5:15 PM - 6:30 PM
[SCG46-P10] Theoretical study on rock anelasticity;
Extension of a grain-boundary sliding model to two dimensions
Keywords:anelasticity, grain-boundary sliding, seismic attenuation
Rock anelasticity has a significant effect on seismic velocity and attenuation structure in the upper mantle. However, experiments are difficult and data are limited. Therefore, theoretical approaches to rock anelasticity are important. Existing experimental data indicate that grain boundary sliding is one of the major mechanisms of rock anelasticity under upper mantle conditions (e.g., Jackson & Faul, 2010; Takei et al., 2014). A model of grain boundary sliding was developed by Raj & Ashby (1971). Their model is a quasi-one-dimensional model that deals with the sliding between two elastic blocks with interlocking nonplanar boundary. When the amplitude of the nonplanarity is small, they analytically obtained the effective shear modulus and attenuation as functions of frequency. Their model successfully reproduced the seamless transition of a polycrystalline material from elastic, through anelastic, to viscous body with decreasing frequency. Morris & Jackson (2009) introduced a minute quantity ε to represent the amplitude of the nonplanarity, and reformulated the model of Raj & Ashby (1971) more rigorously using the perturbation method. In these previous quasi-one-dimensional models, the base state only represents the relaxation of shear stress applied to a single planar grain boundary, and does not represent the real grain boundary in a polycrystalline material where both normal and shear stresses act. In addition, the previous models predict the existence of a large peak on the high-frequency side, but experimental results using polycrystalline olivine (Jackson & Faul, 2010) and rock analogs (Takei et al., 2014) do not show such a peak. In this study, we develop a two-dimensional model for grain boundary sliding in a polycrystalline material. By modeling with a more realistic geometry, the base state reflects self-locking at the mineral grain scale, and hence we can consider atomic-scale steps along the grain boundary in the first order perturbation. For a quantitative prediction of the peak amplitude, it is important to consider a granular aggregate interlocked both at mineral grain scale and atomic scale.
In this study, we obtain the shear modulus and attenuation of a two-dimensional polycrystalline material with arbitrary grain shape as functions of frequency. Using the perturbation method proposed by Morris & Jackson (2009), we first solve for the case where the grain shape is a perfect circle as the base state. The general solution of the elastic displacement field and stress field of a circle was obtained by Love (1927). By adding boundary conditions for grain boundary diffusion and grain boundary viscosity, we can obtain the displacement and stress fields of a grain in the presence of matter diffusion and grain boundary sliding. For a grain of arbitrary shape deviating from the circle, the approximate solution depending on the detailed grain shape can be obtained analytically by using the perturbation method. So far, we have obtained the base state solution and found that it has the viscoelastic properties of the Burgers model. In the next step, we plan to obtain solutions up to the first order perturbation.
In this study, we obtain the shear modulus and attenuation of a two-dimensional polycrystalline material with arbitrary grain shape as functions of frequency. Using the perturbation method proposed by Morris & Jackson (2009), we first solve for the case where the grain shape is a perfect circle as the base state. The general solution of the elastic displacement field and stress field of a circle was obtained by Love (1927). By adding boundary conditions for grain boundary diffusion and grain boundary viscosity, we can obtain the displacement and stress fields of a grain in the presence of matter diffusion and grain boundary sliding. For a grain of arbitrary shape deviating from the circle, the approximate solution depending on the detailed grain shape can be obtained analytically by using the perturbation method. So far, we have obtained the base state solution and found that it has the viscoelastic properties of the Burgers model. In the next step, we plan to obtain solutions up to the first order perturbation.