Ground-roll extraction using the Karhunen-Loeve transform in the time-frequency domain

Ground-roll suppression is critical for seismic reflection data when spatially aliased surface wave interference is present in the data. Spatial aliasing is a common problem; receiver spacing is often not dense enough to extract wavenumbers of low-velocity surface waves. It has long been known that the Karhunen-Loeve (KL) transform can be used to suppress aliased ground roll. However, the ground roll should be flattened before suppression, which is challenging due to the dispersion of surface wave velocities. I propose to solve this problem via the time-frequency domain. I apply the S-transform, which was previously shown to perform well in the multichannel analysis of surface waves. A simple complex-valued constant phase shift is a suitable model of surface wave propagation in common-frequency S-transform gathers. Therefore, it frequency surface wave packet and extract it from the data by principal component analysis of the corresponding complexvalued data-covariance matrix. As the result, our S-transform KL (SKL) method filters the aliased ground roll without damaging the reflection amplitudes. The advantages of SKL filtering have been confirmed by synthetic- and field-data processing.