Applications of 3D Multiple Frequency High-order Parabolic Radon Transform in Amplitude-preserved Data Regularization

The time-invariant Radon transform (RT) is commonly used to regularize and interpolate sparsely sampled or irregularly acquired prestack seismic data. The sparseness of the Radon model significantly influences the results of regularization. We have developed an effective and efficient method for the regularization and interpolation of 2D as well as 3D prestack seismic data. We used an accelerated sparse time-invariant RT in the mixed frequency-time domain to improve the performance of RT-based seismic data regularization. This 2D sparse RT incorporated the iterative 2D model shrinkage algorithm instead of the traditional iteratively reweighted least-squares (IRLS) algorithm in the time domain, and we computed the forward and inverse RTs in the frequency domain to solve the sparse inverse problem, which dramatically reduced the computational cost while obtaining a high-resolution result. The 2D synthetic and real data examples revealed that our 2D approach can better interpolate beyond aliasing a 2D prestack seismic record that contains a large gap, compared with the least-squares-based RT and the frequency-domain sparse RT methods. To extend the 2D technique to 3D more efficiently, we first formulate the 3D RT as a problem of solving a special matrix equation. Next, we use the iterative 3D model shrinkage algorithm to obtain a high-resolution 3D Radon model. The proposed 3D sparse RT method can be applied in the regularization of 3D prestack gathers, such as in the cable interpolation in a 3D marine survey. We achieved robustness and effectiveness with our 3D approach with successful applications to 3D synthetic and real data.

This paper presents a generalized Radon transform defined on conic sections called Conic Radon Transform (CRT) for image analysis. The proposed CRT extends the classical Radon transform (RT) which integrates a image function $f(x, y)$ over straight lines. As the CRT is capable of detecting conic sections with any position and orientation in original images it makes possible to build a new descriptor based on integrating an image over conic sections. In order to test and verify the utility and performance of this new approach we have developed, in this work, the Radon transforms defined on circles and on parabolas, then built a descriptor combining the features extracted by the circular RT, parabolic RT and linear RT. This descriptor is applied to object classification. A number of experiments on both synthetic and real datasets illustrates the efficiency and the advantages of this new approach taking into account the global features of different (circular, parabolic and linear) shapes of images under study.

Ultra-low dose abdominal MDCT: Using a knowledge-based Iterative Model Reconstruction technique for substantial dose reduction in a prospective clinical study

We present a fast and robust sparse time-invariant Radon transform (RT) in the mixed frequency-time domain. In the proposed method, the 2D alternating split Bregman algorithm is introduced to solve the optimization problem. Two proximity operators are applied to promote the robustness and sparseness of the RT in the time domain, while the forward and inverse RTs are computed in the frequency domain. With high efficiency and easy implementation, the proposed method is resistant to the outliers. The synthetic and real data examples demonstrate the better performance of the proposed method when applied on the noise-contaminated data, compared with the traditional non-robust RTs.

PreviousNext No AccessSEG Technical Program Expanded Abstracts 2010Seismic data compression and regularization via wave packetsAuthors: Shen WangJianchao LiStephen K. ChiuPhil D. AnnoShen WangPurdue UniversitySearch for more papers by this author, Jianchao LiConocoPhillipsSearch for more papers by this author, Stephen K. ChiuConocoPhillipsSearch for more papers by this author, and Phil D. AnnoConocoPhillipsSearch for more papers by this authorhttps://doi.org/10.1190/1.3513609 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Abstract Seismic data compression and regularization are crucial, faced with large data volumes and incomplete data measurements in the oil industry. In this research, we present a comprehensive method of utilizing wave packets to perform seismic data compression and regularization. Wave packets, which can be regarded as symmetric “curvelets”, are viewed as optimally localized plane waves. With its intrinsic multi‐scale and multi‐ azimuth properties, we show that wave packet achieves a high compression rate for a sparse representation of seismic data volume. Besides, we demonstrate that via an iterative thresholding algorithm, irregular data can be regularized in wave packet domain without creating artifacts or losing original dip‐dependent information. Compared with regularization methods based on τ − p transform and wave atom transform, wave packet achieves the best result, demonstrated by some numerical examples.Permalink: https://doi.org/10.1190/1.3513609FiguresReferencesRelatedDetailsCited ByDeep Neural Networks with Extreme Learning Machine for Seismic Data Compression23 May 2019 | Arabian Journal for Science and Engineering, Vol. 45, No. 3Two effective approaches to reduce data storage in reverse time migrationComputers & Geosciences, Vol. 56 SEG Technical Program Expanded Abstracts 2010ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2010 Pages: 4453 publication data© 2010 Copyright © 2010 Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished: 21 Oct 2010 CITATION INFORMATION Shen Wang, Jianchao Li, Stephen K. Chiu, and Phil D. Anno, (2010), "Seismic data compression and regularization via wave packets," SEG Technical Program Expanded Abstracts : 3650-3655. https://doi.org/10.1190/1.3513609 Plain-Language Summary PDF DownloadLoading ...

