Effect of tensile stress concentration around magma chambers on intrusion and extrusion frequencies

What controls the intrusion and extrusion frequencies associated with volcanoes is still poorly understood. I propose that for volcanoes at divergent plate boundaries, these frequencies may be largely determined by the tensile stress concentration around the magma chambers that feed them. This stress concentration is mainly a function of the applied tensile stress, associated with spreading, and the aspect (height/width) ratios of the chambers. High spreading rates and/or aspect ratios lead to high rates of tensile stress concentration around the chambers and to an increase in their intrusion frequencies. It is found that for chambers at the same depth in a volcanic zone, the one of the highest aspect ratio will normally intrude magma most frequently. Also, if the chambers are of equal aspect ratios, the one at the greatest depth will intrude magma most frequently. Because the extrusion frequency of a volcano is a fraction of its intrusion frequency, the extrusion frequency may also be largely determined by the rate of tensile stress concentration around the magma chamber that feeds the volcano. These results are applied to the divergent plate boundary in Iceland, where many of the volcanoes appear to be fed by “double chambers”, that is, shallow chambers fed by deep-seated chambers. It is found that, except when the aspect ratio of the deep-seated chamber is much less than that of the shallow chamber, the intrusion frequency of the shallow chamber is normally largely controlled by that of the deep-seated chamber. It is concluded that whereas the short-term (i.e., ≤10³ yrs) extrusion frequencies of volcanoes at the plate boundary in Iceland may be similar to the dike intrusion frequencies of the source chambers, the long-term (i.e., ≥10⁴ yrs) extrusion frequencies may be about ten times lower than the intrusion frequencies.