Thesis (Ph.D.) University of Alaska Fairbanks, 1996Seismicity parameters can be visualized as an almost continuous function of space and time by using dense grids. This mapping technique is used to: (1) Study the seismic quiescence preceding the 1992 Landers earthquake sequence. Both the Landers and Big Bear earthquake were found to be preceded by periods of significant seismic quiescence lasting 2-4 years. (2) Image the frequency-magnitude distribution in the subducting slab underneath Alaska and New Zealand. A high b-value anomaly at 100 km depth on the top of the slab suggests that slab dehydration causes an increase in the pore pressure. (3) Investigate the plumbing system of Mt. St. Helens and Mt. Spurr. This study suggests that the detailed spatial mapping of the frequency-magnitude distribution is potentially capable of resolving the location of magma chambers and the depth of vesiculation underneath volcanoes. (4) Map out the spatial distribution of asperities along the San Andreas fault in California. Based on the observation that the Parkfield and Morgan Hill asperities show an extremely low b-value (b< 0.5), a new model to calculate recurrence times for moderate size earthquakes is proposed. (5) Investigate the correlation between a currently observed period of seismic quiescence in the Tokyo region and the frequency-magnitude distribution. A modification to the seismic quiescence hypothesis is proposed, which uses the frequency-magnitude distribution as a tool to distinguish between precursory seismic quiescence and false alarms not followed by a main shock. All of these case studies show that applying these new tools in seismicity analyses can advance the understanding of a variety of complex and heterogeneous tectonic regimes in the seismogenic part of the earth's crust and upper mantle