This paper presents a study on the applicability of a method for the statistical characterization of seismic signals which is based on the statistics of their wavelet sub-band coefficients using stable distributions. The method was originally applied to underwater acoustic signals of the type used in ocean acoustic tomography and seabed classification applications. The same protocol was applied to seismic signals representing the vertical displacement, measured on a traditional seismograph. The study showed that this process can indeed provide a means of characterizing a seismic signal and be used to estimate similarities between seismic signals, which is an important factor in studying seismic activity in an area.