On the Mathematical Analysis of an Elastic-gravitational Layered Earth Model for Magmatic Intrusion: The Stationary Case |
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Authors: | A Arjona J I Díaz J Fernández J B Rundle |
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Institution: | (1) Instituto de Astronomía y Geodesia (CSIC-UCM), Facultad de Matemáticas, Plaza de Ciencias n.3, 28040 Madrid, Spain;(2) Departamento de Matemática Aplicada, Facultad de Matemáticas, Plaza de Ciencias n.3, 28040 Madrid, Spain;(3) Center for Computational Science and Engineering, University of California, Davis, CA 95616, USA |
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Abstract: | In the early eighties Rundle (1980, 1981a,b, 1982) developed the techniques needed for calculations of displacements and gravity changes due to internal
sources of strain in layered linear elastic-gravitational media. The approximation of the solution for the half space was
obtained by using the propagator matrix technique. The Earth model considered is elastic-gravitational, composed of several
homogeneous layers overlying a bottom half space. Two dislocation sources can be considered, representing magma intrusions
and faults. In recent decades theoretical and computational extensions of that model have been developed by Rundle and co-workers
(e.g., Fernández and Rundle, 1994a,b; Fernández
et al., 1997, 2005a; Tiampo
et al., 2004; Charco
et al., 2006, 2007a,b). The source can be located at any depth in the media. In this work we prove that the perturbed equations
representing the elastic-gravitational deformation problem, with the natural boundary and transmission conditions, leads to
a well-posed problem even for varied domains and general data. We present constructive proof of the existence and we show
the uniqueness and the continuous dependence with respect to the data of weak solutions of the coupled elastic-gravitational
field equations. |
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Keywords: | Gravity changes elastic-gravitational Earth model displacement weak solution |
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