{
    "home": "Home",
    "options": "Options",
    "help": "Help",
    "defaults": "Defaults",
    "clear": "Clear",
    "open": "Open",
    "save": "Save",
    "plot": "PLOT",
    "run": "RUN",
    "intro": "IsoplotR is an R package for geochronology that was designed to be free, flexible and future-proof. The package was named after (but is not based on) Ken Ludwig's popular Isoplot add-in to Microsoft Excel. It implements functions for U-Pb, Pb-Pb, Th-Pb, <sup>40</sup>Ar/<sup>39</sup>Ar, K-Ca, Rb-Sr, Sm-Nd, Lu-Hf, Re-Os, U-Th-He, fission track and U-series disequilibrium dating as well as detrital geochronology. <p></p>This website provides easy to use point-and-click access to IsoplotR's most commonly used functions (see the <a href='#' onclick='$.tutorial();'>TUTORIAL</a> for details). Alternatively, the same functions (and more) can also be accessed from the command-line through the IsoplotR package on <a href='https://cran.r-project.org/package=IsoplotR'>CRAN</a> and <a href='https://github.com/pvermees/IsoplotR/'>GitHub</a>.\t<p></p>IsoplotR is currently available in English, Chinese and Spanish (under construction). Translation errors can be fixed <a href='http://lgc.es.ucl.ac.uk/weblate/projects/isoplotrgui/#languages'>here</a>. If you would like to help translate the software into other languages, then please contact p.vermeesch[at]ucl.ac.uk. Bug reports and feature requests should be sent to the same email address.<p></p>",
    "tutorial_title": "Tutorial:",
    "tutorial_gui": "<a href='images/geochronometer.png'><img class='limitwidth thumbnail' src='images/geochronometer.png'></a><figcaption>1. <tt>IsoplotR</tt>'s graphical user interface (GUI) has four components: a top bar with selection menus for the various chronometers and plot devices, optional settings and documentation; an input table into which data can be pasted from spreadsheet applications; an output window displaying the graphical or numerical results; and a lower bar to import and export data and results.</figcaption>",
    "tutorial_alternative_formats": "<a href='images/formats_en.png'><img class='limitwidth thumbnail' src='images/formats_en.png'></a><figcaption>2. Alternative input formats are available through the <tt>Options</tt> menu.</figcaption>",
    "tutorial_contextual_help": "<a href='images/context_en.png'><img class='limitwidth thumbnail' src='images/context_en.png'></a><figcaption>3. Contextual help can be accessed by clicking on any text within the <tt>Options</tt> menu.</figcaption>",
    "tutorial_further_documentation": "<a href='images/help_en.png'><img class='limitwidth thumbnail' src='images/help_en.png'></a><figcaption>4. Further documentation is provided under the <tt>Help</tt> menu. This includes information about the input and output parameters, and a brief summary of the theoretical background with essential references.</figcaption>",
    "tutorial_saving": "<a href='images/json_en.png'><img class='limitwidth thumbnail' src='images/json_en.png'></a><figcaption>5. Data and settings can be saved in a <tt>.json</tt> database format for future use.</figcaption>",
    "ArAr_format_1": "1. Normal",
    "ArAr_format_2": "2. Inverse",
    "ArAr_format_3": "3. Three ratios",
    "help_Ar40Ar36": "Non-radiogenic <sup>40</sup>Ar/<sup>36</sup>Ar ratio:",
    "help_LambdaK40": "<sup>40</sup>K decay constant:",