Accurate subsurface modeling and characterization require the prediction of facies and rock properties within the reservoir model. This is commonly achieved by inverting geophysical data, such as seismic reflection data, using a two-step approach either in the discrete or the continuous domain. We have adopted an iterative simultaneous method, namely, stochastic perturbation optimization, to invert seismic reflection data jointly for facies and rock properties. Facies first are simulated according to a Markov chain model, and then rock properties are generated with stochastic sequential simulation and cosimulation conditioned to each facies. Elastic and seismic data are computed by applying a rock-physics model to the realizations of petrophysical properties and a seismic convolutional model. The similarity between observed and synthetic seismic data is used to update the solution by perturbing facies and rock properties until convergence. Coupling the discrete and continuous domains ensures a consistent perturbation of the reservoir models throughout the iterations. We have evaluated the method in a 1D synthetic example for the estimation of facies and porosity from zero-offset seismic data assuming a linear rock-physics model to demonstrate the validity of the method. Then, we apply the method to a real 3D data set from the North Sea for the joint estimation of facies and petrophysical properties from prestack seismic data. The results show spatially consistent rock and fluid inverted models in which the predicted facies reproduce the vertical ordering as observed in the well data.

Summary The seismic data spectral inversion method, arisen in recent years, can improve the resolution of seismic data for obtaining reservoir characteristics. It does not rely on prior information such as well-logging data. By using partial spectrum information from the input seismic trace data, a sparse reflectivity series can be inverted. The inverted reflectivity series can be used to improve the resolution and impedance inversion for thin layer reservoir prediction. In this paper, we implement seismic spectral inversion based on a compressed sensing algorithm, which can solve the ill-posed problem of the inversion process. In the process of inversion, we introduce a quadratic spectrum method to calculate the spectrum of seismic wavelet in the frequency domain, which can stabilize the inversion and handle real field data. Synthetic and real field seismic data examples show that the proposed spectral inversion based on compressed sensing algorithm is stable and effective. Moreover, the real field data inversion results show a good signal-to-noise ratio (SNR) and lateral continuity.

The seismic data regularization, which maps the acquired irregularly sampled seismic traces to a regular grid, is an important processing for preparing the data for regular sampling based algorithm, such as wave equation migration, 3D SRME etc. The wide azimuth seismic data generally contains the shooting locations covering a patch over a 2D surface and the geophone locations as well. Combining with the recording time, the seismic data is fully represented in a five dimensional coordinate. Conventional data regularization scheme splits the five dimension problem in to two pass three dimensional procedures. The interpolation algorithm in higher dimension generally gives better chance to fill the acquisition holes. In this paper, we generalized the anti‐leakage Fourier Transform algorithm to five dimensions, which regularizes the seismic data in one pass. The initial tests on Gulf of Mexico data demonstrate promising results.

Seismic data interpolation and denoising play vital roles in obtaining complete and clean data in seismic data processing. Seismic data usually misses along various spatial axes and always mix with random noise. In order to obtain complete and clean seismic data, reconstruction technology can interpolate missing data and attenuate random noise. Nonsubsampled contourlet transform is an effective transform to obtain multi-scale and multi-direction sparse domain data for compression sensing interpolation and denoising. However, conventional iterative shrinkage/thresholding cannot handle ill-posed and ill-conditioned equations for solving linear inverse problem. We present a two-step iterative log thresholding method to overcome ill-posed and ill-conditioned problems and improve the convergence rate and solution accuracy, which can interpolate and denoise seismic data simultaneously in the nonsubsampled contourlet transform framework. First, we use nonsubsampled contourlet transform to convert the seismic missing data with random noise to sparse domain. Then, we apply two-step iterative log thresholding algorithm to interpolate and denoise data in sparse domain. The result of each iteration is based on the results of the previous two iterations, which can accelerate convergence rate. In addition, log thresholding can further improve convergence rate and solution accuracy. Finally, we use inverse nonsubsampled contourlet transform to obtain the interpolated and denoised seismic data. The new method can reconstruct the irregularly missing data and attenuate random noise to obtain complete and clean seismic data with high accuracy, which is crucial for seismic imaging and inversion. We demonstrate the applicability and effectiveness of this simultaneous interpolation and denoising technique with successful applications to both synthetic and field data examples.

Deep-learning-based methods have been successfully applied to seismic data random noise attenuation. Among them, the supervised deep-learning-based methods dominate the unsupervised ones. The supervised methods need accurate noise-free data as training labels. However, the field seismic data cannot meet this requirement. To circumvent it, some researchers utilized realistic-looking synthetic data or denoised results via conventional methods as labels. The former ones encounter the problem of weak generalization ability because it requires the same distribution of test and training data. The latter ones encounter the issue of insufficient denoising ability because its denoising ability is difficult to significantly exceed the conventional methods which were used to generate labels. To avoid preparing noise-free labels, we propose a novel deep learning framework for attenuating random noise of prestack seismic data in an unsupervised manner. The prestack seismic data, such as common-reflection-point (CRP) gathers and common-midpoint (CMP) gathers after normal moveout (NMO) correction, have high self-similarity. It is because their events are coherent in the time–space domain and approximately horizontal from shallow to deep layers. The generator convolutional neural network (GCN) first learns self-similar features before any learning. The useful signals are more self-similar than random noise, which is incoherent and randomly distributed. Therefore, the GCN extracts features of useful signals before random noise. We select the specific training iteration and adopt the early stopping strategy to suppress random noise. Both synthetic and field prestack seismic data examples demonstrate the validity of our methods.

