Coupling of energy into and out of submerged layered elastic topographies via scattering centers on the top surface is of interest for a variety of applications in bottom-interacting acoustics. To understand and parametrize the basic wave phenomena which are operative here, this study was begun with a simple model wherein a finite periodic array of scatterers situated on a single elastic layer is insonified by an incident plane wave. The problem is analyzed rigorously by spectral wave-number decomposition, and the scattered fields are obtained by asymptotic evaluation of the spectral intergrals. The results can be interpreted in terms of array-modified leaky waves and slab-modified Bragg modes, with Bragg-leaky mode coupling occurring due to end effects as well as bulk effects of the array. The coupling effects are optimized when one of the slab-modified modes is phased matched to one of the Bragg modes. The asymptotic algorithms are calibrated against numerically evaluated spectral integral reference solutions. Windowed space-wave-number processing is then applied to extract the above phenomenology from the reference data.