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lpf
Figure 8. Benchmark test of nonstationary deconvolution from Claerbout (2008). Top: input signal, bottom: deconvolved signal using nonstationary regularized regression. |
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Figure 8 shows an application of regularized nonstationary
regression to a benchmark deconvolution test from Claerbout (2008). The
input signal is a synthetic trace that contains events with variable
frequencies. A prediction-error filter is estimated by setting ,
and
. I use triangle smoothing with a
5-sample radius as the shaping operator
. The deconvolved
signal (bottom plot in Figure 8) shows the nonstationary
reverberations correctly deconvolved.
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freq
Figure 9. Frequency of different components in the input synthetic signal from Figure 8 (solid line) and the local frequency estimate from non-stationary deconvolution (dashed line). |
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A three-point prediction-error filter can predict an
attenuating sinusoidal signal
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(11) |
According to equations 9-10, one can get an
estimate of the local frequency from the non-stationary
coefficients
and
as follows:
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