A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs

Augustin, Matthias

doi:10.1007/978-3-319-17079-4

Cited by 19 publications

(17 citation statements)

References 188 publications

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“…More material can be found in Augustin (2014), Augustin et al (2012), Bauer et al (2014), Nutz (2014), andOstermann (2011).…”

Section: Circuit: Seismic Processing From Acoustic Wave Tomographymentioning

confidence: 95%

Geomathematics: Its Role, Its Aim, and Its Potential

Freeden

2014

Handbook of Geomathematics

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During the last decades, geosciences and geoengineering were influenced by two essential scenarios: First, the technological progress has completely changed the observational and measurement techniques. Modern high-speed computers and satellite-based techniques are more and more entering all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, and its environment and about an expected shortage of natural resources. Obviously, both aspects, viz., efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne, as well as spaceborne data of better and better quality, explain the strong need of new mathematical structures, tools, and methods, i.e., geomathematics.This paper deals with geomathematics, its role, its aim, and its potential. Moreover, the "circuit" geomathematics is exemplified by three problems involving the Earth's structure, namely, gravity field determination from terrestrial deflections of the vertical, ocean flow modeling from satellite (altimeter measured) ocean topography, and reservoir detection from (acoustic) wave tomography.

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“…More material can be found in Augustin (2014), Augustin et al (2012), Bauer et al (2014), Nutz (2014), andOstermann (2011).…”

Section: Circuit: Seismic Processing From Acoustic Wave Tomographymentioning

confidence: 95%

Geomathematics: Its Role, Its Aim, and Its Potential

Freeden

2014

Handbook of Geomathematics

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“…The fundamental solutions in dynamic poroelasticity have been constructed by Burridge and Vargas [41], Cleary [42] and Kaynia and Banerjee [43]. Basic results on the method of fundamental solutions in poroelasticity are given by Augustin [44].…”

Section: Theorem 4 Each Column Of the Matrix G(x) Is A Solution Of The Homogeneous Equationmentioning

confidence: 99%

“…Obviously, on the basis of Green's third identities (44) and (45), the regular vector U in O + is represented by the sum of the single-layer, double-layer and volume potentials as follows:…”

Section: Surface and Volume Potentialsmentioning

confidence: 99%

Steady vibration problems in the coupled linear theory of porous elastic solids

Svanadze

2019

Mathematics and Mechanics of Solids

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This paper concerns the coupled linear theory of elasticity for isotropic porous materials. In this theory the coupled phenomena of the concepts of Darcy’s law and the volume fraction is considered. The basic internal and external boundary value problems (BVPs) of steady vibrations are investigated. Indeed, the fundamental solution of the system of steady vibration equations is constructed explicitly by means of elementary functions, and its basic properties are presented. The radiation conditions are established and Green’s identities are obtained. The uniqueness theorems for the regular (classical) solutions of the BVPs are proved. The surface (single layer and double layer) and volume potentials are constructed and the basic properties of these potentials are given. Finally, the existence theorems for classical solutions of the BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations.

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“…is the fundamental solution of equations (17), where the matrices L (r) ( ) and Y (r) (x) are given by formulas (47) and (48), respectively.…”

Section: Fundamental Solution Of Equations (17)mentioning

confidence: 99%

Fundamental solutions in the linear theory of thermoelasticity for solids with triple porosity

Svanadze

2018

Mathematics and Mechanics of Solids

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This paper deals with the fully coupled linear theory of thermoelasticity for triple porosity materials. The system of general governing equations of motion is expressed in terms of the displacement vector field, the pressures in the three pore systems (macro-, meso- and micropores) and the temperature. The fundamental solutions are constructed explicitly by means of elementary functions for the five special cases of the equations of motion: (1) equations of steady vibrations; (2) equations in the Laplace transform space; (3) equations of steady vibrations in the quasi-static theory; (4) equations of equilibrium; and (5) equations of steady vibrations for rigid body with triple porosity. Finally, the basic properties of these solutions are established.

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A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs

Cited by 19 publications

References 188 publications

Geomathematics: Its Role, Its Aim, and Its Potential

Geomathematics: Its Role, Its Aim, and Its Potential

Steady vibration problems in the coupled linear theory of porous elastic solids

Fundamental solutions in the linear theory of thermoelasticity for solids with triple porosity

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