efficiency, we adopt the information divergence instead of the eigenvalue calculation of the C3-based algorithms. By applying our coherence algorithm to constant-frequency seismic volumes, we obtain the HOSC attribute. To test the validity of the proposed workflow, we evaluate the HOSC attribute using synthetic data. After applying our workflow to 3D real seismic data located in eastern China, the HOSC attribute characterizes seismic geologic discontinuities and subtle features clearly and accurately, such as fluvial channels and subtle faults.

Coherence algorithm with a high‐resolution time–time transform and feature matrix for seismic data

ABSTRACTTraditional coherence algorithms are often based on the assumption that seismic traces are stationary and Gaussian. However, seismic traces are actually non‐stationary and non‐Gaussian. A constant time window and the canonical correlation analysis in traditional coherence algorithms are not optimal for non‐stationary seismic traces and cannot describe the similarity between adjacent seismic traces in detail. To overcome this problem, a new coherence algorithm using the high‐resolution time–time transform and the feature matrix is designed. The high‐resolution time–time transform used to replace the constant time window can produce a frequency‐dependent time local series to analyse non‐stationary seismic traces. The feature matrix, constructed by the frequency‐dependent time local series and the related local gradients, defines a new correlation metric that enhances more details of the geological discontinuities in seismic images than does the canonical correlation analysis. Additionally, the Riemannian metric is introduced for related calculations because the feature matrices are not defined in a Euclidean space but rather in a manifold space. Application to field data illustrates that the proposed method reveals more details of structural and stratigraphic features.

A Generalized Coherence Algorithm Based on Kernel Correlation

Traditional coherence algorithms are mostly based on the assumption that seismic traces are Gaussian and linear correlative. However, for nonGaussian seismic traces, the linear correlation analysis cannot accurately describe the similarity between adjacent seismic traces. To solve this issue, we adopt the kernel correlation instead of the linear correlation to improve coherence-based algorithms. Note that the kernel correlation is a generalized correlation with various kernel functions. It provides a framework for expanding the coherence algorithm based on linear correlation. Moreover, we discuss how to choose an appropriate kernel function in detail. To testify the validity of the kernel correlation, we apply it to field data using different kernels. The results demonstrate the effectiveness of the proposed algorithm to describe geological discontinuity and heterogeneity, such as fluvial channels and faults.

Multi‐trace basis‐pursuit seismic inversion for resolution enhancement

ABSTRACTSeismic inversion is an important tool that transfers interface information of seismic data to formation information, which renders the seismic data easily understood by geologists or petroleum engineers. In this study, a novel multi‐trace basis‐pursuit inversion method based on the Bayesian theory is proposed to enhance the vertical resolution and overcome the lateral instability of inversion results between different traces occasionally seen in the traditional trace‐by‐trace basis‐pursuit inversion method. The Markov process is initially introduced to describe the relationship between adjacent seismic traces and their correlation, which we then close couple in the equation of our new inversion method. A recursive function is further derived to simplify the inversion process by considering the particularity of the coefficient matrix in the multi‐trace inversion equation. A series of numerical‐analysis and field data examples demonstrates that both the traditional and the new methods for P‐wave impedance inversion are helpful in enhancing the resolution of thin beds that are usually difficult to discern from original seismic profiles, thus highlighting the importance of acoustic‐impedance inversion for thin bed interpretation. Furthermore, in addition to yielding thin bed inversion results with enhanced lateral continuity and high vertical resolution, our proposed method is robust to noise and cannot be easily contaminated by it, which we verify using both synthetic and field data.

