Preface 1. Introduction to rock physics 2. Rock physics interpretation of texture, lithology and compaction 3. Statistical rock physics: combining rock physics, information theory, and statistics to reduce uncertainty 4. Common techniques for quantitative seismic interpretation 5. Case studies: lithology and pore-fluid prediction from seismic data 6. Workflows and guide lines 7. Hands-on References Index.

Quantitative Seismic Interpretation: Applying Rock Physics Tools to Reduce Interpretation Risk

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

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.

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Non-parametric seismic data recovery with curvelet frames

We introduce a digital waveletlike transform, which is tailored specifically for representing seismic data. The transform provides a multiscale orthogonal basis with basis functions aligned along seismic events in the input data. It is defined with the help of the wavelet-lifting scheme combined with local plane-wave destruction. In the 1D case, the seislet transform is designed to follow locally sinusoidal components. In the 2D case, it is designed to follow local plane-wave components with smoothly variable slopes. If more than one component is present, the transform turns into an overcomplete representation or a tight frame. In these terms, the classic digital wavelet transform is simply a seislet transform for a zero frequency (in one dimension) or zero slope (in two dimensions). The main objective of the new transform is an effective seismic-data compression for designing efficient data-analysis algorithms. Traditional signal-processing tasks such as noise attenuation and trace interpolation become simply defined in the seislet domain. When applied in the offset direction on common-midpoint or common-image-point gathers, the seislet transform finds an additional application in optimal stacking of seismic records.

/pdf/seislet-transform-and-seislet-frame-48cfnpmvcv.pdf

Seislet transform and seislet frame

We present a new, discrete undersampling scheme designed to favor wavefield reconstruction by sparsity-promoting inversion with transform elements localized in the Fourier domain. The work is motivated by empirical observations in the seismic community, corroborated by results from compressive sampling, that indicate favorable (wavefield) reconstructions from random rather than regular undersampling. Indeed, random undersampling renders coherent aliases into harmless incoherent random noise, effectively turning the interpolation problem into a much simpler denoising problem. A practical requirement of wavefield reconstruction with localized sparsifying transforms is the control on the maximum gap size. Unfortunately, random undersampling does not provide such a control. Thus, we introduce a sampling scheme, termed jittered undersampling, that shares the benefits of random sampling and controls the maximum gap size. The contribution of jittered sub-Nyquist sampling is key in formu-lating a versatile wavefi...

Simply denoise: Wavefield reconstruction via jittered undersampling

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

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.

Comparisons of adaptive subtraction methods for multiple attenuation

The purpose of this article is to illustrate the characteristics of various interpolation methods. Seismic data need to be interpolated when the spatial sampling of acquired data is coarser than the spatial sampling required for a multichannel process. This multichannel process can be as simple as stacking traces to reduce coherent noise or as complex as prestack depth migration. Interpolation requires some assumptions about the character of the seismic data. One assumption in the methods considered for this article is that seismic events are linear. In practice, the data are not perfectly linear, and we will show later the results of violating the assumption of linearity.

Comparisons of interpolation methods

3D Interpolation of Irregular Data With a POCS Algorithm

Density extraction from amplitude-variation-with-offset (AVO) inversion is thought to be unstable and difficult. Recent research has, however, shown that it is possible to reliably extract density from P-wave reflection data if the interface has significant contrast.

Nurul Kabir

Papers

3D interpolation of irregular data with a POCS algorithm

Comparisons of adaptive subtraction methods for multiple attenuation

Comparisons of interpolation methods

3D Interpolation of Irregular Data With a POCS Algorithm

Density extraction from P-wave AVO inversion: Tuscaloosa Trend example