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Time-space varying spectra for seismic processing

  • US 8,185,316 B2
  • Filed: 05/21/2008
  • Issued: 05/22/2012
  • Est. Priority Date: 05/25/2007
  • Status: Expired due to Fees
First Claim
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1. A method for estimating amplitude and phase spectra of data consisting of time-varying sensor signals sampled continuously in time with uniform high frequency-resolution, comprising:

  • (a) obtaining a representation of said data sampled at an input (Δ

    T) time-rate wherein the data are acquired by deploying a plurality of seismic sensors proximate a surface of the earth or in a body of water, the data representing seismic amplitude detected by the sensors with respect to time in response to actuation of a seismic energy source;

    (b) specifying an output sample time-rate (Δ

    T′

    ) that is an integer multiple of Δ

    T;

    (c) specifying a data analysis window Δ

    t that is larger than the output sample time rate (Δ

    T′

    ), wherein the analysis window is an integer multiple of Δ

    T;

    (d) specifying a frequency sample rate (Δ

    f);

    (e) computing in a processor a time window (2/Δ

    f) that would produce the frequency sample rate and that is an integer multiple of the input time rate (Δ

    T);

    (f) generating in the processor a model that extrapolates data inside the data analysis window to fill the frequency sample rate (2/Δ

    f) window, wherein(g) the model uses a continuity relationship between data within and data outside of the data analysis (Δ

    t) window,(h) wherein the model has the property that forward and backward extrapolated values decrease in amplitude with respect to time from edges of the data analysis (Δ

    t) window,(i) capturing data in the processor within the data analysis (Δ

    t) window at a start of data time;

    (j) extrapolating in the processor in forward and backward directions the captured data to fill the (2/Δ

    f) time window;

    (k) computing fast Fourier transform (FFT) coefficients in the processor for the data in the (2/Δ

    f) time window;

    (l) incrementing in the processor by the output sample time (Δ

    T′

    ) from the start time of data capture for a next FFT computation;

    (m) repeating (i) through (l) until an end of data time is reached; and

    at least one of(n) saving in a storage medium the FFT coefficients sampled at (Δ

    T′

    , Δ

    f) intervals, and(o) saving in the storage medium a transformation of the FFT coefficients into amplitude and phase spectra sampled at (Δ

    T′

    , Δ

    f) intervals.

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