Free oscillations of a fluid sphere in an infinite elastic medium and long-period volcanic earthquakes

A source model of long-period volcanic earthquakes is presented. We consider that a fluid-filled spherical cavity surrounded by an infinite elastic medium is excited into resonance like the Earth’s free oscillations. The eigenequation of this system is derived in a general manner, making use of the spherical harmonic and spherical Bessel expansions. The solution is given as a complex number; its real part is the eigenfrequency and the imaginary part represents the attenuation coefficient of the oscillation. The eigenmodes are classified into five groups: (1) the compressional modes in a fluid sphere, (2) the compressional modes in a solid medium, (3) the shear modes in a solid medium, (4) the Stoneley modes, and (5) the torsional modes. We apply them to the long-period volcanic earthquake observed at Asama volcano, Japan. Estimating the characteristic frequencies and attenuation coefficients of the observed vibrations and assuming that the primary component (f = 1.73 Hz) corresponds to the fundamental translation mode of a fluid sphere as one of the compressional modes in fluid, we conclude that the resonator which is a spherical cavity of diameter 220 m filled with steam of temperature 500°C and pressure 170 atm is favorable.