{"id":100,"date":"2026-04-10T02:53:04","date_gmt":"2026-04-10T02:53:04","guid":{"rendered":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/chapter\/ch032-xhtml\/"},"modified":"2026-05-11T22:13:32","modified_gmt":"2026-05-11T22:13:32","slug":"4-4-calculation-of-tracer-age","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/chapter\/4-4-calculation-of-tracer-age\/","title":{"raw":"4.4 Calculation of Tracer Age","rendered":"4.4 Calculation of Tracer Age"},"content":{"raw":"
\r\n
\r\n\r\nFigure 15<\/span><\/a> shows five to six typical steps that can be followed to determine [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] age from noble gas and tritium data. Step 1 is a data triage step to evaluate whether the groundwater sample is likely to be in the applicable age range for the [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] method and evaluate whether the sample may be a mixture of old and young groundwater (Step 1d). A key variable in step 1 is [latex]\\frac{R}{R_{a}}[\/latex], which is the ratio of [latex]_{}^{3}{He}[\/latex] to [latex]_{}^{4}{He}[\/latex] measured in the sample ([latex]R)[\/latex] and the [latex]_{}^{3}{He}[\/latex]\/[latex]_{}^{4}{He}[\/latex] of air ([latex]R_{a}[\/latex]) as shown in Figure 15<\/span><\/a>, steps 1a, b, and d. Either [latex]\\frac{R}{R_{a}}[\/latex] or the [latex]R[\/latex] measured for each groundwater sample should be included in the results reported by the noble gas laboratory analyzing the samples.\r\n\r\n<\/div>\r\n
\r\n\r\n\"\"\r\n\r\n<\/div>\r\n
\r\n
\r\n
\r\n\r\n<\/span>Figure 15\u00a0\u2013<\/strong>\u00a0The process for interpreting 3<\/sup>H and noble gas data for tritium\u2011helium age dating. Shaded and numbered boxes are major steps of the process. Text boxes below the first five steps show key criteria to consider while interpreting noble gas and 3<\/sup>H data. Dashed lines and outlines indicate special consideration for samples that may be mixtures of old and young groundwater (modified from Gilmore et al., 2021).\r\n\r\n<\/div><\/blockquote>\r\n<\/div>\r\n
\r\n\r\nInspection of the tritium\u2011helium age calculation shown in Equation\u00a0(14)<\/span> reveals the need to determine [latex]_{}^{3}{He}_{trit}[\/latex], which is just one component of the overall [latex]_{}^{3}{He}[\/latex] budget in any groundwater sample. The complete budget for [latex]_{}^{3}{He}[\/latex] in groundwater, rearranged to solve for [latex]_{}^{3}{He}_{trit}[\/latex], is shown in Equation\u00a0(18)<\/span>.\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n
<\/th>\r\n[latex]_{\\ }^{3}{He}_{trit} =_{\\ }^{3}{He}_{m} -_{\\ }^{3}{He}_{atm} -_{\\ }^{3}{He}_{terr}[\/latex]<\/th>\r\n<\/span>(18)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
\r\n\r\nwhere:\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n
[latex]_{\\ }^{3}{He}_{m}[\/latex]<\/th>\r\n=<\/th>\r\n[latex]_{}^{3}{He}[\/latex] measured in the groundwater sample<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
[latex]_{\\ }^{3}{He}_{atm}[\/latex]<\/td>\r\n=<\/td>\r\nportion of dissolved [latex]_{}^{3}{He}[\/latex] derived from atmospheric sources<\/td>\r\n<\/tr>\r\n
[latex]_{\\ }^{3}{He}_{terr}[\/latex]<\/td>\r\n=<\/td>\r\nportion of dissolved [latex]_{}^{3}{He}[\/latex] derived from terrigenic sources, including crustal [latex]_{}^{3}{He}[\/latex] ([latex]_{}^{3}{He}[\/latex]crust<\/sub>) and mantle [latex]_{}^{3}{He}[\/latex] ([latex]_{}^{3}{He}[\/latex]man<\/sub>)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\nUnits for concentrations in Equation\u00a0(18)<\/span> are typically expressed in ccSTP\/g. [latex]_{\\ }^{3}{He}_{m}[\/latex] may be reported as [latex]\\delta_{}^{3}{He}[\/latex], which is equivalent to [latex]\\left( \\frac{R}{R_{a} - 1} \\right)100\\%,[\/latex] and can therefore be converted to ccSTP\/g based on the definitions of [latex]R[\/latex] and [latex]R_{a}[\/latex] and the measured concentration of [latex]_{}^{4}{He}[\/latex] in ccSTP\/g. The age calculated by Equation\u00a0(14)<\/span> requires that [latex]_{}^{3}H[\/latex] and [latex]_{\\ }^{3}{He}_{trit}[\/latex] be in the same units. Equation\u00a0(19)<\/span> expresses a conversion factor (CF<\/em>) used to convert from ccSTP\/g to TU.\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n
