Saturated and subcooled hydrothermal boiling in groundwater flow channels as a source of harmonic tremor

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Abstract
The potential of hydrothermal boiling in groundwater flow channels for generating harmonic tremor (a relatively monochromatic ground vibration associated with volcanic activity) is examined. We use simple “organ pipe” theory of normal‐mode fluid vibration and fundamental energy considerations to develop a first‐order analytical model of a hydrothermal‐boiling source of harmonic tremor. We use this model to estimate order‐of‐magnitude groundwater flow channel lengths and boiling heat transfer rates required to produce harmonic tremor with dominant frequencies in the range 0.5–5 Hz and surface wave reduced displacements of up to 100 cm2. Depending on groundwater sound speed, flow channel lengths of the order of 1–1000 m are required to produce fluid vibration eigenfrequencies in the range 0.5–5 Hz. The boiling heat transfer rate required to produce tremor with a given surface wave reduced displacement depends on the tremor frequency and on whether saturated boiling or subcooled boiling is the cause of the tremor. Saturated boiling produces groundwater vibration via steam bubble growth, whereas subcooled boiling produces groundwater vibration via steam bubble collapse. We find that subcooled hydrothermal boiling is from 102 to 104 times more efficient than saturated boiling in converting boiling “thermal” power to seismic power. For example, the boiling heat transfer rates required to produce 1‐Hz tremor with reduced displacements of up to 100 cm2 via subcooled boiling are generally less than a few thousand megawatts; for saturated boiling, the required boiling heat transfer rates are several orders of magnitude larger than this. The highest values of heat flow reported in the literature for volcanic crater lakes and terrestrial and ocean floor geothermal areas are of the order of 1000 MW. Taking this value as a first‐order estimate of an upper limit on possible boiling heat transfer rates in volcanic hydrothermal systems, our results suggest that saturated hydrothermal boiling is capable of generating only low‐amplitude harmonic tremor, with surface wave reduced displacements no higher than a few square centimeters. However, subcooled hydrothermal boiling could potentially generate high‐amplitude harmonic tremor, with reduced displacements as large as several hundred square centimeters. As a specific application of our model, we evaluate the potential of hydrothermal boiling for generating harmonic tremor at recently active Mount St. Helens and Nevado Del Ruiz volcanoes. We conclude that subcooled boiling likely could have produced the tremor episodes considered at both volcanoes. Saturated boiling also could explain the Nevado Del Ruiz tremor but probably not the more powerful Mount St. Helens tremor.