Nonstationary Seismic Data Research Articles

High-resolution acoustic-impedance inversion based on a deep-learning-aided representation model of nonstationary seismic data

Building a high-resolution acoustic-impedance (AI) model based on nonstationary seismic data plays a key role in reservoir predictions. However, the common AI inversion methods are faced with two main shortcomings. First, because of the nonstationary feature of seismic data, a multiparameter inverse problem should be considered to not only estimate AI but also to estimate a time-varying wavelet or a quality factor ( Q) model, leading the problem to be more ill posed. Second, the resolution of the estimated AI is limited due to the band-limited nature of nonstationary seismic data. To address these issues, we develop a new nonstationary seismic AI inversion method. Notably, we develop a deep-learning-aided representation model to replace the nonstationary convolution model to solve the forward problem in inversion. Benefiting from multisource information (seismic data and well-log data) and the powerful nonlinear function fitting ability of deep learning, this model can map high-resolution AI to band-limited nonstationary seismic data without requiring a time-varying wavelet or a Q model. A new deep-learning architecture is developed for processing the spatio-temporal seismic data with better accuracy. In addition, total-variation regularization is adopted to enforce a physically reasonable AI model. The results of our 3D synthetic and field data experiments clearly demonstrate that our method has significant advantages over other common methods in building a high-resolution AI model.

Convolutional sparse coding network for sparse seismic time-frequency representation

Seismic time-frequency (TF) transforms are essential tools in reservoir interpretation and signal processing, particularly for characterizing frequency variations in non-stationary seismic data. Recently, sparse TF transforms, which leverage sparse coding (SC), have gained significant attention in the geosciences due to their ability to achieve high TF resolution. However, the iterative approaches typically employed in sparse TF transforms are computationally intensive, making them impractical for real seismic data analysis. To address this issue, we propose an interpretable convolutional sparse coding (CSC) network to achieve high TF resolution. The proposed model is generated based on the traditional short-time Fourier transform (STFT) transform and a modified UNet, named ULISTANet. In this design, we replace the conventional convolutional layers of the UNet with learnable iterative shrinkage thresholding algorithm (LISTA) blocks, a specialized form of CSC. The LISTA block, which evolves from the traditional iterative shrinkage thresholding algorithm (ISTA), is optimized for extracting sparse features more effectively. Furthermore, we create a synthetic dataset featuring complex frequency-modulated signals to train ULISTANet. Finally, the proposed method's performance is subsequently validated using both synthetic and field data, demonstrating its potential for enhanced seismic data analysis.

High-Fidelity OC-Seislet Stacking Method for Low-SNR Seismic Data

Seismic stacking is a core technique in seismic data processing, aimed at enhancing the signal-to-noise ratio (SNR) of data by utilizing seismic data acquisition with multifold geometry. Traditional stacking methods always have certain limitations, such as the reliance on the accuracy of velocity analysis for dip moveout (DMO) in common midpoint (CMP) stacking. The seislet transform, a compression technique tailored to nonstationary seismic data, can compress and stack along the prediction direction of seismic data, which provides a new technical idea for high-fidelity seismic imaging based on the effectiveness of the compression. This paper introduces a high-order OC-seislet stacking method for low-SNR seismic data, capable of achieving the high-fidelity stacking of reflection and diffraction waves simultaneously. With the multi-scale analysis advantages of the seislet transform, this method addresses the dependency of DMO stacking on velocity analysis accuracy. In the frequency–wavenumber–scale domain, the correction compensation of the high-order CDF 9/7 basis function is used to obtain the compression coefficients of the high-order OC-seislet transform. This approach simultaneously stacks frequency–wavenumber information of reflection and diffraction waves with high fidelity while implementing DMO processing. After normalizing the weighting coefficients and applying soft thresholding for denoising, the final result is transformed back to the original time–space domain, yielding high-fidelity stacking sections. The results of applying this method to both synthetic and field data show that, compared with conventional DMO stacking methods, the high-order OC-seislet stacking technique reasonably represents dipping layers and fault amplitudes, and it can achieve a balance of a high SNR and high fidelity in stacked profiles.

