THEORY AS RELATED TO EARLIER WORK

Normally an autoregression filter predicts a value at a point using values at earlier points. In practice a gap may also be set between the predicted value and the earlier values. What is not normally done is to supplement the regression by nearby signals. That is what I did here. I allowed the prediction of a signal to include nearby signals at earlier times. The times I allowed in the regression are inside a triangle of velocity less than about the water velocity. The new information allowed in the prediction is extremely valuable for water velocity events because looking along a trajectory at water velocity slope, water noise is transformed to zero-frequency and hence is easily predicted.

The overall process proceeds independently in each of many overlapping windows. At the end, filter outputs are pieced together as described in Claerbout (1992b). In each window there are two-computational phases, first filter design, and then filter application. Application is simply two dimensional filtering. Filter design restricts nonzero filter coefficients to a triangular (noise) region. As with usual deconvolutions, one filter coefficient is constrained to unity while others are either constrained to zero or they are adjusted to minimize the power out. The coefficients of the filter are easily determined by the conjugate-gradient methodology described in Claerbout (1992a).