Adaptive multiple subtraction using regularized nonstationary regression |

lpf
Benchmark test of nonstationary
deconvolution from Claerbout (2008). Top: input signal, bottom:
deconvolved signal using nonstationary regularized regression.
Figure 8. |
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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.

freq
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).
Figure 9. |
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A three-point prediction-error filter can predict an
attenuating sinusoidal signal

This fact follows from the simple identity

(11) |

According to equations 9-10, one can get an
estimate of the local frequency from the non-stationary
coefficients
and
as follows:

Adaptive multiple subtraction using regularized nonstationary regression |

2013-07-26