Multichannel seismic attenuation compensation and interpolation with curvelet sparse constraint of frequency-wavenumber spectrum

Abstract High-resolution exploration is hampered by seismic attenuation, caused by the viscosity and heterogeneity of underground media. Conventional single-channel attenuation compensation methods can increase the corresponding vertical resolution partially. While the lateral continuity of compensated seismic data is always ignored and the noise resistance can be improved. Therefore, multichannel attenuation compensation methods were proposed, including the algorithm with sparse curvelet coefficient constraint of the time-space (t-x) data. However, nonstationary seismic data may be affected by irregular missing traces in field cases, which severely degrades its lateral continuity and negatively affects the performance of multichannel attenuation compensation. Therefore, we concentrate on simultaneous multichannel attenuation compensation and missing trace interpolation in a unified framework. Based on the inversion framework of sparsity promotion, we propose an approach for simultaneous multichannel compensation and interpolation, utilizing sparse curvelet coefficient constraint of the recovered principal frequency-wavenumber (f-k) spectrum. The size of the principal f-k spectrum is reduced by at least half compared with that of the corresponding t-x band-limited data. It significantly reduces the computational expense of curvelet transform-based processing. Synthetic and field data experiments validate the effectiveness of the proposed method in efficiency improvement with consistent performance when compared to the multichannel method with sparse curvelet coefficient constraint of the t-x data in improving the vertical resolution and lateral continuity. Furthermore, we have discussed a potential acceleration strategy based on random sampling in the normal compensation issue.

Robust Q-compensated multidimensional impedance inversion using seislet-domain shaping regularization

Acoustic impedance (AI) inversion plays a vital role in seismic interpretation because AI contains valuable information on lithology and contributes to reservoir characterization. However, the effect of anelastic attenuation dissipates the energy and distorts the phase of seismic waves during their propagation in the earth. Such attenuation-induced effects will degrade the quality of AI inversion unless some preprocessing routines are performed in advance (e.g., inverse Q filtering). In order to invert for AI from nonstationary seismic data directly and enhance the lateral continuity, we have developed a robust Q-compensated multidimensional AI inversion method. The proposed method incorporates the Q-filtering operator into the conventional convolution model and provides an improved iteration scheme, which can avoid some of the errors introduced by those compensation-related processing routines. Furthermore, with the help of seislet nonlinear shaping regularization, the proposed method can accelerate the convergence rate during inversion and further improve the lateral continuity and accuracy of the final inverted results in the presence of noise. Synthetic and field data have been used to validate the effectiveness and robustness of the proposed method. The results demonstrate that compared with the conventional method, the proposed method can retrieve AI from nonstationary seismic data directly with improved efficiency and remove those possible artifacts caused by ambient noise.

Seismic resolution enhancement with variational modal-based fast-matching pursuit decomposition

Enhancing vertical resolution and signal-to-noise ratio (S/N) is a key objective in seismic data processing. Considering the underground medium is inhomogeneous and incompletely elastic, seismic wave energy attenuation occurs during underground propagation, which has a significant impact on seismic data resolution and S/N. Traditional fast-matching pursuit (FMP) algorithms make it difficult to separate valid signals and noise effectively while reconstructing the noisy signals. Therefore, an improved FMP algorithm that combines the variational-mode decomposition (VMD) strategy is developed. The VMD algorithm is used to obtain intrinsic mode functions with varying amplitudes, frequencies, and center times. It can achieve a multiscale decomposition of nonstationary seismic data. Based on the intrinsic mode functions of different scales, the FMP algorithm can reconstruct prior information of the amplitude, frequency, and center time of valid signals and noise signals in the mode functions. Thus, the high-resolution sparse representation of intrinsic mode functions is achieved. The numerical results indicate that our method not only separates the effective signal and noise but also preserves the valid signal as much as possible. In addition, the feasibility of the method is further verified by field exploration data. The results indicate that this strategy can enhance the resolution of seismic data while restoring the attenuated energy using multiscale seismic data.

