Artículo
Abstract:
Field theory applies to elastodynamics, electromagnetism, quantum mechanics, gravitation and other similar fields of physics, where the basic equations describing the phenomenon are based on constitutive relations and balance equations. For instance, in elastodynamics, these are the stress-strain relations and the equations of momentum conservation (Euler-Newton law). In these cases, the same mathematical theory can be used, by establishing appropriate mathematical equivalences (or analogies) between material properties and field variables. For instance, the wave equation and the related mathematical developments can be used to describe anelastic and electromagnetic wave propagation, and are extensively used in quantum mechanics. In this work, we obtain the mathematical analogy for the reflection/refraction (transmission) problem of a thin layer embedded between dissimilar media, considering the presence of anisotropy and attenuation/viscosity in the viscoelastic case, conductivity in the electromagnetic case and a potential barrier in quantum physics (the tunnel effect). The analogy is mainly illustrated with geophysical examples of propagation of S (shear), P (compressional), TM (transverse-magnetic) and TE (transverse-electric) waves. The tunnel effect is obtained as a special case of viscoelastic waves at normal incidence. © 2014 by the Istituto Nazionale di Geofisica e Vulcanologia. All rights reserved.
Registro:
| Documento: | Artículo |
| Título: | Mathematical analogies in physics. Thin-layer wave theory |
| Autor: | Carcione, J.M.; Grünhut, V.; Osella, A. |
| Filiación: | Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Sgonico (Trieste), Italy Universidad de Buenos Aires, Departamento de Física IFIBA Conicet, Buenos Aires, Argentina |
| Palabras clave: | anisotropy; elastodynamics; electromagnetic wave; gravity field; quantum mechanics; theoretical study; viscoelasticity; wave equation; wave propagation; wave reflection |
| Año: | 2014 |
| Volumen: | 57 |
| Número: | 1 |
| DOI: | http://dx.doi.org/10.4401/ag-6324 |
| Título revista: | Annals of Geophysics |
| Título revista abreviado: | Ann. Geophys. |
| ISSN: | 15935213 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15935213_v57_n1_p_Carcione |
Referencias:
- Anderson, E., (1971) Modern Physics and Quantum Mechanics, , W.B. Saunders Co
- Bakke, N.E., Ursin, B., Thin-bed AVO effects (1998) Geophysical Prospecting, 46, pp. 571-587
- Born, M., Wolf, E., (1964) Principles of Optics, , Oxford: Pergamon Press
- Bradford, J.H., Deeds, J.C., Ground-penetrating radar theory and application of thin-bed offset-dependent reflectivity (2006) Geophysics, 71, pp. K47-K57
- Brekhovskikh, L.M., (1960) Waves In Layered Media, , Academic Press Inc
- Carcione, J.M., Cavallini, F., On the acousticelectromagnetic analogy (1995) Wave Motion, 21, pp. 149-162
- Carcione, J.M., Radiation patterns for GPR forward modeling (1998) Geophysics, 63, pp. 424-430
- Carcione, J.M., Robinson, E., On the acousticelectromagnetic analogy for the reflection-refraction problem (2002) Studia Geophysica Et Geodaetica, 46, pp. 321-345
- Carcione, J.M., Wave Fields in Real Media (2007) Theory and Numerical Simulation of Wave Propagation In Anisotropic, Anelastic, Porous and Electromagnetic Media, , 2nd edition, Elsevier
- Carcione, J.M., Ursin, B., Nordskag, J.I., Crossproperty relations between electrical conductivity and the seismic velocity of rocks (2007) Geophysics, 72, pp. E193-E204
- Carcione, J.M., Helbig, K., Elastic medium equivalent to Fresnels double refraction crystal (2008) J. Acoust. Soc. Am, 124 (4), pp. 2053-2060
- Deparis, J., Garambois, S., On the use of dispersive APVO GPR curves for thin-bed properties estimation: Theory and application to fracture characterization (2009) Geophysics, 74, pp. J1-J12
- Feynman, R.P., Leighton, R.B., Sands, M., (1965) The Feynman Lectures On Physics, , 13, Addison-Wesley ISBN 0-7382-0008-5
- Gangi, A.F., Carlson, R.L., An asperity-deformation model for effective pressure (1996) Tectonophysics, 256, pp. 241-251
- Liu, L., Schmitt, D.R., Amplitude and AVO responses of a single thin bed (2003) Geophysics, 68, pp. 1161-1168
- Mavko, G., Mukerji, T., Dvorkin, J., (2009) The Rock Physics Handbook: Tools For Seismic Analysis In Porous Media, , Cambridge Univ. Press
- Thomsen, L., Weak elastic anisotropy (1986) Geophysics, 51, pp. 1954-1966
- Tonti, E., (1972) On the Mathematical Structure of a Large Class of Physical Theories, 52 (1). , Accademia Nazionale dei Lincei, excerpt from 'Rendiconti della Classe di Scienze fisiche, matematiche e naturali', Series 8
- Tonti, E., The reason for analogies between physical theories (1976) Appl. Math. Modelling, 1, pp. 37-50
- Widess, M.B., How Thin is a Thin Bed? (1973) Geophysics, 38, pp. 1176-1180
Citas:
---------- APA ----------
Carcione, J.M., Grünhut, V. & Osella, A. (2014) . Mathematical analogies in physics. Thin-layer wave theory. Annals of Geophysics, 57(1).http://dx.doi.org/10.4401/ag-6324
---------- CHICAGO ----------
Carcione, J.M., Grünhut, V., Osella, A. "Mathematical analogies in physics. Thin-layer wave theory" . Annals of Geophysics 57, no. 1 (2014).http://dx.doi.org/10.4401/ag-6324
---------- MLA ----------
Carcione, J.M., Grünhut, V., Osella, A. "Mathematical analogies in physics. Thin-layer wave theory" . Annals of Geophysics, vol. 57, no. 1, 2014.http://dx.doi.org/10.4401/ag-6324
---------- VANCOUVER ----------
Carcione, J.M., Grünhut, V., Osella, A. Mathematical analogies in physics. Thin-layer wave theory. Ann. Geophys. 2014;57(1).http://dx.doi.org/10.4401/ag-6324