<\/th>\r\n[latex]CF = \\left( \\frac{4.021 \\times 10^{14}}{1 - \\frac{S}{1000}} \\right)[\/latex]<\/th>\r\n<\/span>(19)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
\r\n\r\nwhere:\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n
S<\/em><\/th>\r\n=<\/th>\r\nsalinity of the sample in parts per thousand (i.e., \u2030)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
\r\n\r\nDetermination of the atmospheric component ([latex]_{\\ }^{3}{He}_{atm}[\/latex]) of the [latex]_{}^{3}{He}[\/latex] budget is addressed in Figure 15<\/span><\/a>\u00a0(step\u00a02). [latex]_{\\ }^{3}{He}_{atm}[\/latex] can be broken into two components as shown in Equation\u00a0(20)<\/span>.\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n
<\/th>\r\n[latex]_{\\ }^{3}{He}_{atm} =_{\\ }^{3}{He}_{sol} +_{\\ }^{3}{He}_{EA}[\/latex]<\/th>\r\n<\/span>(20)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
\r\n\r\nwhere:\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n
[latex]_{\\ }^{3}{He}_{sol}[\/latex]<\/th>\r\n=<\/th>\r\n[latex]_{}^{3}{He}[\/latex] concentration at solubility equilibrium with the atmosphere at recharge temperature and elevation<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
[latex]_{\\ }^{3}{He}_{EA}[\/latex]<\/td>\r\n=<\/td>\r\nthe portion of dissolved [latex]_{}^{3}{He}[\/latex] derived from excess air<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\n[latex]_{\\ }^{3}{He}_{EA}[\/latex] describes dissolved [latex]_{}^{3}{He}[\/latex] attributed to an atmospheric source but in excess of solubility equilibrium at recharge temperature and elevation. Excess air is due to vadose zone processes and\/or water table dynamics (i.e., dissolution of air that is trapped in pore spaces as described in Section\u00a02). Selection of a noble gas model as described in Section\u00a02 (e.g., the CE model or graphical method shown in Figure 5<\/span><\/a>) or in Aeschbach\u2011Hertig and Solomon (2013) is necessary to determine the solubility and excess air components of the [latex]_{\\ }^{3}{He}_{atm}[\/latex] budget.\r\n\r\n<\/div>\r\n
\r\n\r\n\u2206[latex]Ne[\/latex]\u2014defined in Equation\u00a0(8)<\/span> of Section\u00a02\u2014is an important variable mentioned in Figure 15<\/span><\/a> (step\u00a02b) because it is sensitive to excess air (Figure 5<\/span><\/a>). When \u2206[latex]Ne[\/latex]\u00a0is negative, it is likely that noble gases have been lost from the sample (Figure 6<\/span><\/a>: steps\u00a02b and c) and noble gas modeling becomes more complex (Aeschbach\u2011Hertig et al., 2008; Aeschbach\u2011Hertig & Solomon, 2013; Gilmore et al., 2021; Gilmore, Genereux, Solomon, Farrell, et al., 2016; Gilmore, Genereux, Solomon, & Solder, 2016; Visser et al., 2007; Visser et al., 2009), as described in the discussion of tracer\u2011specific issues in Section\u00a04.6.\r\n\r\n<\/div>\r\n
\r\n\r\nStep\u00a03 in Figure 15<\/span><\/a> addresses the [latex]_{\\ }^{3}{He}_{terr}[\/latex] component of the [latex]_{}^{3}{He}[\/latex] budget, which is based on an estimate or assumption of [latex]R_{terr} [\/latex](Figure 15<\/span><\/a>: steps\u00a03a and c), the [latex]\\frac{_{}^{3}{He}}{_{}^{4}{He}}[\/latex] of terrigenic [latex]He[\/latex]. The typical assumed value for [latex]R_{terr}[\/latex] is 2\u00a0\u00d7\u00a010\u20118<\/sup> (Mamyrin & Tolstikhin, 1984), with a range of 10-9<\/sup> to 10-7<\/sup> (Solomon, 2000), based on values associated with a crustal source ([latex]R_{crust}[\/latex] in Table\u00a04<\/span><\/a>). If a mantle source ([latex]R_{man}[\/latex], Table\u00a04<\/span><\/a>) of [latex]He[\/latex] is present, age dating becomes very difficult because the [latex]R_{man}[\/latex] is an order of magnitude greater than [latex]R_{a}[\/latex] for atmospheric [latex]He[\/latex].\r\n\r\n<\/div>\r\n
