Spectral Decomposition Of Seismic Data Research Articles

Choice of decomposition in multispectral coherence computation

Abstract The iconic coherence attribute generally computed on the full-bandwidth seismic data has been used for 25 years to delineate structural and stratigraphic subsurface geometric features. More recently, multispectral coherence has been introduced to not only better define the more prominent features, but also more subtle features that may be poorly imaged by traditional broadband coherence attribute displays. Multispectral coherence generation utilizes the spectrally decomposed seismic data in the form of complex voice components within the seismic bandwidth. There are various methods available for spectral decomposition of seismic data, including the continuous wavelet transform, complex matching pursuit and the maximum entropy methods. In addition, a nonlinear spectral probe algorithm is also available and could be utilized for multispectral coherence generation. With all these methods available with the seismic interpreter, a question that pops up is which of these methods could be utilized for a more effective generation of multispectral coherence attribute. We first discuss multispectral coherence itself and its generation and follow that with a description of the different spectral decomposition methods mentioned above. Next, we generate spectral voice components and spectral probe components on two seismic data volumes from northeast British Columbia, Canada, and put them through multispectral coherence generation. A comparative performance of the different methods is then evaluated in terms of the multispectral coherence displays. Finally, some conclusions are drawn from the complete exercise.

A SECOND‐ORDER SYNCHROSQUEEZING S‐TRANSFORM AND ITS APPLICATION IN SEISMIC SPECTRAL DECOMPOSITION

AbstractThe Synchrosqueezing S‐transform (SSST) is a novel approach for time‐frequency (T‐F) representation of non‐stationary signals. By “squeezing” T‐F spectrum of the S‐transform (ST) of a signal, the SSST can obtain a high‐resolution T‐F spectrum. However, when the phase of a signal varies non‐linearly with time, the instantaneous frequency (IF) of the signal calculated by the SSST would be inaccurate, causing reduction of the resolution of the T‐F spectrum. In order to improve its performance in imaging such signals, we modify the formula of IF with the help of the second‐order partial derivatives of time and frequency, and propose a second‐order Synchrosqueezing S‐transform (SSST2nd). Synthetic examples show that the SSST2nd not only has obviously higher resolution than commonly used T‐F transforms, but also images the signals of which the IFs vary quadratically or sinusoidally with time better than the SSST. We apply the SSST2nd to perform spectral decomposition of seismic data for natural gas exploration. The results illustrate that the SSST2nd can be used to well detect frequency spectral anomalies correlated with natural gas accumulations. Therefore, it can be concluded that the SSST2nd is a good potential technique for seismic interpretation.

Spectral decomposition and spectral balancing of seismic data

The interpretation of discrete stratigraphic features on seismic data is limited by its bandwidth and its signal-to-noise ratio. Unfortunately, well-resolved reflections from the top and base of subtle stratigraphic geologic boundaries occur only for thick features imaged by broadband data. Seismically thin stratigraphic features approaching a quarter-wavelength in thickness give rise to composite, or “tuned,” seismic reflections. Different spectral-decomposition methods provide an effective way of examining the seismic response of stratigraphic geologic features in terms of spectral components and thus help in interpretation. Phase components help with interpretation of the discontinuity features as well as stratigraphic features such as onlap, offlap, and erosional unconformities. Applications of an often overlooked attribute derived during spectral decomposition, called the voice components, can be illustrated in terms of more accurate interpretation of the subsurface features. An “amplitude-friendly” method for spectral balancing enhances the frequency content of the data and preserves the geologic tuning features and amplitudes. Spectral decomposition of seismic data that are spectrally balanced and interpreted in terms of voice components leads to more accurate definition of the features of interest.

Use of spectral decomposition technique for delineation of channels at Solar gas discovery, offshore West Nile Delta, Egypt

This paper presents a case study of spectral decomposition of seismic data and how it aids in seismic data interpretation. It is also known as time–frequency analysis where non-stationary signals in time/space are from time/space domain to time/space vs. frequency domain. The frequency domain representation illustrates many important features that are not apparent in time domain representation. Spectral decomposition is a non-unique process for which various techniques exist and newer modified techniques are being discovered. Over the years, spectral decomposition of seismic data has progressed from being a tool for stratigraphic analysis to helping as a Direct Hydrocarbon Indicator (DHI); a potential weapon for reducing dry well drilling. In the coming years, it is expected that spectral decomposition may be able to play a significant role in analyzing time lapse seismic data.In this paper, spectral decomposition technique is applied to the imaging and mapping of bed thickness, geologic discontinuities and channel delineation at Solar discovery. From the study, two distinctively different channels (gas bearing “Red channel” and water bearing “Yellow channel”) were delineated in the area, and are proven by the drilled well, and some stratigraphic features are identified.

