非歐氏介面上板塊運動的理論推導
Date Issued
2005
Date
2005
Author(s)
DOI
932611M002007
Abstract
Plate kinematics on the surface of the Earth has
been described successfully by the Eulerian rotation.
It is, however, difficult to specify the kinematics of the
lithosphere subduction. Connected with the surface
plate velocity across the pivot axis, the trench, the
velocity vector field of the subducted slab had been
conventionally defined by simply rotating the surface
Eulerian kinematics with respect to the local strike
onto the slab surface. It usually results in unrealistic
in-plane deformation within the slab surface.
Alternatively, the flow field as well as the observed
slab geometry can be shown to be natural
consequences of attaining the kinematic field with the
minimum dissipation power. The dependence of the
deformation derived for such flow field upon the
intrinsic geometry of the non-Euclidean surface is,
however, opaque and implicit. We derive, in this
study, the fundamental compatibility equation of the
strain-rate tensor for the specific flow field to highlight
the fundamental dependency. There are two factors;
one is associated with the variation of the product of
the Gaussian curvature and the determinant of the
metric tensor, the two characteristics of the slab
geometry, along the stream lines. The other is the
local compressibility amplified by the same product.
We discuss the implications of these factors and point
out that the argument based on mapping the Gaussian
curvature variation of the subducted slab is not enough
to delineating the potential membrane deformation of
the subducted slab.
Subjects
Plate kinematics
non-Euclidean interface
Gaussian curvature
membrane deformation
Publisher
臺北市：國立臺灣大學海洋研究所
Type
report
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