    "help_ArAr_i2i": "Use isochron intercept as initial <sup>40</sup>Ar/<sup>36</sup>Ar-ratio?",
    "help_KCa_i2i": "Use isochron intercept as initial <sup>40</sup>Ca/<sup>44</sup>Ca-ratio?",
    "help_SmNd_i2i": "Use isochron intercept as initial <sup>143</sup>Nd/<sup>144</sup>Nd-ratio?",
    "help_RbSr_i2i": "Use isochron intercept as initial <sup>87</sup>Sr/<sup>86</sup>Sr-ratio?",
    "help_LuHf_i2i": "Use isochron intercept as initial <sup>176</sup>Hf/<sup>177</sup>Hf-ratio?",
    "help_ThU_i2i": "Use the isochron intercept to estimate the initial <sup>230</sup>Th/<sup>232</sup>Th-ratio?",
    "help_projerr": "Propagate uncertainty of initial daughter ratio?",
    "help_sigdig": "Significant digits:",
    "help_randomeffects": "Random effects model?",
    "help_outliers": "Reject outliers?",
    "help_ranked": "Rank the ages?",
    "help_UPb_age_type": "Type of U-Pb age:",
    "UPb_age_type_1": "1: 07/35 age",
    "UPb_age_type_2": "2: 06/38 age",
    "UPb_age_type_3": "3: 07/06 age",
    "UPb_age_type_4": "4: 7/6/8 age",
    "UPb_age_type_5": "5: concordia age",
    "UPb_age_type_6": "6: 08/32 age",
    "discordance_none": "none",
    "discordance_before_common_Pb": "before Pb(c) correction",
    "discordance_after_common_Pb": "after Pb(c) correction",
    "help_showdisc": "Show discordance:",
    "help_discoption": "Type:",
    "help_discfilter": "Type:",
    "discoption_t": "absolute age difference",
    "discoption_r": "relative age difference",
    "discoption_sk": "Stacey-Kramers cutoff",
    "discoption_a": "&perp; Aitchison distance",
    "discoption_c": "concordia distance",
    "discoption_p": "p-value",
    "help_mindisc": "Minimum discordance:",
    "help_maxdisc": "Maximum discordance:",
    "help_mint_average": "Minimum age limit:",
    "help_maxt_average": "Maximum age limit:",
    "help_alpha": "Probability cutoff:",
    "help_clabel": "Colour label:",
    "help_outlier_col": "Outlier colour:",
    "help_fill_alpha": "Fill colour opacity",
    "help_bg": "Fill colour:",
    "help_bg_solid": "Fill colour:",
    "ramp_from": "from: ",
    "ramp_to": "to: ",
    "help_cex": "Font magnification:",
    "help_col": "Outline colour:",
    "help_colmap": "Colour map:",
    "help_concordia_type": "Concordia type:",
    "conc_age_option_0": "no",
    "conc_age_option_1": "concordia",
    "conc_age_option_2": "discordia (model-1)",
    "conc_age_option_3": "discordia (model-2)",
    "conc_age_option_4": "discordia (model-3)",
    "no_anchor": "no",
    "common_anchor": "inherited component",
    "age_anchor": "age",
    "sk_anchor": "Stacey-Kramers",
    "help_maxx": "Maximum value:",
    "help_minx": "Minimum value:",
    "no_anchor": "no",
    "helium_anchor": "initial He",
    "intercept_anchor": "intercept",
    "slope_anchor": "slope",
    "help_mint_concordia": "Minimum t:",
    "help_maxt_concordia": "Maximum t:",
    "help_minx_concordia": "Minimum X:",
    "help_maxx_concordia": "Maximum X:",
    "help_miny_concordia": "Minimum Y:",
    "help_maxy_concordia": "Maximum Y:",
    "help_mineral_option": "Mineral:",
    "FT_ICP_absolute": "ICP (absolute)",
    "FT_ICP_zeta": "ICP (&zeta;)",
    "help_ellipsefill": "Ellipse fill colour:",
    "help_ramp_custom_ramp": "Custom colour ramp",
    "help_ramp_rainbow": "Rainbow",
    "help_ramp_rainbow_reversed": "Rainbow (reversed)",
    "help_ramp_rainbow_plus": "Rainbow Plus",
    "help_ramp_rainbow_plus_reversed": "Rainbow Plus (reversed)",
