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-

The combination of high‐speed digital computers and recursive finite difference schemes has become a powerful tool in the theoretical analysis of seismic wave propagation. Using this tool, we have obtained solutions to the viscoelastic, or Voigt, wave equation under the following conditions: First, a pressure impulse is applied to the surface of a spherical cavity in a spherically symmetric system; and, second, an arbitrary function is applied to the surface of a semi‐infinite body in a rectangular system. At and near the cavity wall, the cavity radius appears to be the dominant factor in determining the wavelet shape. The viscosity of the medium plays a minor role. At large distances from the cavity, the pressure impulse response of the medium is controlled by the viscosity. Poisson’s ratio has a small but noticeable effect on the wavelet shape near the source. In the plane‐wave case, our results are in good agreement with those given by Collins (1960) near the source and those of Ricker (1943, 1953) at large distances from the source.