BSDSolver®/2.0

 

 

BCE’s BSDSolver® software package incorporates the proprietary state-of-the-art PPD® algorithm which implements blind seismic deconvolution (BSM) utilizing sequential Monte Carlo filtering (SMC) and iterative forward modeling (IFM). The PPD® algorithm estimates both the source wave and reflection coefficients via IFM until a cost function defined to be the RMS difference between the recorded seismogram and the synthesized seismogram 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 wave as an amplitude modulated sinusoid and a Rao-Blackwellised particle filtering algorithm is utilized to identify and 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 user may then also use the standard frequency domain water level technique (WLT) [4] for estimating the reflection series.

The PPD® also provides the user with an estimation of the dominant frequency of the source wave and an estimation of the  logarithmic decrement which is important within soil dynamic analysis (i.e., http://www.bcengineers.com/soilDynamics.htm). The logarithmic decrement, δ, is directly related to the fraction of critical damping (λ = δ/2π)  in a soil profile which is modeled as a spring-mass-dashpot (SMD) system. In addition, λ  is required for Dynamic Amplification Factor calculations.

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.

Download BSDSolver® User's Manual

 

PPD®:

Example

Mixed Phase Berlage Source Wave with Dominant Frequency of 55 Hz:

Six Reflection Coefficients Convolved with Above Berlage Source Wave:

Resulting Seismogram Inputted into PPD®   Algorithm:

 

 

PPD® Results:

 

PPD®  Estimated Seismogram Superimposed Upon True Seismogram :

 

PPD®  Estimated Reflection Coefficients and Overlapping Source Waves:

 

PPD®  Estimated Reflection Coefficients Superimposed Upon True Reflection Coefficients:

 

PPD®  Estimated Source Wave Superimposed Upon True Source Wave:

 

PPD®  Estimated AMTs with Estimated Source Wave Parameters DF = 55.3 Hz , δ = .988,  λ = 15.73% and h (amplitude attenuation) = 0.055 1/ms:

 

 

References

1)  Baziw, E. (2010). Incorporation of Iterative Forward Modeling into the Principle Phase Decomposition Algorithm for Accurate Source Wave and Reflection Series Estimation. to be published in the IEEE Transactions on Geosci. Remote Sensing.

2)  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.

3)  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.

4)  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.

5) Ulrych, T.J., and Sacchi, M.D. (2005) Information-Based Inversion and Processing with Applications (1st ed.) , Amsterdam, The Netherlands: Elsevier B.V.