Blind Seismic Deconvolution (BSM)
Seismic deconvolution is one of the most widely researched and implemented seismic signal processing tools. The primary goal of seismic deconvolution is to remove the characteristics of the source wave from the recorded seismic time series, so that one is ideally left with only the reflection coefficients. The reflection coefficients identify and quantify the impedance mismatches between different geological layers that are of great interest to the geophysicist.
There are many techniques of seismic deconvolution that can be implemented so that an optimal estimate is made of the earth model. A majority of the standard seismic deconvolution methods utilize the steady state Wiener digital filter that assumes a minimum phase source wave. Other techniques implement inverse theory, minimum entropy deconvolution, adaptive deconvolution, complex cepstrum deconvolution and independent component analysis. Many of these deconvolution techniques are ad hoc in nature, they are effected by the band-limited nature of the source wavelet, they are highly susceptible to additive measurement noise, and they assume that the source wavelet is stationary. However, it is readily known that the higher frequencies are attenuated more rapidly than lower frequencies, resulting in significant variation in the source signal as it travels through the earth. A more effective deconvolution technique would be one that potentially allows for time variation of the source wavelet and it should be able to handle diverse additive measurement noise. In addition, the case where one attempts to deconvolve an unknown source wavelet from an unknown reflection sequence (blind deconvolution) is also of great interest.
BCE offers a state-of-the-art solution for carrying out BSM. This technique is referred to as Principle Phase Decomposition (PPD). The PPD technique models the source wave as an amplitude modulated sinusoid and the blind deconvolution is carried out by initially determining the seismogram’s principle phases. Once the principle phases are determined, a Rao-Blackwellised particle filtering algorithm is utilized to separate the corresponding overlapping source waves. The PPD technique makes use of the fact that the discrete convolution operation can be represented as the summation of several source wavelets of differing arrival times.
Examples of the blind separation of non-stationary source waves in low signal-to-noise ratio seismic time series data:
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Example of blind deconvolution utilizing the PPD algorithm for estimating the source wave and the water level technique (WLT) for extracting the reflection coefficients based upon the estimated PPD source wave:
Raw Seismogram:
PPD Estimated Source Wave (superimposed upon true source wave):
WLT estimated reflection coefficients (black) superimposed upon the true reflection coefficients (red). The true reflections coefficients were obtained by implementing the WLT technique utilizing the true source wave and the noise free seismogram. The estimated reflections coefficients were obtained by implementing the WLT technique utilizing the estimated source wave and the previously illustrated noisy seismogram
In the above illustration, it is apparent that the estimated reflection coefficients do not change form within the time series; therefore, it can be concluded that a stationary source wave is present.
1) Baziw, E. (2007). Application of Bayesian Recursive Estimation for Seismic Signal Processing. Ph.D. Thesis, Dept. of Earth and Ocean Sciences, University of British Columbia, 2006.
2) Baziw, E. (2007). Implementation of the Principle Phase Decomposition Algorithm. IEEE Transactions on Geoscience and Remote Sensing (TGRS), vol. 45, No. 6, pp. 1775-1785, June. 2007.
3) Baziw, E. and Ulrych, T.J. (2006). Principle Phase Decomposition - A New Concept in Blind Seismic Deconvolution. IEEE Transactions on Geoscience and Remote Sensing (TGRS), vol. 44, No. 8, pp. 2271-2281, Aug. 2006.