In the previous chapters, we have seen that time domain methods are good for denoising the seismic data with moderate noisy record. In order to separate true reflection amplitudes from the noisy seismic data, in this chapter, we discuss time slice singular spectrum analysis (TSSSA), a data adaptive signal decomposition based on SSA to alleviate such coloured and complex noise. This method is the time domain version of Cadzow filter but did not gain full attention until 2012. This method is applicable to pre-stack and post-stack data for denoising. By virtue of using seismic amplitudes corresponds to particular time (time slice) to benefit their strong correlation, the method was named as Time Slice SSA. It is a time domain method. In view of the above, in this chapter, Time Slice SSA (TSSSA) denoising algorithm was presented for denoising of 2D seismic reflection data. The first part of this chapter is devoted to provide the testing of the method on synthetic seismic data in comparison with f-x deconvolution (Canales 1984) and f-x SSA (Sacchi 2009) methods. In the second part, the method was applied to high-resolution seismic pre-stack and post data field data.

A breakthrough has been made in the early exploration of shale oil in Gulong area of Songliao Basin in northeast China, however, the shale type in the study area belongs to pure shale, with high clay content and low carbonate content, which is significantly different from other oil fields at home and abroad. Due to the influence of many factors, the reflection characteristics of sweet spot in the post-stack seismic section are not obvious, so it is urgent to carry out pre-stack inversion to predict reservoir parameters and sweet spot location. However, at present, the quality of prestack CRP gathers cannot meet the geological requirements of shale oil exploration, the main problem is that the amplitude of prestack gathers event generally has the characteristics of “Weak - Strong - Weak” due to the objective influence of seismic acquisition and observation system, which is inconsistent with the theoretical AVO characteristics. We adopted a strategy based on diagonalization of Hessian matrix to realize true amplitude imaging in the migration process, and realized the illumination compensation of prestack gathers by estimating the spatial illumination contribution. The weighted spatial median filter and other processing techniques are used to improve the SNR of the true amplitude CRP gathers, which provides high-quality prestack gathers for Gulong shale oil prestack inversion. The continuity of event and SNR comparison of pre-stack true-amplitude prestack gathers obtained by the fidelity and amplitude preserving processing technology are improved obviously, and the amplitude of event is in line with AVO characteristics, which provides strong support for the prediction of seismic sweet spot of Gulong shale oil.KeywordsSongliao BasinShale oilPre-stack inversionIllumination compensationGathers optimization

A simple shearlet-based 2D Radon inversion with an application to computed tomography

Multiscale frequency-domain seismic inversion for fracture weakness

SUMMARY Full waveform inversion (FWI) is a powerful method to estimate high-resolution physical parameters of the subsurface by iteratively minimizing the misfit between the observed and synthetic seismic data. Standard FWI algorithms measure seismic misfit between amplitude-preserved seismic data (true-amplitude FWI). However, in order to mitigate the variations in sources and recording systems acquired on complex geological structures and the physics that cannot be modelled using an approximation of the seismic wave equation, the observed and synthetic seismic data are normalized trace-by-trace and then used to perform FWI. Trace-by-trace normalization removes the amplitude effects related to offset variations and only keeps the phase information. Furthermore, trace-by-trace normalization changes the true amplitude difference because of different normalization factors used for the corresponding synthetic and observed traces. In this paper, we study the performance of true-amplitude FWI and trace-normalized-residual-based FWI in the time domain. The misfit function of trace-normalized-residual-based FWI is defined such that the adjoint source used in gradient calculation is the trace-normalized seismic residual. We compare the two inversion schemes with synthetic seismic data simulated on laterally invariant models and the more complex 2-D Marmousi model. In order to simulate realistic scenarios, we perform the elastic FWI ignoring attenuation to noisy seismic data and to the synthetic data modelled using a viscoelastic modelling scheme. Comparisons of seismic data and adjoint sources show that trace-by-trace normalization increases the magnitude of seismic data at far offsets, which are usually more cycle-skipped than those at near offsets. The inverted results on linear-gradient models demonstrate that trace-by-trace normalization increases the non-linearity of FWI, so an initial model with sufficient accuracy is required to guarantee the convergence to the global minimum. The inverted results and the final seismic residuals computed using seismic data without trace-by-trace normalization demonstrate that true-amplitude FWI provides inverted models with higher accuracy than trace-normalized-residual-based FWI, even when the unknown density is updated using density–velocity relationship in inversion or in the presence of noise and complex physics, such as attenuation.