Dictionary:Tau-p mapping (τ-p)

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FIG. T-1. Tau-p (τ-p) mapping. (a) An end-on seismic record is f(x,t) where x=source-geophone distance (offset) and t=arrival time. (b) Its tau-p transform is F(τ,p) where p=dt/dx=1/Va and τ=intercept time at x=0. The reciprocal of the apparent velocity, p, is called slowness. Hyperbolic reflections transform into ellipses, straight events into points (the direct wave into P1, the head wave into P2).

An unstacked seismic record or a common-midpoint gather can be described in terms of slope dt/dx = p and intercept time τ, the arrival time obtained by projecting the slope back to x = 0, where x is source–geophone distance; see Figure T-1. The transform process is also called slant stack, the Radon transform, and plane-wave decomposition. Filtering can be done on the τ-p map and the filtered result transformed back into a record. Negative offsets can be padded with zeroes to avoid wraparound problems. See Diebold and Stoffa (1981)[1]. Similar to tau-gamma mapping, where gamma is angle of emergence, gamma = γ = sin–1(pV0).


  1. Diebold, John B.; Stoffa, Paul L. (1981). "The traveltime equation, tau‐pmapping, and inversion of common midpoint data". Geophysics 46 (3): 238–254. doi:10.1190/1.1441196.