Ground roll and the Radial Trace Transform – revisited

The Radial Trace Transform (RTT) is an attractive tool for wavefield separation because it lowers the apparent temporal frequency of radial events like ground roll, making it possible to remove them from the data by simple bandpass filtering in the Radial Trace (RT) domain. We discuss two implementations of the RTT. In the first, and better known, the RT domain is well-sampled, and thus suitable for post-filtering, but is prone to interpolation errors. We present an alternate implementation, which is pseudo-unitary in the limit of an infinitely densely sampled RT space, with the side effect that the RT domain has missing data. Using a simple 2-D filter for regularization, we estimate the missing data in the RT domain by least squares optimization, without affecting the invertibility of the RTT. Our implementation suppresses radial noise while preserving signal, including static shifts. Although it runs into trouble when noise is spatially aliased, we show that application of a linear moveout correction prior to processing increases our scheme’s effectiveness.