Preferred Mineral Orientation by Recrystallization under non-Hydrostatic Stress and Geotectonic Stress in the Upper Mantle

Abstract

Significant elastic anisotropy of olivine single crystal is well known. The velocity of P waves has a maximum in the direction of crystallographic a-axis (identical to optical-acoustic Z-axis). It is also known that dunite and peridotite which are found at the central core of an orogenic zone have a strong tendency to preferred orientation of olivine. The preferred orientation of olivine and elastic anisotropy of dunite in the tectonic zone of Japan are measured optically and acoustically. The latter is carried out using the ultrasonic wave at high pressures. The direction dependence of P wave velocity is expressed by V, = a + b cos2 8, where the direction of 8 = 0 is found to be nearly equal to the direction of lineation which coincides statistically with the direction of a-axis concentration. Recently the existence of anisotropy of the uppermoFt mantle came to be convincing by analysing the results of seismic refraction profiles at the ocean bottom. The P wave velocity can be expressed empirically as V, = a + b cos2 8 where 0 is the azimuth to the perpendicular to the ridge direction. Here the observed seismic anisotropy is attributed to the regional preferred orientation of constituent minerals of rocks composing the upper mantle. The mechanism to produce preferred orientation is known to be either a recrystallization due to elastic anisotropy of minerals or a non-elastic effect such as gliding. In olivine the translation gliding in (010) plane is known. However, it does not seem that such a pure translation gliding can give rise to the significant preferred lattice orientation under stress. Let the preferred orientation of olivine aggregates be due to recrystallization. The stable mineral orientation is specified by the minimum condition of a certain thermodynamic function 4. It must be consistent with the stress and strain continuities at the grain boundary. According to our theory (1) and (2) 4 is represented by a sum of: (a) A function dependent upon a grain shape (interface configuration between grains) (first order). It plays a significant role in mineral orientation of tectonite. However, it is insensitive to the elastic anisotropy. (b) A linear function of deviatric stress component (second order). (c) A quadratic function of stress component (second order). Terms (b) and (c) are related to the stored energy and potential due to deformation and are dependent upon the stress-strain relation, while (a) is independent of stressstrain relation. The expression of C#J is shown in Table 1. Under high hydrostatic pressures greater than lOkb, term (b) becomes predominant. In the actual mineral aggregates, the grain boundary is not a plane, and the surface integral expression of 4 is necessary. To find the condition C#J = min the variational problem for the relative angle between the axis of anisotropy and the axis of external