\r\n
\r\n\r\n<\/span>Table\u00a04\u00a0\u2011<\/strong>\u00a03<\/sup>He\/4<\/sup>He ratios (Rx<\/sub><\/em>) for different 3<\/sup>He reservoirs (i.e., sources).\r\n\r\n<\/div>\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
3<\/sup>He reservoir<\/th>\r\nVariable<\/th>\r\nTypical Value<\/th>\r\nNotes<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
Atmosphere<\/td>\r\nRa<\/sub><\/em><\/td>\r\n1.382[latex]\\mathbf{\\times}[\/latex]10-6<\/sup><\/td>\r\n\r\n
\r\n
Considered a constant for all practical purposes, based on 4<\/sup>He outgassing from the earth, production of 3<\/sup>He from cosmic rays, and loss of 3<\/sup>He to atmosphere.<\/blockquote>\r\n<\/div><\/td>\r\n<\/tr>\r\n
Atmosphere, adjusted for fractionation<\/td>\r\nRsol<\/sub><\/em><\/td>\r\n1.357[latex]\\mathbf{\\times}[\/latex]10-6<\/sup><\/td>\r\n\r\n
\r\n
Because there is a slight fractionation of 4<\/sup>He and 3<\/sup>He when dissolved, R<\/em> for water in equilibrium with the atmospheric air is 0.98\u00a0[latex]\\mathbf{\\times}[\/latex]\u00a0R<\/em>.<\/blockquote>\r\n<\/div><\/td>\r\n<\/tr>\r\n
Crustal source of Rterr<\/sub><\/em><\/td>\r\nRcrust<\/sub><\/em><\/td>\r\n2[latex]\\mathbf{\\times}[\/latex]10-8<\/sup>, theoretically, although in practice may reach 2[latex]\\mathbf{\\times}[\/latex]10-7<\/sup><\/td>\r\n\r\n
\r\n
Theoretical value based on production of 3<\/sup>He by hitting 6<\/sup>Li with a neutron. Actual values based on old (3<\/sup>H below detection) groundwater range from 2[latex]\\mathbf{\\times}[\/latex]10-8<\/sup> to 2[latex]\\mathbf{\\times}[\/latex]10-7<\/sup>.<\/blockquote>\r\n<\/div><\/td>\r\n<\/tr>\r\n
Mantle source of Rterr<\/sub><\/em><\/td>\r\nRman<\/sub><\/em><\/td>\r\n1.1[latex]\\mathbf{\\times}[\/latex]10-5<\/sup> to 1.4[latex]\\mathbf{\\times}[\/latex]10-5<\/sup><\/td>\r\n\r\n
\r\n
Given the magnitude of Rman<\/sub><\/em>, 3<\/sup>H\/3<\/sup>He age dating becomes very difficult.<\/blockquote>\r\n<\/div><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\nStep\u00a04 in Figure 15<\/span><\/a> is trivial if the calculated [latex]_{\\ }^{3}{He}_{trit}[\/latex] is positive and initial tritium, [latex]_{}^{3}{He}[\/latex](t<\/em>0<\/sub>) as determined using Equation\u00a0(16)<\/span> is reasonable compared to historical atmospheric [latex]_{}^{3}H[\/latex] records. Similarly, Step\u00a05 is a simple calculation of groundwater tracer age based on Equation\u00a0(14)<\/span>. However, it is important to perform the checks\u00a0a and b for Steps\u00a04 and 5 to confirm that the calculated age is reasonable. An example of a graph used for Step\u00a04b is shown in Figure 16<\/span><\/a>. Samples that plot below the precipitation curve are likely to be mixtures of young and old water. When appropriate, tracer results need to be modeled as mixtures of groundwater with different ages, as described in Step 6\u00a0of Figure 15<\/span><\/a>.\r\n\r\n<\/div>\r\n
\r\n\r\n\"\"\r\n
\r\n
\r\n
\r\n\r\n<\/span>Figure 16\u00a0\u2013\u00a0<\/strong>Graph showing initial tritium (3<\/sup>H(t<\/em>0<\/sub>), calculated from measured 3<\/sup>H plus 3<\/sup>H equivalent of tritiogenic helium from the sample) for groundwater samples collected in the streambed of a gaining stream in North Carolina (NC), USA, in July 2012 (modified from Gilmore, Genereux, Solomon, & Solder, 2016). Black dots are streambed samples with the initial 3<\/sup>H on the y\u2011axis and recharge year determined from tracer age using the 3<\/sup>H\/3<\/sup>He method on the x\u2011axis.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
\n
\n

