Recovery of material parameters in transversely isotropic media. (English) Zbl 1437.74009
The authors discuss some elastic properties of transversely isotropic materials.
The main result is that the varying symmetry axis can be locally recovered. To recover these elastic
parameters one needs to know some interrelationships between them, that can
be deduced from the geometric model used in the description.
The mathematical setting is indeed a background Riemannian metric
(usually the Euclidean metric). The first theorem states that under some convexity assumptions,
some parameters are determined by the qSH wave travel times (or qSH lens relations in the global case).
The authors also prove additional results for the remaining parameters, that depends
on the knowledge of qP and pSV travel data.
The main application of the methods developed in this paper concerns seismic tomography, due to the anisotropy detected in Earth’s interior.
The main application of the methods developed in this paper concerns seismic tomography, due to the anisotropy detected in Earth’s interior.
Reviewer: Manuel de León (Madrid)
MSC:
| 74J05 | Linear waves in solid mechanics |
| 74B20 | Nonlinear elasticity |
| 74E10 | Anisotropy in solid mechanics |
| 74L05 | Geophysical solid mechanics |
| 53C80 | Applications of global differential geometry to the sciences |
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