Although regions of continental margins that consist of subduction zones are not currently prospects for the exploration of oil and gas; they do host a large proportion of the global accumulation of methane hydrates. The last several decades have witnessed an accelerated interest in gas hydrates for multiple reasons. Before our concerns about globing warning, hydrates were thought to be an untapped hydrocarbon resource. Some scientist fear that ocean warming could release methane in these hydrates into the atmosphere, further contributing to climate change. Whether we wish to place offshore oil production platforms, CO2 sequestration wells, or offshore windmills, gas hydrates and their associated free gas can pose geohazard risks that need to be understood and minimized. Many of these studies have used both well and seismic data among other data types to infer gas hydrates in the subsurface of continental deep-water environments for potential energy exploration. One of the most common ways to detect gas hydrates using seismic data, is via a bottom-simulating reflector (BSR) which indicates the transition of seismic waves from gas hydrate-bearing sediments of the gas hydrate stability zone (GHSZ) to free gas or water filled sediments below due to an attenuation response. Unfortunately, the presence of a BSR does not always indicate the presence of hydrates, nor does the lack of a BSR indicate the absence of hydrates. Because several of these studies that use seismic reflection data do not use a direct measurement for attenuation, the main motivation of this research is to apply a recently developed method that directly measures the seismic attenuation response to help delineate gas hydrates such settings. Utilizing 2D seismic reflection data acquired in the Pegasus Basin, east of central New-Zealand, I apply attribute analyses using frequency attributes that are traditionally known to image BSRs and indirectly infer attenuation. The attribute analysis was followed by a spectral decomposition method (continuous wavelet transform) that is expected to perform a better job. Finally, I use a Sparse-Spike Decomposition (SSD) to quantitatively estimate seismic attenuation. I show that while SSD does not directly indicate gas hydrate presence, the attenuation response associated with free gas beneath the GHSZ indicates an overlying gas hydrate or other type of seal.