Multi-trace stochastic sparse-spike inversion for reflectivity

Sparse-spike reflectivity inversion can be generally regarded as the combination of a non-linear problem of finding the locations and a linear problem of solving the amplitudes of a series of non-zero spikes. The input parameters of the inversion, including the trade-off parameter and the number of the non-zero spikes, are always determined by presetting under the rule of thumb. The improper choices of the input parameters are likely to cause the overfitting issue. Moreover, because the convergence is affected by the fitness between the observed data and the synthetic data derived by using the inverted spikes, the spikes with large amplitudes will have larger influence on the determination of the convergence. As a result, the outliers with large amplitudes are likely to affect the inversion result seriously. Under the assumption of layered-earth model and lateral continuity of subsurface layer, multi-trace stochastic inversion method is developed with adjacent seismic traces served as a constraint. By simultaneously non-linear search for the locations and the slopes of non-zero spikes of the target trace, the proposed method enhances the robustness of inversion results to the choice of input parameters and relieves the influence of outliers to some extent. As an extension of the single-trace stochastic sparse-spike inversion, the detecting ability to thin-beds is reserved and the uncertainty of the obtained reflectivities can be estimated. Synthetic data examples illustrate the effectiveness of the proposed method. The details of subsurface geologically structure are derived in the field data example, which could be helpful to the interpretation.

Semblance, coherence, and other discontinuity attributes

Discontinuity calculations, also called coherence or semblance, are some of the most commonly used seismic attributes. They measure the amount of similarity between adjacent seismic traces. However, there are several types of discontinuity estimates and a plethora of names for similar attributes. As a result, it can be difficult to understand the differences among them. Although the discontinuity algorithm that any particular software package uses might be unknown, most are based on one of a few published methods. Understanding published discontinuity attributes gives insight into the trade-offs among different proprietary implementations. Therefore, in this tutorial and the accompanying Jupyter notebook, we will explore simplified Python implementations of a few widely used discontinuity algorithms.

A seismic coherency method using spectral amplitudes

Seismic coherence is used to detect discontinuities in underground media. However, strata with steeply dipping structures often produce false low coherence estimates and thus incorrect discontinuity characterization results. It is important to eliminate or reduce the effect of dipping on coherence estimates. To solve this problem, time-domain dip scanning is typically used to improve estimation of coherence in areas with steeply dipping structures. However, the accuracy of the time-domain estimation of dip is limited by the sampling interval. In contrast, the spectrum amplitude is not affected by the time delays in adjacent seismic traces caused by dipping structures. We propose a coherency algorithm that uses the spectral amplitudes of seismic traces within a predefined analysis window to construct the covariance matrix. The coherency estimates with the proposed algorithm is defined as the ratio between the dominant eigenvalue and the sum of all eigenvalues of the constructed covariance matrix. Thus, we eliminate the effect of dipping structures on coherency estimates. In addition, because different frequency bands of spectral amplitudes are used to estimate coherency, the proposed algorithm has multiscale features. Low frequencies are effective for characterizing large-scale faults, whereas high frequencies are better in characterizing small-scale faults. Application to synthetic and real seismic data show that the proposed algorithm can eliminate the effect of dip and produce better coherence estimates than conventional coherency algorithms in areas with steeply dipping structures.

Intermediate-Frequency Seismic Record Discrimination by Radial Trace Time–Frequency Filtering

In this letter, we research a spatiotemporal-domain-based time-frequency peak filtering (TFPF) method in order to remove the large error (bias) of the conventional TFPF in intermediate-frequency seismic record discrimination. An intermediate-frequency seismic signal is one whose dominant frequency is about 40 Hz or higher. To find a balance between noise attenuation and reflected signal preservation, the radial-trace TPFT (RT-TFPF) takes both the unbiased condition and the adjacent seismic traces' correlation into consideration, and uses the RT transform to obtain a reduced-frequency input to decrease the TFPF error. Therefore, this method can discriminate some reflection events weakened by the conventional TFPF algorithm. First, we decrease the intermediate frequencies along RTs nearly aligned with the reflection event. Then, we obtain a less biased TFPF estimation with suitable window length τ. Finally, we recover the original intermediate frequency with the inverse RT transform. With the RT-TFPF, we can enhance reflection events without sacrificing frequency components while attenuating as much random noise as possible. Experiments on both synthetic model and field data demonstrate that the RT-TFPF performs well both in random noise attenuation and intermediate-frequency preservation, in addition to presenting advantages over the conventional TFPF.

