A Review of Frequency-Magnitude Relation Studies at Volcanoes

The frequency-magnitude relation is one of the most widely studied topics in seismology. In volcanic areas very high b-values have been observed. Recent studies used dense spatial grids to study b-values at >13 volcanoes. Such studies require a well-distributed group of earthquakes; if the events all occur at one point then no meaningful spatial mapping can be done. All volcanoes studied to date have shown high spatial variability of b, with regions of normal b (1.0) adjacent to regions with anomously high b (up to 3.0). In general b is high at depths of 7-10 km where the earthquakes are adjacent to inferred magma bodies identified by other techniques. However, about half of the studied volcanoes also show significant high b anomalies at depths of 3-4 km. This is the approximate depth at which magma with 4 wt percent gas starts to exsolve the gas, and further, is near the depth at which open cracks may exist in the host rock. The data sets used for these analyses show that the b-value anomalies are long-lived (years to decades) features. This is somewhat in contrast with previous studies of b as a function of time, or rather, the documented spatial variation has created an ambiguity in interpreting whether b varies as a function of space, time, or both. A new result is the elucidation of a common temporal pattern of b for earthquake swarms associated with eruptions and intrusions. The b changes from a normal background value to a short-lived high, then decreases, then increases again to a secondary (generally lower) high with a longer time constant, eventually returning to a low background level. Based on knowledge of b from lab and field studies, these observations suggest that the short-lived high b is probably a result of high thermal gradients that dissipate quickly. The heat may be carried by gases, liquid water, or magma. The longer-lived secondary high b is consistent with an increase in pore pressure, similar to observations at Rangely, Colorado in association with fluid injection in deep wells. This suggests that diffusion is a main controlling factor. Note that b-value anomalies are features of both the earthquakes themselves and the space they occupy. This is in contrast to tomography studies in which the rays from earthquakes pass through the region of interest, but the earthquakes themselves are not required to be within it. The b-value techniques, while powerful, are limited to those regions that produce earthquakes in sufficiently high numbers to perform the analyses.