    "help_ramp_iridesce": "Iridesce",
    "help_ramp_iridesce_reversed": "Iridesce (reversed)",
    "help_ramp_red_blue_black": "Red-Blue-Black",
    "help_ramp_red_blue_black_reversed": "Red-Blue-Black (reversed)",
    "help_ramp_salmon": "Salmon",
    "help_ramp_salmon_reversed": "Salmon (reversed)",
    "help_ramp_heat": "Heat",
    "help_ramp_heat_reversed": "Heat (reversed)",
    "help_ramp_viridis": "Viridis",
    "help_ramp_viridis_reversed": "Viridis (reversed)",
    "help_ramp_rocket": "Rocket",
    "help_ramp_rocket_reversed": "Rocket (reversed)",
    "help_ramp_topo": "Topographic",
    "help_ramp_terrain": "Terrain",
    "help_ramp_cm": "Cyan-Magenta",
    "help_ellipsefill_alpha": "Ellipse fill opacity",
    "help_ellipsestroke": "Ellipse stroke colour:",
    "help_concordia_ticks": "Age ticks:",
    "help_evolution_tticks": "Age ticks:",
    "help_evolution_aticks": "Activity ticks:",
    "help_shownumbers": "Show sample numbers?",
    "help_headers_on": "Sample names on first row?",
    "help_hide_detritals": "Samples to omit:",
    "help_transform_evolution": "Plot as <sup>234</sup>U/<sup>238</sup>U vs. age?",
    "help_isochron_evolution": "Calculate isochron age?",
    "help_evolution_isochron_models": "Regression model:",
    "FT_EDM": "EDM",
    "help_FT_formats": "Method:",
    "help_max08or82": "Maximum <span class='show4ThU1 show4ThU2 hide4ThU3 hide4ThU4'><sup>230</sup>Th/<sup>238</sup>U</span><span class='hide4ThU1 hide4ThU2 show4ThU3 show4ThU4'><sup>238</sup>U/<sup>232</sup>Th</span>:",
    "help_min08or82": "Minimum <span class='show4ThU1 show4ThU2 hide4ThU3 hide4ThU4'><sup>230</sup>Th/<sup>238</sup>U</span><span class='hide4ThU1 hide4ThU2 show4ThU3 show4ThU4'><sup>238</sup>U/<sup>232</sup>Th</span>:",
    "help_max48or02": "Maximum <span class='show4ThU1 show4ThU2 hide4ThU3 hide4ThU4'><sup>234</sup>U/<sup>238</sup>U</span><span class='hide4ThU1 hide4ThU2 show4ThU3 show4ThU4'><sup>230</sup>Th/<sup>232</sup>Th</span>:",
    "help_min48or02": "Minimum <span class='show4ThU1 show4ThU2 hide4ThU3 hide4ThU4'><sup>234</sup>U/<sup>238</sup>U</span><span class='hide4ThU1 hide4ThU2 show4ThU3 show4ThU4'><sup>230</sup>Th/<sup>232</sup>Th</span>:",
    "help_maxt_evolution": "Maximum age:",
    "help_mint_evolution": "Minimum age:",
    "isochron_model_4": "4. Left/rightmost isochron",
    "isochron_model_3": "3. Maximum likelihood with overdispersion",
    "isochron_model_2": "2. Total least squares",
    "isochron_model_1": "1. Maximum likelihood",
    "help_wtype": "Age dispersion?",
    "help_wtype_regression": "Dispersed slope?",
    "apatite": "apatite",
    "zircon": "zircon",
    "help_U238U235": "<sup>238</sup>U/<sup>235</sup>U ratio:",
    "help_LambdaU238": "<sup>238</sup>U decay constant:",
    "help_LambdaFission": "<sup>238</sup>U fission decay constant:",
    "help_etchfact": "efficiency factor:",
    "help_tracklength": "equivalent isotropic track length:",
    "help_mindens": "mineral density:",
    "help_log": "Take logarithms?",
    "help_logratio": "Logratio plot?",
    "help_showbarycentre": "Show barycentric composition?",
    "help_helioplot_models": "Model:",
    "helioplot_model_1": "1. Weighted mean",
    "helioplot_model_2": "2. Unweighted mean",
    "helioplot_model_3": "3. Weighted mean with overdispersion",
    "help_minx_helioplot": "Minimum log[U/He] limit:",
    "help_maxx_helioplot": "Maximum log[U/He] limit:",