Figure 15<\/span><\/a> shows five to six typical steps that can be followed to determine [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] age from noble gas and tritium data. Step 1 is a data triage step to evaluate whether the groundwater sample is likely to be in the applicable age range for the [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] method and evaluate whether the sample may be a mixture of old and young groundwater (Step 1d). A key variable in step 1 is [latex]\\frac{R}{R_{a}}[\/latex], which is the ratio of [latex]_{}^{3}{He}[\/latex] to [latex]_{}^{4}{He}[\/latex] measured in the sample ([latex]R)[\/latex] and the [latex]_{}^{3}{He}[\/latex]\/[latex]_{}^{4}{He}[\/latex] of air ([latex]R_{a}[\/latex]) as shown in Figure 15<\/span><\/a>, steps 1a, b, and d. Either [latex]\\frac{R}{R_{a}}[\/latex] or the [latex]R[\/latex] measured for each groundwater sample should be included in the results reported by the noble gas laboratory analyzing the samples.<\/p>\n<\/div>\n

\n

\"\"<\/p>\n<\/div>\n

\n
\n
\n

<\/span>Figure 15\u00a0\u2013<\/strong>\u00a0The process for interpreting 3<\/sup>H and noble gas data for tritium\u2011helium age dating. Shaded and numbered boxes are major steps of the process. Text boxes below the first five steps show key criteria to consider while interpreting noble gas and 3<\/sup>H data. Dashed lines and outlines indicate special consideration for samples that may be mixtures of old and young groundwater (modified from Gilmore et al., 2021).<\/p>\n<\/div>\n<\/blockquote>\n<\/div>\n

