PPD-WE®
BCE’s PPD-WE® proprietary state-of-the-art algorithm is designed to implement blind seismic deconvolution (BSM) utilizing sequential Monte Carlo filtering and iterative forward modeling (IFM). The PPD-WE® algorithm estimates the first two arriving source waves where only two filter parameters are modified via IFM until a cost function defined to be the RMS difference between the normalized first two arriving source waves is minimized. For each iteration of the IFM a cost function is calculated based upon BCE’s Principle Phase Decomposition (PPD) SMC filtering technique [1]-[3]. The PPD technique models the source wavelet as an amplitude modulated sinusoid and 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 waves of differing arrival times. Once the source wave is estimated the standard frequency domain water level technique (WLT) [4] is implemented for estimating the reflection series.
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. The estimation of the reflection coefficients are extremely important within oil and gas exploration, mining exploration and site characterization within geotechnical engineering such as designing foundations to withstand large earthquakes. Blind seismc deconvolution refers to the case where one attempts to deconvolve an unknown source wave from an unknown reflection sequence.
PPD-WE®:
Example
Raw Seismogram:
Seismogram with 240 Hz 8th Order Zero Phase Shift Low Pass Filter Applied:
Amplitude Spectrum (dominant bandwidth of 40 Hz to 60 Hz):
Implementation of the PPD-WE® Algorithm with Source Wave Dominant Frequency Bandwidth Specified as 40 Hz to 60 Hz:
PPD-WE® Output (estimating source wave):
The three source waves with sequentially minimum rms error residuals for dominant frequency bandwidth 40 Hz to 60 Hz are displayed. The figure below illustrates the estimated first arriving source waves SW1 (blue), SW2 (blue) and SW3 (blue) superimposed upon the normalized and time shifted (for maximum correlation) second arriving source waves (green time series -displayed for 1.5 period of dominant frequency) and true source wave (red time series). The light blue panel in the figure below shows the corresponding estimated Dominant Frequency and Error Residual (relatively normalized) for source waves SW1 (48.7/0.265), SW2 (47.3/0.274) and SW3(50.7/0.462).
Also illustrated below is the un-normalized and non-time shifted second arriving source waves (light green time series). The second arriving source wave's corresponding reflection coefficient's relative arrival time and amplitude (wrt the first arriving source wave) is displayed in the cream colored panel (Time Offset [ms] / Scale Factor). These values are derived by comparing the maximum amplitudes of the estimated first and second arriving source waves and deriving the time shift for maximum cross-correlation.
The investigator can then average the output for SW1 and SW2 due to the fact that they have similar dominant frequencies, similar second arriving source waves and relatively small error residuals . The figure below illustrates the averaged estimated source wave (bold dark black) superimposed upon the true source wave (red time series) and the second arriving source wave's corresponding averaged reflection coefficient's relative arrival time (17.3 ms) and amplitude (0.3). The averaged source wave is then saved and utilized within the WLT technique.
PPD-WE® WLT Technique (estimating reflection series) :
Input estimated source wave and select corresponding seismogram.
The figure below shows the correct WLT estimated reflection series (green time series) for the filtered seismogram and previously estimated source wave. If there is minimal source wave variation within the time series, the estimated reflection coefficients will be very similar in shape as is illustrated below. If variation in shape of the reflection coefficient is evident the user can derive the residual seismogram for the reflection series where a change in shape of the reflection series becomes evident. This is accomplished by interactively selecting the time location just prior to the arrival of the reflection coefficient which changes shape (i.e., time denoted by T0 in figure below).
The PPD-WE® algorithm then calculates the residual seismogram so that a new source wave can be derived and the previously described process can be repeated on the residual seismogram. For example, in the figure below the blue time series is the seismogram determined by convolving the estimated source wave with the reflection series before T0. The red time series is the residual seismogram which is derived by subtracting the blue seismogram from the original seismogram.
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.
4) Ulrych, T.J., and Sacchi, M.D. (2005) Information-Based Inversion and Processing with Applications (1st ed.) , Amsterdam, The Netherlands: Elsevier B.V.