    "help_miny_helioplot": "Minimum log[Th/He] limit:",
    "help_maxy_helioplot": "Maximum log[Th/He] limit:",
    "help_fact": "Scaling factors:",
    "help_ierr": "Input errors:",
    "help_oerr": "Output errors:",
    "1se_abs": "1&sigma; (abs)",
    "2se_abs": "2&sigma; (abs)",
    "ci_abs": "ci (abs)",
    "1se_rel": "1&sigma; (%)",
    "2se_rel": "2&sigma; (%)",
    "ci_rel": "ci (%)",
    "help_conc_age_option": "Calculate",
    "help_anchor_option": "Anchored discordia line?",
    "help_isochron_anchor_option": "Anchored isochron line?",
    "help_regression_anchor_option": "Anchored regression line?",
    "help_ThU_y0option": "Report:",
    "help_UPb_y0option": "Report:",
    "help_ThU_isochron_types": "Type:",
    "help_UPb_isochron_types": "Type:",
    "help_joint": "3D regression?",
    "Rosholt_A": "1. <tt>0/2</tt> vs. <tt>8/2</tt> (Rosholt A)",
    "Rosholt_B": "3. <tt>4/2</tt> vs. <tt>8/2</tt> (Rosholt B)",
    "Osmond_A": "2. <tt>0/8</tt> vs. <tt>2/8</tt> (Osmond A)",
    "Osmond_B": "4. <tt>4/8</tt> vs. <tt>2/8</tt> (Osmond B)",
    "UPb_isochron_type_1": "1. <tt>(04 or 08c)/06</tt> vs. <tt>38/06</tt>",
    "UPb_isochron_type_2": "2. <tt>(04 or 08c)/07</tt> vs. <tt>35/07</tt>",
    "UPb_isochron_type_3": "3. <tt>06c/08</tt> vs. <tt>32/08</tt>",
    "UPb_isochron_type_4": "4. <tt>07c/08</tt> vs. <tt>32/08</tt>",
    "help_isochron_models": "Model:",
    "help_regression_models": "Model:",
    "help_taxis": "Label the x-axis by geologic time?",
    "help_PbPb_growth": "Add Stacey-Kramers Pb-Pb growth curve?",
    "help_isochron_minx": "Minimum X:",
    "help_isochron_maxx": "Maximum X:",
    "help_isochron_miny": "Minimum Y:",
    "help_isochron_maxy": "Maximum Y:",
    "help_binwidth": "Histogram binwidth:",
    "help_bandwidth": "Kernel bandwidth:",
    "help_ncol": "Number of columns:",
    "help_Ca40Ca42": "<sup>40</sup>Ca/<sup>42</sup>Ca ratio:",
    "help_Ca40Ca43": "<sup>40</sup>Ca/<sup>43</sup>Ca ratio:",
    "help_Ca40Ca44": "<sup>40</sup>Ca/<sup>44</sup>Ca ratio:",
    "help_Ca40Ca48": "<sup>40</sup>Ca/<sup>48</sup>Ca ratio:",
    "help_KCa_sister": "Sister:",
    "KCa_format_3": "3. Three ratios",
    "KCa_format_2": "2. Inverse",
    "KCa_format_1": "1. Normal",
    "help_showhist": "Show histogram?",
    "help_adaptive": "Adaptive KDE?",
    "help_samebandwidth": "Same bandwidth for all samples?",
    "help_normalise": "Normalise area under the KDEs?",
    "help_Lu176Lu175": "<sup>176</sup>Lu/<sup>175</sup>Lu ratio:",
    "help_Hf174Hf177": "<sup>174</sup>Hf/<sup>177</sup>Hf ratio:",
    "help_Hf176Hf177": "<sup>176</sup>Hf/<sup>177</sup>Hf ratio:",
    "help_Hf178Hf177": "<sup>178</sup>Hf/<sup>177</sup>Hf ratio:",
    "help_Hf179Hf177": "<sup>179</sup>Hf/<sup>177</sup>Hf ratio:",
    "help_Hf180Hf177": "<sup>180</sup>Hf/<sup>177</sup>Hf ratio:",
    "help_LambdaLu176": "<sup>176</sup>Lu decay constant:",
    "help_classical": "Classical MDS?",
    "help_diss": "Dissimilarity measure",
    "help_shepard": "Shepard plot?",
    "help_nnlines": "Add nearest neighbour lines?",
    "help_rug": "Add rug plot?",
    "help_nmodes": "Label",
    "nmodes_all": "all",
    "modes": "modes",
    "help_pcex": "Plot symbol magnification:",
    "help_pos": "Label position:",
    "PbPb_format_1": "1. Normal",
    "PbPb_format_2": "2. Inverse",
    "PbPb_format_3": "3. Three ratios",
    "help_common_Pb_option": "Common Pb correction:",
