Seismic depth imaging with the Gabor transform

Ma, Yongwang; Margrave, Gary F.

doi:10.1190/1.2903821

Cited by 7 publications

(1 citation statement)

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“…In more sophisticated applications, extremely complicated windows can be constructed, each one unique from the others; yet they still sum precisely to unity. Such partitions are called nonuniform or sometimes adaptive (for examples, see Ma andMargrave, 2008, or Wards et al, 2008). As a nearly trivial example of a uniform POU, let I c;d t ð Þ be the indicator function, or boxcar function, defined by…”

Section: Appendix a Construction Of A Partition Of Unitymentioning

confidence: 98%

Gabor deconvolution: Estimating reflectivity by nonstationary deconvolution of seismic data

2011

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We have extended the method of stationary spiking deconvolution of seismic data to the context of nonstationary signals in which the nonstationarity is due to attenuation processes. As in the stationary case, we have assumed a statistically white reflectivity and a minimum-phase source and attenuation process. This extension is based on a nonstationary convolutional model, which we have developed and related to the stationary convolutional model. To facilitate our method, we have devised a simple numerical approach to calculate the discrete Gabor transform, or complex-valued time-frequency decomposition, of any signal. Although the Fourier transform renders stationary convolution into exact, multiplicative factors, the Gabor transform, or windowed Fourier transform, induces only an approximate factorization of the nonstationary convolutional model. This factorization serves as a guide to develop a smoothing process that, when applied to the Gabor transform of the nonstationary seismic trace, estimates the magnitude of the time-frequency attenuation function and the source wavelet. By assuming that both are minimum-phase processes, their phases can be determined. Gabor deconvolution is accomplished by spectral division in the time-frequency domain. The complex-valued Gabor transform of the seismic trace is divided by the complex-valued estimates of attenuation and source wavelet to estimate the Gabor transform of the reflectivity. An inverse Gabor transform recovers the time-domain reflectivity. The technique has applications to synthetic data and real data.

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Section: Appendix a Construction Of A Partition Of Unitymentioning

confidence: 98%

Gabor deconvolution: Estimating reflectivity by nonstationary deconvolution of seismic data

2011

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The Application of S‐transform Spectrum Decomposition Technique in Extraction of Weak Seismic Signals

Gong

Feng

et al. 2016

Chinese J of Geophysics

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In processing of deep seismic reflection data, when the frequency band difference between the weak useful signal and noise both from the deep subsurface is very small and hard to distinguish, the usefulness of traditional method of filtering will be limited. To solve this problem, we apply different spectral decomposition methods respectively to experimental data and real data and compare the results from these methods. Our purpose is to find an effective way to protect weak signals during processing deep seismic reflection data. The spectral decomposition method is based on the discrete Fourier transform, which uses the signal frequency‐amplitude spectrum and other information to generate a high‐resolution seismic image. Typically, it is used to identify the lateral distribution of medium properties, solve spectrum changes within complex media and local phase instability and other issues, such as locating faults and small‐scale complex fractures. S‐transform as a new time‐frequency analysis method, which is a generalization of STFT developed by Stockwell in 1994, has the ability to automatically adjust the resolution. This method has been widely applied to exploration seismic, MT and other geophysical datasets in recent years. It has become one of the effective methods in noise suppressing during geophysical data processing. Comparing with conventional oil reflection seismic data, in order to probe deep structure, deep seismic reflection employs a large quantity of explosives, long observing systems, leading to a phenomenon that valid signals from the deep and noise are mixed together both in time domain and frequency domain. Considering these characteristics of deep reflection data, this paper combines spectral decomposition with S transform technology. First we design a simple pulse function experimental data to confirm the validity of the S transform method. Then we illustrate the effectiveness of spectral decomposition which is influenced by the choice of frequency analysis methods, especially the transform window function which determines the resolving power of the method. On this basis, S transform spectrum decomposition is applied to a single channel of deep reflection seismic data and the stacked profile, then the application results of traditional transform spectral decomposition and S transform spectral decomposition are compared. Comparison of single channel data shows that compared with traditional spectral decomposition, the S transform spectral decomposition method is able to automatically adjust the resolution, accurately calibrate frequency component of weak signals at different times in deep reflection seismic data. Application to stacked profile data shows that the results obtained by the S transform spectral decomposition and those from other spectral decomposition method are largely consistent, while the results of S transform spectral decomposition clearly depict the characteristics of low‐frequency details which are superimposed by noise in original stacked profile. At the same tim...

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