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On the Mathematical Analysis of an Elastic-gravitational Layered Earth Model for Magmatic Intrusion: The Stationary Case


Díaz Díaz, Jesús Ildefonso and Arjona, Alicia and Fernández, José and Rundle, J.B. (2008) On the Mathematical Analysis of an Elastic-gravitational Layered Earth Model for Magmatic Intrusion: The Stationary Case. Pure and Applied Geophysics, 165 (8). pp. 1465-1490. ISSN 0033-4553

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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., Fernandez and Rundle, 1994a,b; Fernandez 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.

Item Type:Article
Uncontrolled Keywords:long-valley-caldera; radar interferometry; surface deformation; gravity changes; volcanic areas; gps; displacement; california; island; fault; gravity changes; elastic-gravitational earth model; displacement; weak solution
Subjects:Sciences > Physics > Geophysics
ID Code:15181

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