    "help_concordia_projection_option": "Concordia projection:",
    "common_Pb_correction_none": "none",
    "common_Pb_correction_nominal": "nominal",
    "common_Pb_correction_isochron": "isochron",
    "help_LambdaU235": "<sup>235</sup>U decay constant:",
    "help_Pb206Pb204": "Initial <sup>206</sup>Pb/<sup>204</sup>Pb:",
    "help_Pb207Pb204": "Initial <sup>207</sup>Pb/<sup>204</sup>Pb:",
    "help_transformation": "Transformation:",
    "radial_log": "logarithmic",
    "radial_lin": "linear",
    "radial_arcsin": "arcsin",
    "radial_sqrt": "sqrt",
    "help_mixtures": "Finite mixtures:",
    "peakfit_none": "0 (none)",
    "peakfit_auto": "auto",
    "peakfit_min": "minimum",
    "help_np4": "4 parameters",
    "help_discordance_filter": "Discordance filter:",
    "help_verticals": "Draw vertical lines at steps?",
    "help_mint_radial": "Minimum value:",
    "help_z0": "Central value:",
    "help_maxt_radial": "Maximum value:",
    "help_xlim_radial": "Maximum precision:",
    "PD_format_1": "1. Normal",
    "PD_format_2": "2. Inverse",
    "PD_format_3": "3. Concentrations",
    "help_Rb85Rb87": "<sup>85</sup>Rb/<sup>87</sup>Rb ratio:",
    "help_Sr84Sr86": "<sup>84</sup>Sr/<sup>86</sup>Sr ratio:",
    "help_Sr87Sr86": "<sup>87</sup>Sr/<sup>86</sup>Sr ratio:",
    "help_Sr88Sr86": "<sup>88</sup>Sr/<sup>86</sup>Sr ratio",
    "help_LambdaRb87": "<sup>87</sup>Rb decay constant:",
    "help_Re185Re187": "<sup>185</sup>Re/<sup>187</sup>Re ratio:",
    "help_Os184Os188": "<sup>184</sup>Os/<sup>188</sup>Os ratio:",
    "help_Os186Os188": "<sup>186</sup>Os/<sup>188</sup>Os ratio:",
    "help_Os187Os188": "<sup>187</sup>Os/<sup>188</sup>Os ratio:",
    "help_Os189Os188": "<sup>189</sup>Os/<sup>188</sup>Os ratio:",
    "help_Os190Os188": "<sup>190</sup>Os/<sup>188</sup>Os ratio:",
    "help_Os192Os188": "<sup>192</sup>Os/<sup>188</sup>Os ratio:",
    "help_LambdaRe187": "<sup>187</sup>Re decay constant:",
    "help_Sm144Sm152": "<sup>144</sup>Sm/<sup>152</sup>Sm ratio:",
    "help_Sm147Sm152": "<sup>147</sup>Sm/<sup>152</sup>Sm ratio:",
    "help_Sm148Sm152": "<sup>148</sup>Sm/<sup>152</sup>Sm ratio:",
    "help_Sm149Sm152": "<sup>149</sup>Sm/<sup>152</sup>Sm ratio:",
    "help_Sm150Sm152": "<sup>150</sup>Sm/<sup>152</sup>Sm ratio:",
    "help_Sm154Sm152": "<sup>154</sup>Sm/<sup>152</sup>Sm ratio:",
    "help_Nd142Nd144": "<sup>142</sup>Nd/<sup>144</sup>Nd ratio:",
    "help_Nd143Nd144": "<sup>143</sup>Nd/<sup>144</sup>Nd ratio:",
    "help_Nd145Nd144": "<sup>145</sup>Nd/<sup>144</sup>Nd ratio:",
    "help_Nd146Nd144": "<sup>146</sup>Nd/<sup>144</sup>Nd ratio:",
    "help_Nd148Nd144": "<sup>148</sup>Nd/<sup>144</sup>Nd ratio:",
    "help_Nd150Nd144": "<sup>150</sup>Nd/<sup>144</sup>Nd ratio:",
    "help_LambdaSm147": "<sup>147</sup>Sm decay constant:",
    "help_plateau": "Extract plateau?",
    "help_Th0i": "initial <sup>230</sup>Th correction:",
    "help_U8Th2": "whole rock <sup>238</sup>U/<sup>232</sup>Th:",
    "help_LambdaU234": "<sup>234</sup>U decay constant:",
    "help_LambdaTh230": "<sup>230</sup>Th decay constant:",
    "detrital_correction_isochron": "isochron",
    "detrital_correction_assumed": "assumed",
    "detrital_correction_measured": "measured",
    "diseq_none": "none",
    "help_U48_UPb": "<sup>234</sup>U disequilibrium:",
    "help_diseq": "Apply disequilibrium correction?",
    "diseq_initial": "initial",
