A New Approach to Vibroseis Deconvolution*

Abstract

A method is proposed to obviate the shortcomings of conventional deconvolution approaches applied to vibroseis data. The vibroseis wavelet reduces the time domain resolution of the earth's impulse response by restricting its passband. The spectrum of the wavelet is assumed to be a “low quefrency”phenomenon, and hence it can be estimated by low cut cepstral filtering. The wavelet's amplitude spectrum can then be removed by spectral division. By using an approach which is consistent with the principle of maximum entropy, the undetermined portions of the seismogram's Fourier transform can be filled in by autoregressive prediction. The process of initially deconvolving in a restricted passband reduces the enhancement of noise contaminated parts of the spectrum, and the spectral extension scheme increases the time domain resolution of the process.

Resolution enhancement of ultrasonic defect signals for crack sizing

“…One of the first practical applications demonstrated by Lines and Clayton [7] showed the potential of using AR deconvolution to retrieve the source wavelet from a seismic signal. Walker and Ulrych [8] added the gap prediction method and impedance constraints to the original concept.…”

“…This can be achieved by combining the deconvolution operation of Eq. (4) with a signal processing technique called autoregressive (AR) spectral extrapolation [6][7][8]. In this signal processing technique which we abbreviate as AR deconvolution, we fit an autoregressive model to the available data in the frequency domain at frequencies bound by low and high limits where we have a strong signal-to-noise ratio (o L oo oo H ).…”

Further improvement of temporal resolution of seismic data by autoregressive (AR) spectral extrapolation

“…Spectral extrapolation algorithms based on AR techniques have been commonly used for modeling the past values (backward) and future values (forward) of a signal (Lines and Clayton, 1977;Walker and Ulrych, 1983;Oldenburg et al, 1983;Miyashita et al, 1985;Kim et al, 2001Kim et al, , 2003Doğan and Erer, 2004). In applying AR spectral extrapolation, R(ω) is first obtained by Wiener deconvolution.…”

“…The AR technique has been used to predict the missing low and high frequencies and consequently to recover acoustic impedance by inversion of seismic reflection data (Lines and Clayton, 1977;Oldenburg et al, 1983;Walker and Ulrych, 1983). However, the combination of Wiener filtering and autoregressive spectral extrapolation have also been used to improve temporal resolution in analyzing ultrasonic signals which are also used in the discrimination of closely spaced reflectors as well as the detection of the discontinuities in coarse-grained materials, such as austenitic steel welds (Miyashita et al, 1985;Zala et al, 1988;Sin and Chen, 1992;Honarvar et al, 2004).…”

Maximum-Likelihood Deconvolution

“…Equation (6-7) is often the starting point for Vibroseis deconvolution (e.g., Lines and Clayton, 1977). Observe that the "wavelet" h(k) is noncausal.…”