Multichannel seismic data attenuation compensation via curvelet‐based sparsity promotion

AbstractDue to subsurface viscosity and heterogeneity, the vertical resolution of observed seismic data is decreased after wave propagation, generating nonstationary seismic data with amplitude attenuation and phase distortion. Inverse Q filtering techniques are always used to enhance the vertical resolution of seismic data. However, the majority of inverse Q filtering methods treat attenuation compensation trace by trace, which may produce non‐robust compensation results with poor transverse continuity and amplify noise energy in noisy cases. Thus, we develop a novel sparsity‐promoting inversion‐based multichannel seismic data attenuation compensation approach by introducing a sparse constraint for curvelet coefficients of multichannel compensated data, which takes the transverse continuity of compensated data into account. Besides, the proposed method with a sparse constraint for curvelet coefficients has a better noise‐resistance property, which can attenuate the noise energy in noisy cases during attenuation compensation, improving compensation accuracy and robustness. To improve its computational efficiency, a fast iterative shrinkage–thresholding algorithm is adopted to solve the established lasso problem. Synthetic data examples with different noise levels and two post‐stack field data examples validate the effectiveness of the proposed multichannel method. Its compensation results have superior vertical resolution, transverse continuity and noise robustness in comparison to the conventional single‐channel compensation method using a damped least squares algorithm.

Self-supervised time-frequency representation based on generative adversarial networks

Time-frequency (TF) transforms are commonly used to analyze local features of nonstationary seismic data and to help uncover structural or geologic information. Traditional TF transforms, such as short-time Fourier transform, continuous wavelet transform, and S-transform, suffer from the Heisenberg uncertainty principle, and their TF resolution is limited. The sparse TF (STF) transform has been proposed to address this disadvantage; however, expensive calculation and parameter selection present difficulties. We have developed a self-supervised TF representation based on a generative adversarial networks (STFR-GANs) model to map a 1D seismic signal into a 2D STF image. This model includes three components: a generator, a discriminator, and a reconstruction module. The generator is used to generate the STF spectrum of the input seismic trace, whereas the discriminator distinguishes if this generated STF spectrum is optimal. The reconstruction module serves as a physical constraint to ensure the accuracy of the generated STF spectrum. When implementing model training, the discriminator learns to identify the ideal STF and guides the generator to produce a TF spectrum closer to the ideal one. After model training, we applied the model to synthetic and field data to demonstrate its effectiveness and stability in characterizing the TF features of seismic data. Our results find that STFR-GAN can effectively provide TF representations with higher readability than those of traditional TF methods, further benefiting fluvial channel delineation.

Attenuation Compensation and Q Estimation of Nonstationary Data Using Semi-Supervised Learning

Traditional inverse Q filtering methods for post-stack seismic data attenuation compensation (AC) have the drawback of instability or under-compensation. Besides, the quality factor (Q) should be known as a prerequisite, which is commonly estimated using the attribute difference between the reference and observed wavelets of pre-stack VSP data. The alternating iterative AC and Q estimation method is also researched for post-stack data, while the instability or huge computation becomes a defect. In this letter, we propose a simultaneous AC and Q estimation method for nonstationary post-stack seismic data based on semi-supervised learning. Specifically, we choose the Long Short-Term Memory algorithm which is sensitive to time series and can characterize seismic signal nonlinearly with high accuracy. The proposed AC and Q estimation method employs the Q information from well-logs and the compensated high-resolution data for supervised learning, and uses nonstationary seismic data beyond wells for self-supervised learning, without the wavelet extraction procedure. The synthetic data analysis and field data applications prove the feasibility of the designed semi-supervised method in improving the vertical resolution and Q estimation. The field data impedance inversion after AC further demonstrates its effectiveness.

Improved generalized S-transform deconvolution for non-stationary seismic data

Improving the vertical resolution is one of the significant tasks for seismic data processing. Most traditional resolution-enhancement techniques assume that the seismic wavelet is time-invariant. However, the seismic wavelet varies with seismic wave propagation in the subsurface. To solve this issue, a new spectral-modeling method is proposed to extract the time-varying wavelet using improved generalized S-transform (IGST) and higher-order Fourier series. The IGST based on modified time-window function can effectively improve the resolution of the time-frequency (t-f) spectrum. The high-order Fourier series is used to fit on the logarithm t-f spectrum and achieve the high-precision time-varying wavelet. The proposed method is composed of four steps in the implementation. Firstly, the seismic data is decomposed by the IGST and converted to the logarithm t-f domain. Secondly, the time-varying wavelet spectrum is modeled at each time sample using a higher-order Fourier series. Thirdly, the boxcar smoothing method is used to smooth the time-varying wavelet spectrum and extract the time-varying wavelet with Hilbert transform. Finally, using the time-varying wavelet spectrum to spectrally balance seismic data to flatten the seismic response. Synthetic and field data examples demonstrate the feasibility of the proposed method in improving the signal-to-noise ratio and enhancing the vertical resolution.

