Seismic wavelet estimation: a frequency domain solution to a geophysical noisy input-output problem

In seismic reflection prospecting for oil and gas a key step is the ability to estimate the seismic wavelet (impulse response) traveling through the Earth. Such estimation enables filters to be designed to deblur the recorded seismic time series and allows the integration of "downhole" and surface seismic data for seismic interpretation purposes. An appropriate model for the seismic time series is a noisy-input/noisy-output linear model. The authors tackle the estimation of the impulse response in the frequency domain by estimating its frequency response function. They use a novel approach where multiple coherence analysis is applied to the replicated observed output series to estimate the output signal-to-noise ratio (SNR) at each frequency. This, combined with an estimate of the ordinary coherence between observed input and observed output, and with the spectrum of the observed input and cross-spectrum of the observed input and output, enables estimation of the frequency response function. The methodology is seen to work well on real and synthetic data.

[1]  Melvin J. Hinich,et al.  Estimating linear filters with errors in variables using the Hilbert transform , 1994, Signal Process..

[2]  Andrew T. Walden,et al.  An investigation of the spectral properties of primary reflection coefficients , 1985 .

[3]  R. White,et al.  Partial coherence matching of synthetic seismograms with seismic traces , 1980 .

[4]  Gwilym M. Jenkins,et al.  General Considerations in the Analysis of Spectra , 1961 .

[5]  Melvin J. Hinich.  Estimating the gain of a linear filter from noisy data , 1983 .

[6]  Donald B. Percival,et al.  Spectral Analysis for Physical Applications , 1993 .

[7]  B. Kennett.  Geophysical Signal Analysis E. A. Robinson and S. Treitel, Prentice-Hall, Inc., Englewood Cliffs, N.J. xiv + 466 pp. £23.40 , 1981 .

[8]  A. T. Walden,et al.  The nature of the non-Gaussianity of primary reflection coefficients and its significance for deconvolution , 1986 .

[9]  Andrew T. Walden,et al.  On errors of fit and accuracy in matching synthetic seismograms and seismic traces , 1984 .

[10]  Jitendra Tugnait,et al.  Stochastic system identification with noisy input-output measurements using polyspectra , 1995, IEEE Trans. Autom. Control..

[11]  A. Walden,et al.  CHOOSING THE AVERAGING INTERVAL WHEN CALCULATING PRIMARY REFLECTION COEFFICIENTS FROM WELL LOGS1 , 1988 .

[12]  R. White,et al.  THE ESTIMATION OF SIGNAL SPECTRA AND RELATED QUANTITIES BY MEANS OF THE MULTIPLE COHERENCE FUNCTION , 1973 .

[13]  R. White,et al.  Measurements of Earth Attenuation from Downhole and Surface Seismic RECORDINGS , 1984 .

[14]  Jitendra Tugnait.  Stochastic system identification with noisy input using cumulant statistics , 1992 .

[15]  D. G. Watts,et al.  Spectral analysis and its applications , 1968 .

[16]  R. Shumway,et al.  Deconvolution of Multiple Time Series , 1985 .

[17]  Sven Treitel,et al.  Geophysical Signal Analysis , 2000 .

[18]  Physical Applications of Stationary Time-Series. , 1981 .

[19]  V. Pisarenko.  Statistical Estimates of Amplitude and Phase Corrections , 1970 .

[20]  Y. Inouye,et al.  Identification of linear systems using input-output cumulants , 1991 .

[21]  Y. Inouye,et al.  Identification of linear systems with noisy input using input-output cumulants , 1994 .

[22]  Georgios B. Giannakis,et al.  Consistent identification of stochastic linear systems with noisy input-output data , 1994, Autom..

[23]  R.E. White,et al.  Signal and noise estimation from seismic reflection data using spectral coherence methods , 1984, Proceedings of the IEEE.