Volcanic tremor: Nonlinear excitation by fluid flow

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 Rossler type. In this model, tremor occurs most easily at local constrictions, and fluid discharge is lower than would occur in unstable steady flow.

[1]  Christopher D. Stephens,et al.  Earthquake classification, location, and error analysis in a volcanic environment: implications for the magmatic system of the 1989–1990 eruptions at redoubt volcano, Alaska , 1994 .

[2]  Christopher D. Stephens,et al.  Precursory swarms of long-period events at Redoubt Volcano (1989–1990), Alaska: Their origin and use as a forecasting tool , 1994 .

[3]  Bernard A. Chouet,et al.  A Seismic Model for the Source of Long-Period Events and Harmonic Tremor , 1992 .

[4]  D. Dzurisin,et al.  Crustal subsidence, seismicity, and structure near Medicine Lake Volcano, California , 1991 .

[5]  J. Mori,et al.  Seismicity associated with eruptive activity at Langila volcano, Papua New Guinea , 1989 .

[6]  M. Ohtake,et al.  A monochromatic earthquake suggesting deep‐seated magmatic activity beneath the Izu‐Ooshima Volcano, Japan , 1987 .

[7]  S. McNutt.  Volcanic tremor at Pavlof Volcano, Alaska, October 1973–April 1986 , 1987 .

[8]  Keiiti Aki,et al.  Slow waves trapped in a fluid‐filled infinite crack: Implication for volcanic tremor , 1987 .

[9]  C. Sammis,et al.  Fracture instabilities accompanying dike intrusion , 1987 .

[10]  Bernard A. Chouet,et al.  Dynamics of a fluid-driven crack in three dimensions by the finite difference method , 1986 .

[11]  A. Hofstetter,et al.  Observations of volcanic tremor at Mount St. Helens in April and May 1980 , 1986 .

[12]  Stephen R. McNutt,et al.  Observations and analysis of B-type earthquakes, explosions, and volcanic tremor at Pavlof Volcano, Alaska , 1986 .

[13]  A. Hurst.  A volcanic tremor monitoring system , 1985 .

[14]  Dynamics of an expanding fluid-filled crack , 1985 .

[15]  R. Crosson,et al.  A spherical source model for low frequency volcanic earthquakes , 1985 .

[16]  B. Chouet.  Excitation of a buried magmatic pipe: A seismic source model for volcanic tremor , 1985 .

[17]  D. Pollard,et al.  Surface deformation in volcanic rift zones , 1983 .

[18]  M. Feigenbaum.  Universal behavior in nonlinear systems , 1983 .

[19]  M. Fehler.  Observations of volcanic tremor at Mount St. Helens Volcano , 1983 .

[20]  S. K. Singh,et al.  Seismic activity related to the March‐April, 1982 eruptions of El Chichon Volcano, Chiapas, Mexico , 1983 .

[21]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[22]  M. G. Ferrick,et al.  Source mechanism of volcanic tremor , 1982 .

[23]  B. Chouet,et al.  Operation of a Digital Seismic Network on Mount St. Helens Volcano and observations of long period seismic events that originate under the volcano , 1982 .

[24]  J. Eckmann.  Roads to turbulence in dissipative dynamical systems , 1981 .

[25]  K. Aki,et al.  Deep volcanic tremor and magma ascent mechanism under Kilauea, Hawaii , 1981 .

[26]  B. Chouet.  Ground motion in the near field of a fluid‐driven crack and its interpretation in the study of shallow volcanic tremor , 1981 .

[27]  J. Latter,et al.  Volcanic earthquakes, and their relationship to eruptions at Ruapehu and Ngauruhoe volcanoes , 1981 .

[28]  T. Pedley.  The Fluid Mechanics of Large Blood Vessels: Contents , 1980 .

[29]  W. Lawrence,et al.  Hydraulic Transients: A Seismic Source in Volcanoes and Glaciers , 1979, Science.

[30]  Neville H Fletcher,et al.  Excitation mechanisms in woodwind and brass instruments , 1979 .

[31]  D. W. Peterson,et al.  Chronological narrative of the 1969-71 Mauna Ulu eruption of Kilauea Volcano, Hawaii , 1979 .

[32]  M. Feigenbaum.  Quantitative universality for a class of nonlinear transformations , 1978 .

[33]  Keiiti Aki,et al.  Source mechanism of volcanic tremor: fluid-driven crack models and their application to the 1963 kilauea eruption , 1977 .

[34]  O. Rössler.  An equation for continuous chaos , 1976 .

[35]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[36]  G. Steinberg,et al.  On possible causes of volcanic tremor , 1975 .

[37]  A. McBirney,et al.  Properties of some common igneous rocks and their melts at high temperatures , 1973 .

[38]  A. Kubotera,et al.  Nature of Non-Volcanic Microtremor Observed on the Aso Caldera , 1970 .

[39]  P. Welch.  The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .

[40]  W. T. Kinoshita,et al.  Volcanic Tremor of Kilauea Volcano, Hawaii, During July-December, 1963. , 1967 .

[41]  J. Stoer,et al.  Numerical treatment of ordinary differential equations by extrapolation methods , 1966 .

[42]  G. Omer.  Volcanic Tremor(Part Two: The Theory of Volcanic Tremor) , 1950 .