Source mechanism of volcanic tremor

Low‐frequency (<10 Hz) volcanic earthquakes originate at a wide range of depths and occur before, during, and after magmatic eruptions. The characteristics of these earthquakes suggest that they are not typical tectonic events. Physically analogous processes occur in hydraulic fracturing of rock formations, low‐frequency icequakes in temperate glaciers, and autoresonance in hydroelectric power stations. We propose that unsteady fluid flow in volcanic conduits is the common source mechanism of low‐frequency volcanic earthquakes (tremor). The fluid dynamic source mechanism explains low‐frequency earthquakes of arbitrary duration, magnitude, and depth of origin, as unsteady flow is independent of physical properties of the fluid and conduit. Fluid transients occur in both low‐viscosity gases and high‐viscosity liquids. A fluid transient analysis can be formulated as generally as is warranted by knowledge of the composition and physical properties of the fluid, material properties, geometry and roughness of the conduit, and boundary conditions. To demonstrate the analytical potential of the fluid dynamic theory, we consider a single‐phase fluid, a melt of Mount Hood andesite at 1250°C, in which significant pressure and velocity variations occur only in the longitudinal direction. Further simplification of the conservation of mass and momentum equations presents an eigenvalue problem that is solved to determine the natural frequencies and associated damping of flow and pressure oscillations. For a simple, constant pressure reservoir‐conduit orifice fluid system, a change in orifice size can cause the source signal duration due to a single disturbance to change from several seconds to in excess of an hour. Fluid kinematic viscosity (0.412 m 2 /s) is both included and neglected in the analysis to illustrate its effect upon system damping. Tremor magnitude is related to the magnitude of the conduit wall motion occurring in response to oscillating fluid pressures. The entire volcanic fluid system does not generally experience a transient flow condition at a given time. Closed end and constant pressure fluid system boundaries reflect pressure waves and isolate components of the fluid system. Total fluid movement may not be accurately monitored by tremor data alone, since steady state and slowly changing flows are aseismic.