Wave Scattering Deconvolution

ABSTRACT The least-squares approach is commonly used for spiking and predictive deconvolution. An alternative approach is wave scattering deconvolution (WSD) proposed by Sarwar which uses the full wave solution of the acoustic wave equation. The discrete causal solutions for one-dimensional forward and inverse problems have been obtained through the method of characteristics and finite differencing; This paper emphasizes the effect of the phase of the input wavelet and gives the results of a noise study. The WSD has direct application for spiking deconvolution, predictive deconvolution, and impedance log reconstruction from both offshore and onshore seismic reflection data. This method can also be used to extract the wavelet by measuring both the pressure and particle velocity. Moreover, from the boundary seismogram one can generate the synthetic VSP. Figures showing the computer model experiments with simulated data are presented in this paper. From my study, I suggest the following conclusion:the WSD accomplishes spiking deconvolution, predictive deconvolution, and impedance log reconstruction from noise-free band-limited data when the input is causal.the method is applicable for minimum-phase, mixed-phase or maximum-phase input wavelets. The wave scattering deconvolution method, unlike Robinson's method, does not assume that the reflectivity is random and' does not depend on the number of layers. Moreover, both the reflectivity and the multiple reflections are predictable directly from the seismic trace. INTRODUCTION Deconvolution is a general term for signal processing (mathematical digital filtering or time series analysis) techniques commonly used to remove the effects of source wavelet and/or multiples from the seismic reflection data. The main objective is to retain only the primary reflection spikes for better resolution of the subsurface. The data are otherwise uninterpretable due to the presence of the source wavelet, near surface ghosting and interbed multiples. Two steps are involved; source wavelet compression, often called spiking deconvolution, and multiple suppression. Both steps can be accomplished by a single method introduced by Robinson.1 The mathematical principle of Robinson's method is the well known Wienerz prediction error filtering based on the 12-norm or least squares. A Wiener operator called a prediction filter is constructed to estimate future sample values of a reflection seismogram by using past sample values. This filter can predict the ghost reverberations and the interbed multiples - commonly called the predictable portion of the seismogram. The prediction error filter is determined by the difference between the actual seismogram and the predicted seismogram. The major components of which are the unpredictable primary reflections. For further discussion of prediction error filtering see the excellent papers of Robinson and Treitel3, and Peacock and Treitel.4 Three significant assumptions associated with Robinson's method are:the randomness of the reflectivity.a minimum-phase source wavelet for zero delay desired output.stationarity of the noise and the desired signal.