Hatsuki Yamauchi

Temperature, grain size, and chemical controls on polycrystal anelasticity over a broad frequency range extending into the seismic range

Recent experimental studies have shown that anelasticity of polycrystalline materials is subject to the Maxwell frequency (fM) scaling: Q−1(f/fM). However, the applicability of this scaling to the seismic waves has not been guaranteed because experimental frequencies normalized to fM of the laboratory samples are usually much lower than the seismic frequencies normalized to fM in the upper mantle (106≤f/fM≤109). In this study, by using polycrystalline organic borneol as an analogue to mantle rock, we measured anelasticity up to f/fM≃108 and found that the Maxwell frequency scaling is not fully applicable at f/fM>104. A closer examination showed that each of the relaxation spectra obtained under various temperature, grain size, and chemical composition can be represented by the superposition of a background dissipation subject to the Maxwell frequency scaling and a peak dissipation centered at f/fM≃103. Significant increases of the peak amplitude and width with increasing temperature, grain size, and impurity content result in failure of the Maxwell frequency scaling at f/fM>104, where the peak dissipation dominates over the background dissipation. The peak is significantly broadened near the solidus temperature (T/Tmelt=0.93), producing an absorption band toward the normalized seismic frequencies. The absorption band suggested by the present data is characterized by variable amplitude and width, indicating a nonlinear reduction of seismic velocity near the solidus.

Polycrystal anelasticity at near-solidus temperatures†

Elasticity, anelasticity, and viscosity of polycrystalline aggregates were measured at the near-solidus temperatures ranging from below to above the solidus temperature (Tm). The result shows that the mechanical effects of the partial melting are twofold; changes just below the solidus temperature in the absence of melt and changes at the solidus temperature due to the onset of partial melting. As homologous temperature (T/Tm) increases from about 0.92 to 1, high-frequency part of the attenuation spectrum significantly grows. Viscosity of the grain boundary diffusion creep is also reduced in this temperature range. These changes are caused by a solid-state mechanism and have a large amplitude even for the samples which can generate very small amounts of melt at the solidus temperature. At the onset of melting, further increases in the elastic, anelastic, and viscous compliances occur. These changes are caused by the direct effects of the melt phase and are very small for the samples with very small melt fractions. Mechanical properties of a partially molten aggregate are determined by these twofold changes, and when melt fraction is small, the former changes are dominant. We performed a parameterization of the present experimental results and applied the obtained empirical formula to the seismic tomographic data in the upper mantle. The present model explains well the steep reduction of the seismic shear wave velocity in the oceanic lithosphere just below the solidus temperature.

Linear stability of plane Poiseuille flow in an infinite elastic medium and volcanic tremors

The linear stability of a plane compressible laminar (Poiseuille) flow sandwiched between two semi-infinite elastic media was investigated with the aim of explaining the excitation of volcanic tremors. Our results show that there are several regimes of instability, and the nature of stability significantly depends on the symmetry of oscillatory fluid and solid motion. It has been shown that long-wave symmetric instability occurs at a very small value of the Reynolds number, but it is unlikely that this is the cause of volcanic tremors. We show that antisymmetric (flexural) instability also occurs, involving two parallel Rayleigh waves traveling against the Poiseuille flow, but the critical flow speed is faster than that of symmetric instability. However, if the basic flow profile is nonparabolic because of a nonuniform driving force or nonuniform viscosity, the critical flow speed of antisymmetric instability can be considerably slower than that of symmetric instability. Based on numerical calculations and analytical consideration, we conclude that this anomalous antisymmetric instability is possibly produced by a basaltic magma flow of a few meters per second through a dike with thickness of 1 m and extending for several kilometers; this origin can explain some of the characteristics of volcanic tremors.