A Multitask Learning-Based Dynamic Wavelet Amplitude Spectra Extraction Method and Its Application in Q Estimation

Dynamic wavelet amplitude spectra extraction (DWASE), which is an ill-posed problem, is of great importance for nonstationary seismic data processing. The most difficult challenge is how to decouple the dynamic wavelets and reflection coefficients. The traditional DWASE methods solve the ill-posed problem depending on some prior information, such as the piecewise stationary hypothesis or estimation of the attenuation factor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> . In this article, we propose a multitask learning-based DWASE method and apply the method for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> estimation. Our proposed method can reduce the multiplicity of the ill-posed problem by estimating the logarithmic time–frequency amplitude spectrum (logarithmic TFAS) of both reflection coefficients and dynamic seismic wavelets, simultaneously. In our method, a parameter-sharing U-net is used to extract the logarithmic TFAS of the reflection coefficients and dynamic wavelets from the logarithmic TFAS of the nonstationary seismic data. To verify the accuracy of the DWASE results of our method, we make a quantitative analysis of the synthetic seismic data, which are obtained by our method and some traditional methods. We also apply the DWASE results of our method for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> estimation and attenuation compensation in both synthetic and field seismic data, to prove the effectiveness of the method. Also, comparisons with some traditional methods are given.

Simultaneous Inversion for Reflectivity and Q Using Nonstationary Seismic Data With Deep-Learning-Based Decoupling

Building reflectivity and quality factor (Q) using nonstationary post-stack seismic data is important for vertical resolution enhancement of seismic data and reservoir identification. However, it is well-known that both reflectivity and Q affect the waveform of seismic data, leading to the fact that simultaneously estimating them is a strong ill-posed multi-parameter inverse problem which faces the crosstalk problem. In this paper, we propose a new method for simultaneous inversion of reflectivity and Q. A deep-learning-based data decoupling operator is proposed to decouple the effects of the two parameters on nonstationary seismic data. Based on the decoupled data, we transform the original multi-parameter inverse problem into two independent singe-parameter inverse problems that are immune to crosstalk and can build reasonable initial models for reflectivity and Q. Then alternative iteration is conducted to update the two built initial models to obtain the final models. A few well-logs are used to train the deep learning architecture and specific regularization terms are constructed for the inverse problem to ensure physically reasonable results. Synthetic and field data examples verify the effectiveness of the proposed method and its advantages over a conventional model-driven joint inversion method.

Absorption Attenuation Compensation Using an End-to-End Deep Neural Network

Absorption attenuation compensation is an important part of seismic data processing. It enhances the resolution of non-stationary seismic data by compensating the amplitude energy and correcting phase distortion. The stabilized inverse <i>Q</i> -filter method, a widely used attenuation compensation method, constructs compensation operators based on stratigraphy-related assumptions and compensates seismic data using time-window analysis, which is computationally complex and sensitive to noise. The essence of attenuation compensation lies in the establishment of a nonlinear mapping relationship between attenuated and non-attenuated seismic traces, which strongly benefits from deep learning. This paper proposes a new method for attenuation compensation based on an end-to-end deep neural network to reduce the hand-crafted step of time-window analysis. Instead, the convolutional blocks of the network automatically learn and process seismic data features to achieve simultaneous amplitude and phase compensation. We have constructed two end-to-end network architectures for attenuation compensation: a fully convolutional network (FCN) and a U-Net. As an effective spectrum-broadening method, the compensation method based on the U-Net is shown to enhance vertical resolution with good lateral continuity, to provide reliable compensation results without complex calculations, and to exhibit high noise robustness. Synthetic data tests indicate that the compensation results from the U-Net are better than those from either the FCN or the stabilized inverse <i>Q</i> -filter method at different noise levels. Moreover, the correlation coefficient between the U-Net compensation results of the synthetic profile and the reference non-attenuated profile is higher than that of the FCN and the stabilized inverse <i>Q</i> -filter method. A field data application further verifies the effectiveness of this method.

