A time-varying deconvolution method has been developed which is based upon adaptive linear filtering techniques. This adaptive deconvolution is applicable for use in processing reflection seismic data which contain multiples with periods that vary with traveltime.Filter coefficients are designed for each sample of the input trace using an adaptive algorithm. Convergence properties of the adaptive processor are discussed and compared to conventional deconvolution techniques. The adaptive deconvolution method is illustrated using both synthetic and field reflection seismic data. By proper selection of parameters and by procesing the data in both time-reverse and time-forward directions, adaptive deconvolution removes multiples with varying periods while leaving primary reflections relatively undistorted. INTRODUCTIOIV This paper presents a new time-varying deconvolution method for use in processing reflectionseismograms. The technique is based on the use of a continuously adaptive linear prediction operator in which the operator coefficients are updated using a simple adaptive algorithm. New coefficient values are computed for each data sample in the seismic record so as to minimize a mean-square error criterion. This procedure differs significantly from time-varying deconvolution methods described by Clarke (1968) Wang (l969), and others, Previous methods have employed the well-known three-stage processes of first. computing autocorrelation estimates from the data; second, solving a set of appropriate normal equations to determine the operator coefficient values; and third, applying the operator to the data to obtain the deconvolved output trace. In the adaptive deconvolution procedure proposed in this paper, new coefficient values are computed directly from the seismic data values as the operator is applied to the data. In effect, the operator is designed as the deconvolved output is produced.Deconvolution operators which employ a min-

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Near-source measurements of seismic waves from gnome have been compared with a theoretical seismic source model derived by Blake (1952). It is estimated that 75 percent of the seismic energy in the primary waves is contained in the first half cycle of the ground displacement as shown on the seismograms from instruments located between 0.3 and 10 km from the explosion. The geometrical attenuation of the radiation field of the displacement wave is probably closely approximated by spherical divergence at ranges near the explosion. There is some evidence that a long-period displacement field may exist near the explosion as predicted by the theoretical model. However, there are not sufficient empirical data from the gnome explosion to make a detailed comparison between theory and observation.

Records of near-source (0.3 to 20 km) primary seismic waves generated by the Hardhat, Haymaker, and Shoal underground nuclear explosions were analyzed in terms of displacement amplitude and energy variations with distance. The observed data were compared to similar data from a theoretical source model to determine the adequacy of the theoretical model. There was evidence that a long-period displacement field existed near the explosions as predicted by the theoretical source. Scatter in the observed amplitude data made it difficult to distinguish between the long-period and the radiation fields. However, the variation of total energy of the observed primary seismic waves with distance showed the presence of the long-period field. The comparison of observed and theoretical data indicates that a theoretical elastic source model approximated the observed sources.

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