{"id":126,"date":"2022-12-25T19:39:49","date_gmt":"2022-12-25T19:39:49","guid":{"rendered":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/?post_type=part&p=126"},"modified":"2023-03-27T01:41:57","modified_gmt":"2023-03-27T01:41:57","slug":"notations","status":"publish","type":"part","link":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/part\/notations\/","title":{"raw":"9 Notations","rendered":"9 Notations"},"content":{"raw":"
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
C<\/em>e<\/em><\/sub><\/td>\r\ncalibrated Brillouin frequency shift strain coefficient of the fiber ( T\u22121<\/sup>)<\/td>\r\n<\/tr>\r\n
C<\/em>p<\/em><\/sub>(\u03b8<\/em>)<\/td>\r\nsoil heat capacity (ML2<\/sup>T\u22122<\/sup>\u0398\u22121<\/sup>)<\/td>\r\n<\/tr>\r\n
c<\/em>S<\/em><\/sub>\u00a0and\u00a0c<\/em>aS<\/em><\/sub><\/td>\r\nConstants related to laser power and responsiveness of the DTS detectors (ML2<\/sup>T\u22122<\/sup>)<\/td>\r\n<\/tr>\r\n
CT<\/em><\/sub><\/em><\/td>\r\ncalibrated Brillouin frequency shift temperature coefficient (\u0398\u22121<\/sup> T\u22121<\/sup>)<\/td>\r\n<\/tr>\r\n
\u0394\u03b1<\/em><\/td>\r\ndifference in attenuation factors between Stokes and anti\u2212Stokes (L\u22121<\/sup>)<\/td>\r\n<\/tr>\r\n
\u0394\u03b5<\/em><\/td>\r\nchange in strain (dimensionless, LL\u22121<\/sup>)<\/td>\r\n<\/tr>\r\n
\u0394v<\/em>B<\/em><\/sub><\/td>\r\nchange in Brillouin frequency (T\u22121<\/sup>)<\/td>\r\n<\/tr>\r\n
\u0394T<\/em><\/td>\r\nchange in temperature (\u0398)<\/td>\r\n<\/tr>\r\n
\u03b3<\/em>(\u03b8<\/em>)<\/td>\r\nsoil thermal conductivity (MLT\u22123<\/sup>\u0398\u22121<\/sup>)<\/td>\r\n<\/tr>\r\n
\u0127<\/td>\r\nreduced Planck\u2019s constant (ML2<\/sup>T\u22121<\/sup>)<\/td>\r\n<\/tr>\r\n
I<\/em>aS<\/em><\/sub><\/td>\r\nmeasured photon intensity of anti\u2212Stokes (ML2<\/sup>T\u22122<\/sup>)<\/td>\r\n<\/tr>\r\n
I<\/em>s<\/em><\/sub><\/td>\r\nmeasured photon intensity of Stokes (ML2<\/sup>T\u22122<\/sup>)<\/td>\r\n<\/tr>\r\n
k<\/em><\/td>\r\nBoltzmann constant (ML2<\/sup>T\u22122<\/sup>\u0398\u22121<\/sup>)<\/td>\r\n<\/tr>\r\n
\u03bb<\/em>S<\/em><\/sub>\u00a0and\u00a0\u03bb<\/em>aS<\/em><\/sub><\/td>\r\nwavelengths of the Raman shifted returning light (L) as discussed by Farahani and Gogolla (1999)<\/td>\r\n<\/tr>\r\n
\u03a9<\/td>\r\nfrequency difference between Stokes and anti\u2212Stokes scattering in typical fiber (T\u22121<\/sup>)<\/td>\r\n<\/tr>\r\n
\u03c1<\/em><\/td>\r\nwater density (ML\u22123<\/sup>)<\/td>\r\n<\/tr>\r\n
\u03b8<\/em><\/td>\r\nsoil volumetric water content (dimensionless, (L3<\/sup>L\u22123<\/sup>)<\/td>\r\n<\/tr>\r\n
z<\/em><\/td>\r\ndistance along the optical fiber (L)<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>","rendered":"
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
