Quick Search:    advanced search

GSW Home   GeoRef Home   My GSW Alerts   Contact GSW   About GSW   Journals List   Help

This Article Figures Only Full Text Full Text (PDF) Submit a response Alert me when this article is cited Alert me when eLetters are posted Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Porsani, M. J. Articles by Ursin, B. Search for Related Content GeoRef GeoRef Citation

Mixed-phase deconvolution and wavelet estimation

Centro de Pesquisa em Geofisica e Geologia, Universidade Federal da Bahia, CPGG/UFBA, Salvador, Bahia, Brazil

Bjørn Ursin

The Norwegian University of Science and Technology, Trondheim, Norway

Corresponding author: porsani@cpgg.ufba.br

Corresponding author: ursin@ipt.ntnu.no

The first 20% of the full text of this article appears below.

The seismic convolutional model describes seismic wave propagation as a linear system. A seismic trace then consists of a wavelet or pulse convolved with the reflection response or reflectivity series plus additive noise.

An important problem in seismic data processing is the removal of the effect of the wavelet (spiking deconvolution or inverse filtering) in order to estimate the reflectivity series. When the wavelet is known, designing an optimal spiking filter by a least-squares approach is straightforward. For a mixed-delay wavelet, we must delay the position of the desired output spike. This delay can later be removed so that the effective filter is no longer causal but operates on both past and future input data values with respect to the output position. When the wavelet is unknown, we must determine both the wavelet and the reflectivity series from the input data.

Solving this ambiguous problem requires additional assumptions about the wavelet, the reflectivity series, and the noise. Common assumptions are that the reflectivity series is a stationary random process and that it is uncorrelated to the stationary random noise. Furthermore, if it is assumed that the signal-to-noise ratio is large, the autocorrelation function (ACF) of the seismic trace can be used as an estimate of the ACF of the wavelet. If, in addition, it is assumed (as it commonly is) that the wavelet is minimum delay, meaning that all roots of its associated polynomial have amplitude greater than 1, an optimal least-squares inverse filter can be computed by solving the normal equations using a Levinson algorithm. The normal equations are also called the Yule-Walker (YW) equations. However, problems can arise with minimum-phase inverse filtering when the wavelet is not minimum delay. In a tutorial on spiking deconvolution (TLE, 1995), Leinbach showed that applying a minimum-phase filter to an . . . [Full Text of this Article]