In an area of complicated structure a stacked record section is likely to be characterized by a low signal-to-noise ratio, even after substantial velocity analysis and other processing. The interpreter identifies signals showing phase coherence across many traces at physically allowable velocities and compiles them into a line drawing. We have developed a nonlinear filter designed to mimic this process, which passes only signals showing spatial coherence and having slowness within an allowed range. In this algorithm, called the 'SSD filter,' overlapping M-trace windows are converted into a p-tau representation, obtained by multiplying the stack along the relevant slant line by the smoothed semblance. The results from all windows are composited in the p-tau domain, then retransformed into x-t. The principal tunable parameter is the width M of the correlation window, adjusted to provide an output which agrees well with the event picks made by an experienced interpreter on a test panel of data. The method was developed to enable production of cleaned-up sections from the often noisy stacks produced in deep crustal seismic studies. An example from the COCORP Southern Appalachian profile illustrates how removal of incoherent noise from the stacked section substantially enhances the quality of the migrated section.