Analysis of High Resolution Marine Seismic Data Using the Wavelet Transform

Pike, Chris J.

doi:10.1016/b978-0-08-052087-2.50014-1

Cited by 15 publications

(8 citation statements)

References 26 publications

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“…For a given signal x(t) in continuous domain the wavelet transform is given by the following [5]; dt a…”

Section: Short Time Fourier Transform (Stft) and Wavelet Transform Apmentioning

confidence: 99%

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Time frequency analysis techniques for long range sediment tomography

Potty¹,

Miller²

2013

Proceedings of Meetings on Acoustics

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Long range sediment tomography inversion technique requires accurate estimation of the arrival times of acoustic normal modes. The inversion technique is based on minimizing the difference between the forward model predictions and the data using a global optimization scheme. Predictions are computed using a trial parameter set which is iteratively modified until the algorithm converges. The modal arrival times are calculated from the time-frequency analysis of broadband acoustic data collected on a single hydrophone. During the initial stages of the development of the inversion scheme, fourier based spectrogram and wavelet based scalograms were used. Taking advantage of some of the recent developments, dispersion based short time fourier transform (DSTFT) and warping transform techniques were used for the timefrequency analysis, in recent times. This paper will summarize and compare the performance of these time frequency techniques in the context of long range sediment tomography. Data from some of the recent field tests (Shelfbreak Primer and Shallow Water-06 experiments) will be analyzed for this study. Finally, time-frequency analysis performance of another new technique, Modified S transform, will be examined using the field data. [Work supported by Office of Naval Research].

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“…For a given signal x(t) in continuous domain the wavelet transform is given by the following [5]; dt a…”

Section: Short Time Fourier Transform (Stft) and Wavelet Transform Apmentioning

confidence: 99%

“…In order to accomplish this the original signal is re-sampled such that, 2 2 '1 · © § c r t t (5) This re-sampling of the time in turn results in the transformation of the modal components to monotones at the modal cut-off frequencies. This can be clearly seen in FIGURE 5.…”

Section: Warping Transform Approachmentioning

confidence: 99%

Time frequency analysis techniques for long range sediment tomography

Potty¹,

Miller²

2013

Proceedings of Meetings on Acoustics

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“…The Gaussian function has the best possible simultaneous compactness in depth and in wavenumber. This function is hence a frequently used wavelet function in the analysis of a geophysical process (Pike 1994). The following analytical Gaussian function is used as the basic wavelet: …”

Section: Theorymentioning

confidence: 99%

Wavelet power spectrum analysis of heterogeneities from sonic velocity logs

Li¹

1998

Geophysical Prospecting

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The continuous wavelet transform (CWT) is used to evaluate local variations in the power‐law exponents of sonic log data. The resulting wavelet spectrum can be compared with the corresponding global estimates obtained by conventional Fourier transform methods. In Fourier analysis, the fundamental tool used to characterize a fluctuating velocity distribution is the power spectrum. It represents the energy contained in each wavenumber and thus provides information regarding the importance of each scale of heterogeneity. However, important spatial information regarding the location of events becomes implicit in the phase angle of the Fourier transform. In this paper, it is shown how the square of the amplitude of the wavelet transform is related to the Fourier spectrum and how spatial information can be expressed in an explicit manner. Using the conservation of energy, it is shown that the average wavelet power spectrum over the total depth range is equal to the global power spectrum. A Gaussian wavelet is chosen to realize the wavelet transform. Two synthetic sonic logs with exponential and von Karman correlation functions are used to demonstrate the potential of the suggested analysis. Furthermore, the wavelet transform is applied to the KTB (Continental Deep Drilling Program) sonic log data. The wide range of applications of the CWT shows that this transform is a natural tool for characterizing the structural properties of underground heterogeneities. It offers the possibility of separating the multiscale components of heterogeneities.

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“…One of the earliest papers on the subject was that by Goupillaud, Grossmann and Morlet (1984) and further use of the transform was made by Morlet et al (1982a, b) in a study of the propagation of plane waves. While this paper was under review, Pike (1994) showed how the modulus of the wavelet transform could be used towards classification of scatterers in high resolution marine seismic data; he also used the wavelet transform for attenuation estimation. These studies used the continuous rather than discrete wavelet transform.…”

Section: Choice Of Attributes and Wavelet Transformmentioning

confidence: 99%