Window length selection for optimum slowness resolution of the local-slant-stack transform

One of the most critical decisions in the design of a localslant-stack transform (LSST) is the selection of its aperture, or more precisely, the selection of the appropriate number of traces and their weighting coefficients for each slant stack. The challenge is to achieve a good compromise between the slowness and the spatial resolution. Conventionally, the window size is chosen in a more intuitive manner by visual inspection and some limited tests. We analyzed the LSST to establish rigorous criteria for the window selection to achieve the optimum slowness and spatial resolution in the transformed domain for a given data set. For this purpose, we estimated the slowness resolution in the LSST domain as a function of the spatial-window bandwidth and of the spectral characteristics of the waves. For a wave with a given bandpass spectrum, the slowness resolution, the stopband attenuation, and the wavefront-tracking capability are determined by the spatial window. For narrowband signals, the spatial window must be larger than the stopband bandwidth divided by the desired slowness resolution and the central frequency of the band. For wideband signals, the window length is determined by the lowest frequency components. Much longer windows can only be used when the slowness and the amplitude variations of the wavefront trajectories are small. We validated our approach with a synthetic example and applied it to a wideangle seismic profile to show the filter performance on real data in which the LSST-window length is determined in an automatic, data-adaptive manner.