Simultaneous Interval-Q Estimation and Attenuation Compensation Based on Fusion Deep Neural Network

Seismic attenuation compensation is a widely used technique for enhancing the resolution of non-stationary seismic data. An accurate and reliable quality factor (Q) is a prerequisite for attenuation compensation and an important indicator of oil and gas. Q-factor estimation and attenuation compensation are ill-posed inverse problems, and they are poorly robust when noise is present. Moreover, the process is usually performed in steps, which leads to an accumulation of errors. Deep learning-based methods have gained great popularity because of their powerful ability to obtain exact solutions for inverse problems. However, most deep learning frameworks rely heavily on huge training datasets and lack clear physical meaning. For these reasons, we propose a fusion neural network architecture to build a physically meaningful network to simultaneously implement interval-Q estimation and seismic attenuation compensation. The fusion neural network consists of two sub-networks based on spatio-temporal neural network. And, the method ensures the coupling relationship between Q-factor and non-attenuated/attenuated seismic data by building a loss function that contain both Q loss term and seismic data loss term. The training dataset is then used to update the sub-networks simultaneously to obtain a fusion network that achieves both interval-Q estimation and seismic attenuation compensation. We demonstrate the effectiveness of the proposed simultaneous interval-Q estimation and seismic attenuation compensation algorithm by applying both synthetic and field data examples.

3-D Structural Complexity-Guided Predictive Filtering: A Comparison Between Different Non-Stationary Strategies

Predictive filtering methods are widely used in industry to remove random noise, owing to their stability and efficiency. Traditional predictive filtering methods use a fixed autoregressive order (filtering factor) in the spatial direction. However, denoising spatially varying seismic data has thus far been ineffective. In this study, the effect of non-stationary seismic data variations is overcome using local windowing or non-stationary denoising methods. We propose a non-stationary predictive filtering method in which an autoregressive model is constructed using spatially varying filtering factors. First, we evaluate the structural complexity of the global data based on a local window selection using plane-wave destruction. Then, adaptive filtering factors are proposed depending on the structural complexity of the seismic data. Finally, the autoregressive model containing the adaptive filtering factors is solved. We use three quality measures to evaluate the denoising performance: the signal-to-noise ratio (S/N), the peak signal-to-noise ratio (PSNR), and local similarity (LS). The proposed method acts on both synthetic and field data, including both pre- and post-stack seismic data. Compared with prior non-stationary filtering methods, experimental results demonstrate that structural complexity-guided predictive filtering enables efficient random noise attenuation and reduces signal leakage.

Seismic data interpolation without iteration using a t-x-y streaming prediction filter with varying smoothness

Although there is an increase in the amount of seismic data acquired with wide-azimuth geometry, it is difficult to achieve regular data distributions in spatial directions owing to limitations imposed by the surface environment and economic factors. To address this issue, interpolation is an economical solution. The current state-of-the-art methods for seismic data interpolation are iterative methods. However, iterative methods tend to incur high computational costs, which restricts their application in cases of large, high-dimensional data sets. Hence, we have developed a two-step noniterative method to interpolate nonstationary seismic data based on streaming prediction filters (SPFs) with varying smoothness in the time-space domain and we extend these filters to two spatial dimensions. Streaming computation, which is the kernel of the method, directly calculates the coefficients of nonstationary SPF in the overdetermined equation with local smoothness constraints. In addition to the traditional streaming prediction-error filter, we adopt a similarity matrix to improve the constraint condition in which the smoothness characteristics of the adjacent filter coefficient change with the varying data. We also design noncausal-in-space filters for interpolation by using several neighboring traces around the target traces to predict the signal; this is performed to obtain more accurate interpolated results than those from the causal-in-space version. Compared to the Fourier projection onto a convex sets interpolation method, our method has the advantages of fast computational speed and nonstationary event reconstruction. Application of our method on synthetic and nonstationary field data finds that it can successfully interpolate high-dimensional data with low computational cost and reasonable accuracy even in the presence of aliased and conflicting events.

