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1

Local Recovery of Sub-Crustal Stress Due to Mantle Convection from Satellite-to-Satellite Tracking Data

Šprlák M., Eshagh M.

Acta Geophysica

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2016

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Vol. 64, no. 4

904--929

EN

Two integral transformations between the stress function, differentiation of which gives the meridian and prime vertical components of the sub-crustal stress due to mantle convection, and the satellite-to-satellite tracking (SST) data are presented in this article. In the first one, the SST data are the disturbing potential differences between twin-satellites and in the second one the line-of-sight (LOS) gravity disturbances. It is shown that the corresponding integral kernels are well-behaving and therefore suitable for inversion and recovery of the stress function from the SST data. Recovery of the stress function and the stress components is also tested in numerical experiments using simulated SST data. Numerical studies over the Himalayas show that inverting the disturbing potential differences leads to a smoother stress function than from inverting LOS gravity disturbances. Application of the presented integral formulae allows for recovery of the stress from the satellite mission GRACE and its planned successor.

2

Geometry of stress function surfaces for an asymmetric continuum

Yajima T., Yamasaki K., Nagahama H.

Acta Geophysica

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2013

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Vol. 61, no. 6

1703--1721

EN

A two-dimensional stress field of dislocation or fault is geometrically studied for an asymmetric con tinuum. For geometric surfaces of the stress and couple-stress functions, the mean and Gaussian curvatures are derived. The mean curvature of couple-stress function surface is connected with the asymmetr ic of stress tensor. Moreover, the Gaussian curvature of stress function surface is characterized by bo th the stress and couple-stress. On the other hand, th e mean curvature of stress function surface is not affected by the asy mmetry of stress. Based on these geometric expressions, the Coulomb’s failure criterion and the friction coefficient are expressed by the curvatur es of couple-stress function surface. Moreover, geometric structures of st ress and couple stress function surfaces are shown for edge and wedge dislocations as faults. The curvatures of these surfaces show that the ef fect of couple-stress is constrained around the dislocations only.

3

Differential geometric approach to the stress aspect of a fault: Airy stress function surface and curvatures

Yamasaki K., Yajima T.

Acta Geophysica

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2012

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Vol. 60, no. 1

4-23

EN

We considered the two-dimensional stress aspect of a fault from the viewpoint of differential geometry. For this analysis, we concentrated on the curvatures of the Airy stress function surface. We found the following: (i) Because the principal stresses are the principal curvatures of the stress function surface, the first and the second invariant quantities in the elasticity correspond to invariant quantities in differential geometry; specifically, the mean and Gaussian curvatures, respectively; (ii) Coulomb's failure criterion shows that the coefficient of friction is the physical expression of the geometric energy of the stress function surface; (iii) The differential geometric expression of the Goursat formula shows that the fault (dislocation) type (strike-slip or dip-slip) corresponds to the stress function surface type (elliptic or hyperbolic). Finally, we discuss the need to use non-biharmonic stress tensor theory to describe the stress aspect of multi-faults or an earthquake source zone.