Cartesian and Cylindrical Slant Stacks

The proper implementation of the τ-p method for surface data excited by a point source, requires the computation of a cylindrical slant stack. Usually, the common (Cartesian) slant stack is computed instead as an approximation to the geometrically-correct procedure. Here, we describe a formulation of the cylindrical slant stack as a weighted sum of Cartesian slant stacks which is accurate for all slownesses and efficient to perform.As examples of the method, we show results computed from synthetic seismograms and from data recorded on the West Florida Shelf. Severe edge-effect noise which overwhelms the Cartesian slant stack, is attenuated by the cylindrical slant stack. Applications of the cylindrical slant stack to other seismological calculations, such as Lamb's problem, are also discussed. In particular, we show that the plane wave reflection coefficients apply exactly in the τ-p domain; hence an amplitude-versus-slowness analysis is unambiguous in this domain and requires no geometrical corrections to the data.