\n

Inspection of the tritium\u2011helium age calculation shown in Equation\u00a0(14)<\/span> reveals the need to determine [latex]_{}^{3}{He}_{trit}[\/latex], which is just one component of the overall [latex]_{}^{3}{He}[\/latex] budget in any groundwater sample. The complete budget for [latex]_{}^{3}{He}[\/latex] in groundwater, rearranged to solve for [latex]_{}^{3}{He}_{trit}[\/latex], is shown in Equation\u00a0(18)<\/span>.<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n
<\/th>\n[latex]_{\\ }^{3}{He}_{trit} =_{\\ }^{3}{He}_{m} -_{\\ }^{3}{He}_{atm} -_{\\ }^{3}{He}_{terr}[\/latex]<\/th>\n<\/span>(18)<\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
\n

where:<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n
[latex]_{\\ }^{3}{He}_{m}[\/latex]<\/th>\n=<\/th>\n[latex]_{}^{3}{He}[\/latex] measured in the groundwater sample<\/th>\n<\/tr>\n<\/thead>\n
[latex]_{\\ }^{3}{He}_{atm}[\/latex]<\/td>\n=<\/td>\nportion of dissolved [latex]_{}^{3}{He}[\/latex] derived from atmospheric sources<\/td>\n<\/tr>\n
[latex]_{\\ }^{3}{He}_{terr}[\/latex]<\/td>\n=<\/td>\nportion of dissolved [latex]_{}^{3}{He}[\/latex] derived from terrigenic sources, including crustal [latex]_{}^{3}{He}[\/latex] ([latex]_{}^{3}{He}[\/latex]crust<\/sub>) and mantle [latex]_{}^{3}{He}[\/latex] ([latex]_{}^{3}{He}[\/latex]man<\/sub>)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Units for concentrations in Equation\u00a0(18)<\/span> are typically expressed in ccSTP\/g. [latex]_{\\ }^{3}{He}_{m}[\/latex] may be reported as [latex]\\delta_{}^{3}{He}[\/latex], which is equivalent to [latex]\\left( \\frac{R}{R_{a} - 1} \\right)100\\%,[\/latex] and can therefore be converted to ccSTP\/g based on the definitions of [latex]R[\/latex] and [latex]R_{a}[\/latex] and the measured concentration of [latex]_{}^{4}{He}[\/latex] in ccSTP\/g. The age calculated by Equation\u00a0(14)<\/span> requires that [latex]_{}^{3}H[\/latex] and [latex]_{\\ }^{3}{He}_{trit}[\/latex] be in the same units. Equation\u00a0(19)<\/span> expresses a conversion factor (CF<\/em>) used to convert from ccSTP\/g to TU.<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n
<\/th>\n[latex]CF = \\left( \\frac{4.021 \\times 10^{14}}{1 - \\frac{S}{1000}} \\right)[\/latex]<\/th>\n<\/span>(19)<\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
\n

where:<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n
S<\/em><\/th>\n=<\/th>\nsalinity of the sample in parts per thousand (i.e., \u2030)<\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
\n

Determination of the atmospheric component ([latex]_{\\ }^{3}{He}_{atm}[\/latex]) of the [latex]_{}^{3}{He}[\/latex] budget is addressed in Figure 15<\/span><\/a>\u00a0(step\u00a02). [latex]_{\\ }^{3}{He}_{atm}[\/latex] can be broken into two components as shown in Equation\u00a0(20)<\/span>.<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n
<\/th>\n[latex]_{\\ }^{3}{He}_{atm} =_{\\ }^{3}{He}_{sol} +_{\\ }^{3}{He}_{EA}[\/latex]<\/th>\n<\/span>(20)<\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
\n

where:<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n\n\n
[latex]_{\\ }^{3}{He}_{sol}[\/latex]<\/th>\n=<\/th>\n[latex]_{}^{3}{He}[\/latex] concentration at solubility equilibrium with the atmosphere at recharge temperature and elevation<\/th>\n<\/tr>\n<\/thead>\n
[latex]_{\\ }^{3}{He}_{EA}[\/latex]<\/td>\n=<\/td>\nthe portion of dissolved [latex]_{}^{3}{He}[\/latex] derived from excess air<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