Spectral decomposition of seismic data with reassigned smoothed pseudo Wigner–Ville distribution

Seismic signals are nonstationary mainly due to absorption and attenuation of seismic energy in strata. Referring to spectral decomposition of seismic data, the conventional method using short-time Fourier transform (STFT) limits temporal and spectral resolution by a predefined window length. Continuous-wavelet transform (CWT) uses dilation and translation of a wavelet to produce a time-scale map. However, the wavelets utilized should be orthogonal in order to obtain a satisfactory resolution. The less applied, Wigner–Ville distribution (WVD) being superior in energy distribution concentration, is confronted with cross-terms interference (CTI) when signals are multi-component. In order to reduce the impact of CTI, Cohen class uses kernel function as low-pass filter. Nevertheless it also weakens energy concentration of auto-terms. In this paper, we employ smoothed pseudo Wigner–Ville distribution (SPWVD) with Gauss kernel function to reduce CTI in time and frequency domain, then reassign values of SPWVD (called reassigned SPWVD) according to the center of gravity of the considering energy region so that distribution concentration is maintained simultaneously. We conduct the method above on a multi-component synthetic seismic record and compare with STFT and CWT spectra. Two field examples reveal that RSPWVD potentially can be applied to detect low-frequency shadows caused by hydrocarbons and to delineate the space distribution of abnormal geological body more precisely.

AVO analyses and spectral decomposition of seismic data from four wells west of Shetland, UK

The first section of the paper focuses principally on the analysis of four wells located west of Shetland, UK to demonstrate that the appropriate use of AVO (amplitude versus offset) analysis forms a worthwhile and valuable tool for exploration. The wells analysed include two with hydrocarbons, the Foinaven oil well 204/24a-2 and the Laggan gas field discovery well 206/1-2, and two wells positioned on amplitude-related prospects (204/17-1 Fleet North Prospect and 204/18-1 Assynt Prospect). Both 204/17-1 and 204/18-1 failed to find hydrocarbons, where the previous work indicated mainly a Class III AVO anomaly. However, these studies demonstrate that both the amplitude anomalies conform to a Class I AVO. For the hydrocarbon-bearing reservoirs encountered in both the 204/24a-2 and 206/1-2 wells, the results confirmed the presence of Class III AVO anomalies. A second aspect to this paper centres on the application of spectral decomposition to the seismic data relating to these four wells, which provides further evidence that there are also apparent differences in the spectral characteristics between them. Both Foinaven and Laggan exhibit Class III AVO anomalies, which are consistent with the theoretical predictions for frequency-dependent AVO behaviours. However, the results from the 204/17-1 and 204/18-1 wells show rather complicated behaviour in the iso-frequency sections that cannot be explained fully. In summary, though the amplitude anomalies seen in the two prospect wells were interpreted originally to be similar to that in Foinaven, this study demonstrates they are different in both their AVO behaviour and spectral characteristics.

Spectral decomposition using Wigner-Ville distribution with applications to carbonate reservoir characterization

Spectral decomposition of seismic data transforms seismic amplitudes as a function of space and time into spectral amplitudes as a function of frequency, space, and time. It has been used for a variety of applications including determination of layer thickness, stratigraphic visualization, reservoir characterization, and direct hydrocarbon detection. The commonly used spectral decomposition methods—such as STFT (short-time Fourier transform), CWT (continuous wavelet transform), and MPD (matching pursuit decomposition)—are linear in that they compute correlations between the signal and a family of time-frequency functions. Thus, they cannot achieve arbitrarily fine resolution in the time and frequency domain simultaneously due to the limitations imposed by the uncertainty principle (Qian, 2005).

Spectral decomposition of seismic data with CWPT

Spectral decomposition, as a special attribute, gives geologists and geophysicists a unique perspective for seeing and interpreting seismic data. The short-time Fourier transform (STFT) is similar to the internal workings of well-established, time-varying, spectral-balancing algorithms used in seismic processing. The continuous wavelet transform (CWT) is an alternative approach and has proven to be a better choice than the STFT for broadband data. As an extension of the CWT, I introduce the continuous wavelet packet-like transform (CWPT). The CWPT is flexible, and has high resolution if it is implemented properly. For interpretation using spectral decomposition with this method, the frequency absorption property is more accurately represented, and thus is a potential technique for gas reservoir interpretation.

Spectral decomposition of seismic data with continuous-wavelet transform

This paper presents a new methodology for computing a time-frequency map for nonstationary signals using the continuous-wavelet transform (CWT). The conventional method of producing a time-frequency map using the short time Fourier transform (STFT) limits time-frequency resolution by a predefined window length. In contrast, the CWT method does not require preselecting a window length and does not have a fixed time-frequency resolution over the time-frequency space. CWT uses dilation and translation of a wavelet to produce a time-scale map. A single scale encompasses a frequency band and is inversely proportional to the time support of the dilated wavelet. Previous workers have converted a time-scale map into a time-frequency map by taking the center frequencies of each scale. We transform the time-scale map by taking the Fourier transform of the inverse CWT to produce a time-frequency map. Thus, a time-scale map is converted into a time-frequency map in which the amplitudes of individual frequencies rather than frequency bands are represented. We refer to such a map as the time-frequency CWT (TFCWT). We validate our approach with a nonstationary synthetic example and compare the results with the STFT and a typical CWT spectrum. Two field examples illustrate that the TFCWT potentially can be used to detect frequency shadows caused by hydrocarbons and to identify subtle stratigraphic features for reservoir characterization.