{"id":66,"date":"2022-12-25T19:16:09","date_gmt":"2022-12-25T19:16:09","guid":{"rendered":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/chapter\/solution-exercise-3\/"},"modified":"2022-12-27T07:56:55","modified_gmt":"2022-12-27T07:56:55","slug":"solution-exercise-3","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/chapter\/solution-exercise-3\/","title":{"raw":"Solution Exercise 3","rendered":"Solution Exercise 3"},"content":{"raw":"
\r\n

In the table below, we have taken (by eye) 6 pairs of stage and % change in seismic velocity from Figure 12. You may chose different times, but try to pick enough times that you span the range of river stage and % change in seismic velocity. The data are presented in the table and plotted in the graph below. Note that we have \u201cestimated\u201d the stage to a precision of 0.1 m and the velocity change to a precition of ~0.25 from the figure. Using these data below, a least squares regression equation can be fit (using Excel or by hand) to the data to relate % velocity change to river stage. Using the points below, the regression equation is approsimated below and suggests a fairly robust relation between changes in seismic velocity and the proxy (river stage) for depth to groundwater.<\/p>\r\n

dv<\/em>\/<\/strong>V<\/em>(<\/strong>%)\u00a0=\u00a0\u22122.2\u00a0*\u00a0stage\u00a0+\u00a05.5,\u00a0\u00a0\u00a0R<\/em><\/strong>2<\/strong><\/sup>= 0.9<\/strong><\/p>\r\n

Reported river stage and corresponding normalized change in seismic velocity<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Date<\/strong><\/td>\r\nStage (m)<\/strong><\/td>\r\ndv<\/em>\/V<\/em> (%)<\/strong><\/td>\r\n<\/tr>\r\n
10\/25\/17<\/td>\r\n2.3<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
11\/19\/17<\/td>\r\n3.0<\/td>\r\n\u22121<\/td>\r\n<\/tr>\r\n
12\/04\/17<\/td>\r\n2.6<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
01\/10\/18<\/td>\r\n3.6<\/td>\r\n\u22122.75<\/td>\r\n<\/tr>\r\n
01\/28\/18<\/td>\r\n3.1<\/td>\r\n\u22121<\/td>\r\n<\/tr>\r\n
02\/22\/18<\/td>\r\n2.6<\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

\"Graph<\/p>\r\n

Observed change in normalized seismic velocity related to river stage fluctuations.<\/p>\r\n

Return to Exercise 3<\/a><\/p>\r\n\r\n<\/div>","rendered":"

\n

In the table below, we have taken (by eye) 6 pairs of stage and % change in seismic velocity from Figure 12. You may chose different times, but try to pick enough times that you span the range of river stage and % change in seismic velocity. The data are presented in the table and plotted in the graph below. Note that we have \u201cestimated\u201d the stage to a precision of 0.1 m and the velocity change to a precition of ~0.25 from the figure. Using these data below, a least squares regression equation can be fit (using Excel or by hand) to the data to relate % velocity change to river stage. Using the points below, the regression equation is approsimated below and suggests a fairly robust relation between changes in seismic velocity and the proxy (river stage) for depth to groundwater.<\/p>\n

dv<\/em>\/<\/strong>V<\/em>(<\/strong>%)\u00a0=\u00a0\u22122.2\u00a0*\u00a0stage\u00a0+\u00a05.5,\u00a0\u00a0\u00a0R<\/em><\/strong>2<\/strong><\/sup>= 0.9<\/strong><\/p>\n

Reported river stage and corresponding normalized change in seismic velocity<\/p>\n\n\n\n\n\n\n\n\n\n
Date<\/strong><\/td>\nStage (m)<\/strong><\/td>\ndv<\/em>\/V<\/em> (%)<\/strong><\/td>\n<\/tr>\n
10\/25\/17<\/td>\n2.3<\/td>\n0<\/td>\n<\/tr>\n
11\/19\/17<\/td>\n3.0<\/td>\n\u22121<\/td>\n<\/tr>\n
12\/04\/17<\/td>\n2.6<\/td>\n0<\/td>\n<\/tr>\n
01\/10\/18<\/td>\n3.6<\/td>\n\u22122.75<\/td>\n<\/tr>\n
01\/28\/18<\/td>\n3.1<\/td>\n\u22121<\/td>\n<\/tr>\n
02\/22\/18<\/td>\n2.6<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"Graph<\/p>\n

Observed change in normalized seismic velocity related to river stage fluctuations.<\/p>\n

Return to Exercise 3<\/a><\/p>\n<\/div>\n","protected":false},"author":1,"menu_order":9,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-66","chapter","type-chapter","status-publish","hentry"],"part":117,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/pressbooks\/v2\/chapters\/66","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":7,"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/pressbooks\/v2\/chapters\/66\/revisions"}],"predecessor-version":[{"id":217,"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/pressbooks\/v2\/chapters\/66\/revisions\/217"}],"part":[{"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/pressbooks\/v2\/parts\/117"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/pressbooks\/v2\/chapters\/66\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/wp\/v2\/media?parent=66"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/pressbooks\/v2\/chapter-type?post=66"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/wp\/v2\/contributor?post=66"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/distributed-fiber-optic-hydrogeophysics\/wp-json\/wp\/v2\/license?post=66"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}