[latex]_{\\ }^{3}{He}_{EA}[\/latex] describes dissolved [latex]_{}^{3}{He}[\/latex] attributed to an atmospheric source but in excess of solubility equilibrium at recharge temperature and elevation. Excess air is due to vadose zone processes and\/or water table dynamics (i.e., dissolution of air that is trapped in pore spaces as described in Section\u00a02). Selection of a noble gas model as described in Section\u00a02 (e.g., the CE model or graphical method shown in Figure 5<\/span><\/a>) or in Aeschbach\u2011Hertig and Solomon (2013) is necessary to determine the solubility and excess air components of the [latex]_{\\ }^{3}{He}_{atm}[\/latex] budget.<\/p>\n<\/div>\n

\n

\u2206[latex]Ne[\/latex]\u2014defined in Equation\u00a0(8)<\/span> of Section\u00a02\u2014is an important variable mentioned in Figure 15<\/span><\/a> (step\u00a02b) because it is sensitive to excess air (Figure 5<\/span><\/a>). When \u2206[latex]Ne[\/latex]\u00a0is negative, it is likely that noble gases have been lost from the sample (Figure 6<\/span><\/a>: steps\u00a02b and c) and noble gas modeling becomes more complex (Aeschbach\u2011Hertig et al., 2008; Aeschbach\u2011Hertig & Solomon, 2013; Gilmore et al., 2021; Gilmore, Genereux, Solomon, Farrell, et al., 2016; Gilmore, Genereux, Solomon, & Solder, 2016; Visser et al., 2007; Visser et al., 2009), as described in the discussion of tracer\u2011specific issues in Section\u00a04.6.<\/p>\n<\/div>\n

\n

Step\u00a03 in Figure 15<\/span><\/a> addresses the [latex]_{\\ }^{3}{He}_{terr}[\/latex] component of the [latex]_{}^{3}{He}[\/latex] budget, which is based on an estimate or assumption of [latex]R_{terr}[\/latex](Figure 15<\/span><\/a>: steps\u00a03a and c), the [latex]\\frac{_{}^{3}{He}}{_{}^{4}{He}}[\/latex] of terrigenic [latex]He[\/latex]. The typical assumed value for [latex]R_{terr}[\/latex] is 2\u00a0\u00d7\u00a010\u20118<\/sup> (Mamyrin & Tolstikhin, 1984), with a range of 10-9<\/sup> to 10-7<\/sup> (Solomon, 2000), based on values associated with a crustal source ([latex]R_{crust}[\/latex] in Table\u00a04<\/span><\/a>). If a mantle source ([latex]R_{man}[\/latex], Table\u00a04<\/span><\/a>) of [latex]He[\/latex] is present, age dating becomes very difficult because the [latex]R_{man}[\/latex] is an order of magnitude greater than [latex]R_{a}[\/latex] for atmospheric [latex]He[\/latex].<\/p>\n<\/div>\n

\n
\n

<\/span>Table\u00a04\u00a0\u2011<\/strong>\u00a03<\/sup>He\/4<\/sup>He ratios (Rx<\/sub><\/em>) for different 3<\/sup>He reservoirs (i.e., sources).<\/p>\n<\/div>\n<\/div>\n\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n\n
3<\/sup>He reservoir<\/th>\nVariable<\/th>\nTypical Value<\/th>\nNotes<\/th>\n<\/tr>\n<\/thead>\n
Atmosphere<\/td>\nRa<\/sub><\/em><\/td>\n1.382[latex]\\mathbf{\\times}[\/latex]10-6<\/sup><\/td>\n\n
\n

Considered a constant for all practical purposes, based on 4<\/sup>He outgassing from the earth, production of 3<\/sup>He from cosmic rays, and loss of 3<\/sup>He to atmosphere.<\/p><\/blockquote>\n<\/div>\n<\/td>\n<\/tr>\n

