This paper deals with the sequential adaptive filtering of body waves based on a systematic analysis of correlations (covariances) between available digital data of deep seismic soundings. The initial step is to develop a fast algorithm for computing the covariance. We show how a simple recursive filter is well-fitted. First, a deconvolution filter based on the prediction error is developed; for ease in computation, it is derived from a one-point analysis. Second, we use a polarization filter defined by Flinn (1965). Through a theoretical analysis of the seismic field, we show how the filter is biased when it is applied to rectilinear signals in a nonisotropic noise, and we justify an empirical adjustment. Third, an original filter is based on the permanent analysis of space correlations between seismic stations, inside an arbitrary discrete fan of apparent velocities. Applied to three contiguous tracks with arbitrary spacings, the filter is able to enhance any phenomenon with a variable velocity so long as that velocity is included inside the fan. By spectral analysis, space aliasing and velocity resolution are specified, and capabilities of other procedures are revised. The three filters are applied to the same experimental data in order to estimate their relative efficiency.