C<\/em>e<\/em><\/sub><\/td>\ncalibrated Brillouin frequency shift strain coefficient of the fiber ( T\u22121<\/sup>)<\/td>\n<\/tr>\n
C<\/em>p<\/em><\/sub>(\u03b8<\/em>)<\/td>\nsoil heat capacity (ML2<\/sup>T\u22122<\/sup>\u0398\u22121<\/sup>)<\/td>\n<\/tr>\n
c<\/em>S<\/em><\/sub>\u00a0and\u00a0c<\/em>aS<\/em><\/sub><\/td>\nConstants related to laser power and responsiveness of the DTS detectors (ML2<\/sup>T\u22122<\/sup>)<\/td>\n<\/tr>\n
CT<\/em><\/sub><\/em><\/td>\ncalibrated Brillouin frequency shift temperature coefficient (\u0398\u22121<\/sup> T\u22121<\/sup>)<\/td>\n<\/tr>\n
\u0394\u03b1<\/em><\/td>\ndifference in attenuation factors between Stokes and anti\u2212Stokes (L\u22121<\/sup>)<\/td>\n<\/tr>\n
\u0394\u03b5<\/em><\/td>\nchange in strain (dimensionless, LL\u22121<\/sup>)<\/td>\n<\/tr>\n
\u0394v<\/em>B<\/em><\/sub><\/td>\nchange in Brillouin frequency (T\u22121<\/sup>)<\/td>\n<\/tr>\n
\u0394T<\/em><\/td>\nchange in temperature (\u0398)<\/td>\n<\/tr>\n
\u03b3<\/em>(\u03b8<\/em>)<\/td>\nsoil thermal conductivity (MLT\u22123<\/sup>\u0398\u22121<\/sup>)<\/td>\n<\/tr>\n
\u0127<\/td>\nreduced Planck\u2019s constant (ML2<\/sup>T\u22121<\/sup>)<\/td>\n<\/tr>\n
I<\/em>aS<\/em><\/sub><\/td>\nmeasured photon intensity of anti\u2212Stokes (ML2<\/sup>T\u22122<\/sup>)<\/td>\n<\/tr>\n
I<\/em>s<\/em><\/sub><\/td>\nmeasured photon intensity of Stokes (ML2<\/sup>T\u22122<\/sup>)<\/td>\n<\/tr>\n
k<\/em><\/td>\nBoltzmann constant (ML2<\/sup>T\u22122<\/sup>\u0398\u22121<\/sup>)<\/td>\n<\/tr>\n
\u03bb<\/em>S<\/em><\/sub>\u00a0and\u00a0\u03bb<\/em>aS<\/em><\/sub><\/td>\nwavelengths of the Raman shifted returning light (L) as discussed by Farahani and Gogolla (1999)<\/td>\n<\/tr>\n
\u03a9<\/td>\nfrequency difference between Stokes and anti\u2212Stokes scattering in typical fiber (T\u22121<\/sup>)<\/td>\n<\/tr>\n
\u03c1<\/em><\/td>\nwater density (ML\u22123<\/sup>)<\/td>\n<\/tr>\n
\u03b8<\/em><\/td>\nsoil volumetric water content (dimensionless, (L3<\/sup>L\u22123<\/sup>)<\/td>\n<\/tr>\n
z<\/em><\/td>\ndistance along the optical fiber (L)<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n","protected":false},"parent":0,"menu_order":9,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-126","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/pressbooks\/v2\/parts\/126","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":10,"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/pressbooks\/v2\/parts\/126\/revisions"}],"predecessor-version":[{"id":225,"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/pressbooks\/v2\/parts\/126\/revisions\/225"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/wp\/v2\/media?parent=126"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/wp\/v2\/contributor?post=126"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/wp\/v2\/license?post=126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}