Atmosphere, adjusted for fractionation<\/td>\nRsol<\/sub><\/em><\/td>\n1.357[latex]\\mathbf{\\times}[\/latex]10-6<\/sup><\/td>\n\n
\n

Because there is a slight fractionation of 4<\/sup>He and 3<\/sup>He when dissolved, R<\/em> for water in equilibrium with the atmospheric air is 0.98\u00a0[latex]\\mathbf{\\times}[\/latex]\u00a0R<\/em>.<\/p><\/blockquote>\n<\/div>\n<\/td>\n<\/tr>\n

Crustal source of Rterr<\/sub><\/em><\/td>\nRcrust<\/sub><\/em><\/td>\n2[latex]\\mathbf{\\times}[\/latex]10-8<\/sup>, theoretically, although in practice may reach 2[latex]\\mathbf{\\times}[\/latex]10-7<\/sup><\/td>\n\n
\n

Theoretical value based on production of 3<\/sup>He by hitting 6<\/sup>Li with a neutron. Actual values based on old (3<\/sup>H below detection) groundwater range from 2[latex]\\mathbf{\\times}[\/latex]10-8<\/sup> to 2[latex]\\mathbf{\\times}[\/latex]10-7<\/sup>.<\/p><\/blockquote>\n<\/div>\n<\/td>\n<\/tr>\n

Mantle source of Rterr<\/sub><\/em><\/td>\nRman<\/sub><\/em><\/td>\n1.1[latex]\\mathbf{\\times}[\/latex]10-5<\/sup> to 1.4[latex]\\mathbf{\\times}[\/latex]10-5<\/sup><\/td>\n\n
\n

Given the magnitude of Rman<\/sub><\/em>, 3<\/sup>H\/3<\/sup>He age dating becomes very difficult.<\/p><\/blockquote>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\n

Step\u00a04 in Figure 15<\/span><\/a> is trivial if the calculated [latex]_{\\ }^{3}{He}_{trit}[\/latex] is positive and initial tritium, [latex]_{}^{3}{He}[\/latex](t<\/em>0<\/sub>) as determined using Equation\u00a0(16)<\/span> is reasonable compared to historical atmospheric [latex]_{}^{3}H[\/latex] records. Similarly, Step\u00a05 is a simple calculation of groundwater tracer age based on Equation\u00a0(14)<\/span>. However, it is important to perform the checks\u00a0a and b for Steps\u00a04 and 5 to confirm that the calculated age is reasonable. An example of a graph used for Step\u00a04b is shown in Figure 16<\/span><\/a>. Samples that plot below the precipitation curve are likely to be mixtures of young and old water. When appropriate, tracer results need to be modeled as mixtures of groundwater with different ages, as described in Step 6\u00a0of Figure 15<\/span><\/a>.<\/p>\n<\/div>\n

\n

\"\"<\/p>\n

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<\/span>Figure 16\u00a0\u2013\u00a0<\/strong>Graph showing initial tritium (3<\/sup>H(t<\/em>0<\/sub>), calculated from measured 3<\/sup>H plus 3<\/sup>H equivalent of tritiogenic helium from the sample) for groundwater samples collected in the streambed of a gaining stream in North Carolina (NC), USA, in July 2012 (modified from Gilmore, Genereux, Solomon, & Solder, 2016). Black dots are streambed samples with the initial 3<\/sup>H on the y\u2011axis and recharge year determined from tracer age using the 3<\/sup>H\/3<\/sup>He method on the x\u2011axis.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":7,"menu_order":18,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-100","chapter","type-chapter","status-publish","hentry"],"part":30,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters\/100","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/users\/7"}],"version-history":[{"count":8,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters\/100\/revisions"}],"predecessor-version":[{"id":409,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters\/100\/revisions\/409"}],"part":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/parts\/30"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters\/100\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/media?parent=100"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapter-type?post=100"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/contributor?post=100"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/license?post=100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}