Getting it right: source-receiver offsets in the radial trace transform
David C. Henley
Our original radial trace (RT) transform was intended to be applied only to 2D data, for which the distribution of source-receiver offset values for traces within a typical source/receiver ensemble is nearly always linear. Hence, we constructed the inverse RT transform using a simplification in which the source-receiver offset values used by the inverse transform to populate the trace headers of the output X/T source gather are interpolated from the values of XMIN and XMAX, stored in the radial trace headers by the forward transform. Eventually, however, we extended the use of the RT transform to 3D receiver line gathers. Here, the linear offset approximation is no longer accurate, since offset distributions become hyperbolic as the source position is displaced laterally from a receiver line.
We recognized this problem and have recently updated our RT transform module for SeisSpace so that it now offers the option of restoring original offset values to the headers of the inverse transform, in addition to the original offset interpolation options implemented as diagnostics. We document the changes here, describe the steps necessary in order to use the updated module, and show examples of the new module applied to 2D data with source positions offset from the line (3D applications have not been tested yet, but are expected to work properly, as long as the 3D equivalent of the described database operations are successfully performed). We also review the original 2D offset interpolation options available in the current version of the inverse transform.