Point‐source τ‐p transform: A review and comparison of computational methods

The τ‐p transformation of reflection seismic data excited by a point source requires a cylindrical slant stack, which includes compensation for the phase shift and geometrical spreading associated with cylindrical geometry. Using a simple test model, we review and compare the different computational methods used for the cylindrical slant stack. The two major method types are the Bessel‐Fourier transform (BFT) method and a set of methods (TD2D, TDX, TDTC and TDTS) based on time‐domain convolution. The stack integral in each of these approaches can be separated into two parts, with the part corresponding to the contribution of incoming waves being negligible for large ray parameter p. Neglecting the latter term for large p generally avoid a major problem caused by aliasing between time and space domains. The TDTS method introduced here has the advantage of being expressed in terms of a conventional 2-D slant stack (weighted by offset x) plus a correction term. This formulation facilitates a quantitative com...