Higher-order-statistics and supertrace-based coherence-estimation algorithm

This article proposes a new higher-order-statistics-based coherence-estimation algorithm, which we denote as HOSC. Unlike the traditional crosscorrelation-based C1 coherence algorithm, which sequentially estimates correlation in the inline and crossline directions and uses their geometric mean as a coherence estimate at the analysis point, our method exploits three seismic traces simultaneously to calculate a 2D slice of their normalized fourth-order moment with one zero-lag correlation and then searches for the maximum correlation point on the 2D slice as the coherence estimate. To include more seismic traces in the coherence estimation, we introduce a supertrace technique that constructs a new data cube by rearranging several adjacent seismic traces into a single supertrace. Combining our supertrace technique with the C1 and HOSC algorithms, we obtain two efficient coherence-estimation algorithms, which we call ST-C1 and ST-HOSC. Application results on the real data set show that our algorithms are able to reveal more details about the structural and stratigraphic features than the traditional C1 algorithm, yet still preserve its computational efficiency.

Structural analysis of 3D seismic data, using the correlation attribute: a case study – Carboniferous of the Southern North Sea (UK)

With the advent of a new seismic attribute, generically termed correlation, interpreters have a non-specialist tool which enables decisions to be made on structural and stratigraphic patterns within a 3D dataset. The process behind the attribute may appear to be black box technology, however, the resultant data are straightforward and enable the interpreters to make their own conclusions about the seismic information presented. Correlation data are simply a quantified comparison of adjacent seismic traces. The value to be unlocked from this attribute lies in rapid delineation of fault and stratigraphic patterns. This requires a revised approach to the interpretation workflow, involving analysis of the correlation attribute volume during primary stages of any 3D-interpretation project. Using a technique termed ‘ribbon interpretation’, correlation data are analysed for information relating to lineaments and data inconsistencies. The identification of features using ribbons, which are short 2 point segments, can then be stacked and filtered by the interpreter to give direct information on faulting and stratigraphic features. The filtered ribbon data are then progressed through to horizon interpretation, where they can be integrated to provide a more robust structural or stratigraphic solution. Application of the ribbon interpretation technique within the mature environment of the structurally complex, Carboniferous play (UK SNS) (Fig. 1) has allowed faster and better results across exploration, appraisal and production scenarios.

3-D seismic interpretation using the coherency cube: An example from the South Embra Precaspian Basin, Kazakhstan

Coherency measures the similarity between adjacent seismic traces. The more similar the traces, the higher the coherency. For example, a 3-D time slice which transects a fault would show low coherency values at the fault cut because the similarity of traces decreases across the fault plane.

Nonlinear seismic trace interpolation

The nonlinear correlation technique has been used to guide a seismic trace interpolant to fill gaps in seismic surveys, replace noisy traces, and produce evenly spaced arrays. Given an initial alignment (NMO correction for prestack data and manually inserted correlation lines for post‐stack data), the correlation aligns corresponding features between adjacent seismic traces and quantifies the traveltime difference between the traces on a point‐for‐point basis. This information is used to construct synthetic (interpolated) traces, at any arbitrary distance between the correlated traces, which preserve dip and amplitude changes of the individual reflectors, assuming that such dip and amplitude changes occur linearly (or some other specified functional form) between the correlated traces. The technique is applied to a 48-channel, NMO corrected, CDP gather and to a stacked seismic section to demonstrate its use, sensitivities, and limitations in processing and geologic interpretation studies. Traces synthesized in the CDP gather filling an artificial gap 0.85 km wide reproduce the true traces from the gap with good fidelity (correlation coefficients between the synthetic and real traces average ≳0.85). In another example, ∼85 percent of the variance of the original 48-channel CDP gather is recovered through interpolation by using only 16 channels. A stacked section, with true trace spacing of 25 m, was decimated to 100 m trace spacing, then interpolated to restore the original 25 m spacing. The interpolated traces reproduce the real traces with correlations of ⩾0.95, thus recovering ⩾90 percent of the variance of the original section.