Multichannel adaptive deconvolution based on streaming prediction-error filter

Abstract Deconvolution mainly improves the resolution of seismic data by compressing seismic wavelets, which is of great significance in high-resolution processing of seismic data. Prediction-error filtering/least-square inverse filtering is widely used in seismic deconvolution and usually assumes that seismic data is stationary. Affected by factors such as earth filtering, actual seismic wavelets are time- and space-varying. Adaptive prediction-error filters are designed to effectively characterise the nonstationarity of seismic data by using iterative methods, however, it leads to problems such as slow calculation speed and high memory cost when dealing with large-scale data. We have proposed an adaptive deconvolution method based on a streaming prediction-error filter. Instead of using slow iterations, mathematical underdetermined problems with the new local smoothness constraints are analytically solved to predict time-varying seismic wavelets. To avoid the discontinuity of deconvolution results along the space axis, both time and space constraints are used to implement multichannel adaptive deconvolution. Meanwhile, we define the parameter of the time-varying prediction step that keeps the relative amplitude relationship among different reflections. The new deconvolution improves the resolution along the time direction while reducing the computational costs by a streaming computation, which is suitable for handling nonstationary large-scale data. Synthetic model and field data tests show that the proposed method can effectively improve the resolution of nonstationary seismic data, while maintaining the lateral continuity of seismic events. Furthermore, the relative amplitude relationship of different reflections is reasonably preserved.

Time-varying wavelet estimation and deconvolution for nonstationary data based on a FWE function

• We present a nonstationary convolution model constituted of the reflectivity series and a time-varying wavelet matrix. • We propose a novel wavelet estimation method toextract time-varying wavelet at every instant for nonstationary seismic data . • We achieve blind deconvolution without assumptions about factor Q value and the source wavelet.

Nonstationary signal inversion based on shaping regularization for random noise attenuation

Prediction filtering is one of the most commonly used random noise attenuation methods in the industry; however, it has two drawbacks. First, it assumes that the seismic signals are piecewise stationary and linear. However, the seismic signal exhibits nonstationary due to the complexity of the underground structure. Second, the method predicts noise from seismic data by convolving with a prediction error filter (PEF), which applies inconsistent noise models before and after denoising. Therefore, the assumptions and model inconsistencies weaken conventional prediction filtering’s performance in noise attenuation and signal preservation. In this paper, we propose a nonstationary signal inversion based on shaping regularization for random noise attenuation. The main idea of the method is to use the nonstationary prediction operator (NPO) to describe the complex structure and obtain seismic signals using nonstationary signal inversion instead of convolution. Different from the convolutional predicting filtering, the proposed method uses NPO as the regularization constraint to directly invert the effective signal from the noisy seismic data. The NPO varies in time and space, enabling the inversion system to describe complex (nonstationary and nonlinear) underground geological structures in detail. Processing synthetic and field data results demonstrate that the method effectively suppresses random noise and preserves seismic reflection signals for nonstationary seismic data.

Matching pursuit-based sparse spectral analysis: Estimating frequency-dependent anomalies from nonstationary seismic data

Spectral decomposition has been widely used to detect frequency-dependent anomalies associated with hydrocarbons. By ignoring the time-variant feature of the frequency content of individual reflected wavelets, we have adopted a sparse time-frequency spectrum and developed a matching pursuit-based sparse spectral analysis (MP-SSA) method to estimate the sparse time-frequency representation of the seismic data. Further, we evaluate a generalized nonstationary convolution model concerning propagation attenuation and frequency-dependent reflectivity, and we mathematically evaluate the sparse time-frequency spectrum of the nonstationary seismic data as being equal to the product of the Fourier spectrum of the source wavelet, frequency-dependent reflection coefficient, and the cumulative attenuation during seismic wave propagation. Therefore, the reflectivity spectrum, which is a combination of the frequency-dependent reflectivity and the propagation attenuation, can be determined by dividing the sparse time-frequency spectrum of the seismic data by the Fourier spectrum of the source wavelet. Application of the matching pursuit-based decomposition methods to synthetic nonstationary convolutional data illustrates that the adopted MP-SSA spectrum shows a higher time resolution than the matching pursuit-based Wigner-Ville distribution and the matching pursuit-based instantaneous spectral analysis spectra. Notably, the MP-SSA method can avoid spectral smearing, which may introduce distortions to the frequency-dependent anomaly estimation. Application of the amplitude versus frequency analysis based on MP-SSA to field data illustrates the potential of using the sparse reflectivity spectral intercept and gradient to detect the hydrocarbon reservoirs.