Recurrence rate is often used to describe volcanic activity. There are numerous documented ex- amples of non-constant recurrence rate (e.g. Dohrenwend et al., 1984; Condit and Connor, 1996; Cronin et al., 2001; Bebbington and Cronin, 2011; Bevilacqua, 2015), but current techniques for calculating recurrence rate are unable to fully account for temporal changes in recurrence rate. A local–window recurrence rate model, which allows for non-constant recurrence rate, is used to calculate recurrence rate from an age model consisting of estimated ages of volcanic eruption from a Monte Carlo simulation. The Monte Carlo age assignment algorithm utilizes paleomagnetic and stratigraphic information to mask invalid ages from the radiometric date, represented as a Gaussian probability density function. To verify the age assignment algorithm, data from Heizler et al. (1999) for Lathrop Wells is modeled and compared. Synthetic data were compared with expected results and published data were used for cross comparison and verification of recurrence rate and volume flux calculations. The latest recurrence rate fully constrained by the data is reported, based upon data provided in the referenced paper: Cima Volcanic Field, 33 +55/-14 Events per Ma (Dohren- wend et al., 1984), Cerro Negro Volcano, 0.29 Events per Year (Hill et al., 1998), Southern Nevada Volcanic Field, 4.45 +1.84/-0.87 (Connor and Hill, 1995) and Arsia Mons, Mars, 0.09 +0.14/-0.06 Events per Ma (Richardson et al., 2015). The local–window approach is useful for 1) identifying trends in recurrence rate and 2) providing the User the ability to choose the best median recurrence rate and 90% confidence interval with respect to temporal clustering.

Volcanic activity, and the resultant deposits and structures at the Earth's surface, are the outcome of the inner workings of underground magmatic plumbing systems. These systems, essentially, consist of magma reservoirs which supply magma to the surface through volcanic conduits feeding volcanic eruptions. The mechanics and structure of plumbing systems remain largely unknown due to the obvious challenges involved in inferring volcanic processes occurring underground from observations at the surface. Nevertheless, volcanologists are beginning to gain a deeper understanding of the workings and architecture of magmatic plumbing systems from geophysical observations on active volcanoes, as well as from geological studies of the erosional remnants of ancient volcanic systems. In this work, I explore the relationship between the structure and mechanics of shallow plumbing systems and the volcanic eruptions these systems produce. I attempt to contribute to the understanding of this complex relationship by linking geological and geophysical observations of an eroded basaltic subvolcanic system, and the eruptive and tectonic activity of an active volcano, with mathematical models of magma ascent and stress transfer. The remarkable exposures of the Carmel outcrop intrusions, near the San Rafael swell, southeast Utah, U. S. A., allow detailed geological and geophysical observations of the roots of volcanic conduits that emerge from a subhorizontal magma feeder reservoir. These observations reveal a new mechanism for magma ascent and eruption triggering through gravitational instabilities created from an underlying feeding sill, and shed light on the mechanics of sill emplacement. Geophysical and geological observations of the 1999 and xii 1992 eruptions of the Cerro Negro volcano, Nicaragua, are used to explore the coupling between changes in the stress field and the triggering of volcanic eruptions, and magma ascent through the shallow crust. Modeling results of stress transfer and conduit flow highlight the importance of the surrounding stress field and geometry of the volcanic conduits that comprise shallow plumbing systems.