Volcanic tremor: Nonlinear excitation by fluid flow

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Abstract
A nonlinear process analogous to the excitation mechanism of musical wind instruments and human vocal cords can explain many characteristics of volcanic tremor, including (1) periodic and “chaotic” oscillations, with peaked and irregular spectra respectively, (2) rapid pulsations in eruptions occurring at the same frequency as tremor, (3) systematic changes in tremor amplitude as channel geometry evolves during an eruption, (4) the period doubling reported for Hawaiian deep tremor, and (5) the fact that the onset of tremor can be either gradual or abrupt. Volcanic “long‐period” earthquakes can be explained as oscillations excited by transient disturbances produced by nearby earthquakes, fluid heterogeneity, or changes in channel geometry, when the magma flow rate is too low to excite continuous tremor. A simple lumped‐parameter tremor model involving the flow of an incompressible viscous fluid through a channel with movable elastic walls leads to a third‐order system of nonlinear ordinary differential equations. For different driving fluid pressures, numerical solutions exhibit steady flow, simple limit‐cycle oscillations, a cascade of period‐doubling subharmonic bifurcations, and chaotic oscillations controlled by a strange attractor of Rössler type. In this model, tremor occurs most easily at local constrictions, and fluid discharge is lower than would occur in unstable steady flow.