Knowing the subsurface velocity structure is crucial to being able to generate accurate Images from geophysical reflection data. For seismic reflection and georadar (GPR) surveys, preliminary velocity information commonly comes from moveout analysis on shot and/or CMP gathers. In cases where we do not have offset information, we can collapse diffractions in the data through migration to obtain velocities. However, there are a number of reflection geometries where the reflection signature appears hyperbolic in shape similar to that of a point diffractor. Collapsing such hyperbolic events gives inaccurate velocity information which may distort the final image. We investigate three geometrical cases where this may occur: circular, hyperbolic, and parabolic. We derive zero-offset traveltime equations for each case, assuming a simple homogeneous media between the surface and a reflector. Generating a set of randomly distributed diffractors over a range of depths and medium velocities at georadar scale, we use a grid-search method to determine the best fitting parameters for each of the geometric cases. We find that in all three cases, observed diffractor velocities are always higher than the "true" medium velocities, and in the circular and hyperbolic cases we are able to estimate a crude velocity factor relying only on an estimate of one scale parameter. We apply a velocity correction to a georadar dataset with circular culverts, and show that it gives a more accurate final image than using just a diffractor velocity.
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