This article describes a new development in seismic wave gradiometry. The work follows previous work on time-domain wave gradiometry but proposes applying a wavelet transform to the data prior to wave gradiometric analysis. The result is a more complete picture of wave attributes, which vary in time as well as frequency. In this article, the new data analysis approach is used to analyze two underwater shots that were recorded by a portion of the Glendora Array. The Glendora site is a former surface coal mine that has subsequently been filled by mine tailings and, as such, forms an artificial sedimentary basin in which the geometry is well known. The array used for the analysis was located in a corner formed by the intersection of two vertically oriented boundaries between mine tailings and the surrounding bedrock. The analysis of the data revealed the presence of typical body waves and surface waves, in addition to several phases that are interpreted to be (1) reflections of surface waves off of the vertical tailings–bedrock boundaries, (2) surface waves generated by the interaction of direct-arrival waterborne acoustic waves with the water–tailing interface (the lake shore), and (3) the interaction of other waterborne acoustic waves in Glendora Lake with other water–tailing interfaces. The surface waves are highly time dependent and frequency dependent and highlight the extreme complexity of surface wave propagation in geologically complex areas.