    "diseq_measured": "measured",
    "help_ThU_UPb": "<sup>230</sup>Th disequilibrium:",
    "diseq_magma": "magma",
    "help_PaU_UPb": "<sup>231</sup>Pa disequilibrium:",
    "help_LambdaTh232": "<sup>232</sup>Th decay constant:",
    "help_LambdaRa226": "<sup>226</sup>Ra decay constant:",
    "help_LambdaPa231": "<sup>231</sup>Pa decay constant:",
    "help_Pb207Pb206": "Initial <sup>207</sup>Pb/<sup>206</sup>Pb ratio:",
    "help_Pb206Pb208": "Initial <sup>206</sup>Pb/<sup>208</sup>Pb ratio:",
    "help_Pb207Pb208": "Initial <sup>207</sup>Pb/<sup>208</sup>Pb ratio:",
    "help_RaU_UPb": "<sup>226</sup>Ra disequilibrium:",
    "help_ReOs_i2i": "Use isochron intercept as initial <sup>187</sup>Os/<sup>188</sup>Os-ratio?",
    "ages": "The <span class='hidden show4PbPb'> Pb-Pb </span> <span class='hidden show4ArAr'> Ar-Ar </span> <span class='hidden show4RbSr'> Rb-Sr </span> <span class='hidden show4SmNd'> Sm-Nd </span> <span class='hidden show4ReOs'> Re-Os </span> <span class='hidden show4LuHf'> Lu-Hf </span> <span class='hidden show4UThHe'> U-Th-He </span> <span class='hidden show4fissiontracks'> fission track </span> <span class='hidden show4ThU1 show4ThU2'> <sup>230</sup>Th-<sup>234</sup>U-<sup>238</sup>U</span> <span class='hidden show4ThU3 show4ThU4'> <sup>230</sup>Th-<sup>238</sup>U</span> ages.",
    "ages_75": "The <sup>207</sup>Pb/<sup>235</sup>U-ages.",
    "UPb_75": "Measured <sup>207</sup>Pb/<sup>235</sup>U-ratios.",
    "UPb_err_75": "Analytical uncertainty of the <sup>207</sup>Pb/<sup>235</sup>U-ratios",
    "UPb_68": "Measured <sup>206</sup>Pb/<sup>238</sup>U-ratios.",
    "UPb_err_68": "Analytical uncertainty of the <sup>206</sup>Pb/<sup>238</sup>U-ratios",
    "UPb_86": "Measured <sup>238</sup>U/<sup>206</sup>Pb-ratios.",
    "UPb_err_86": "Analytical uncertainty of the <sup>238</sup>U/<sup>206</sup>Pb-ratios",
    "UPb_76": "Measured <sup>207</sup>Pb/<sup>206</sup>Pb-ratios.",
    "UPb_err_76": "Analytical uncertainty of the <sup>207</sup>Pb/<sup>206</sup>Pb-ratios",
    "UPb_rho_7568": "Error correlation between the <sup>207</sup>Pb/<sup>235</sup>U- and <sup>206</sup>Pb/<sup>238</sup>U-ratios.",
    "UPb_rho_8676": "Error correlation between the <sup>238</sup>U/<sup>206</sup>Pb- and <sup>207</sup>Pb/<sup>206</sup>Pb-ratios (optional).",
    "UPb_48": "Measured <sup>204</sup>Pb/<sup>238</sup>U-ratios.",
    "UPb_err_48": "Analytical uncertainty of the <sup>204</sup>Pb/<sup>238</sup>U-ratios",
    "UPb_57": "Measured <sup>235</sup>U/<sup>207</sup>Pb-ratios.",
    "UPb_err_57": "Analytical uncertainty of the <sup>235</sup>U/<sup>207</sup>Pb-ratios",
    "UPb_47": "Measured <sup>204</sup>Pb/<sup>207</sup>Pb-ratios.",
    "UPb_err_47": "Analytical uncertainty of the <sup>204</sup>Pb/<sup>207</sup>Pb-ratios",
    "UPb_46": "Measured <sup>204</sup>Pb/<sup>206</sup>Pb-ratios.",
    "UPb_err_46": "Analytical uncertainty of the <sup>204</sup>Pb/<sup>206</sup>Pb-ratios",
    "UPb_rhoXZ_8646": "Error correlation between the <sup>238</sup>U/<sup>206</sup>Pb- and <sup>204</sup>Pb/<sup>206</sup>Pb-ratios.",
    "UPb_rhoYZ_8676": "Error correlation between the <sup>238</sup>U/<sup>206</sup>Pb- and <sup>207</sup>Pb/<sup>206</sup>Pb-ratios.",
    "UPb_rhoYZ_6848": "Error correlation between the <sup>206</sup>Pb/<sup>238</sup>U- and <sup>204</sup>Pb/<sup>238</sup>U-ratios.",
    "UPb_rhoXZ_7548": "Error correlation between the <sup>207</sup>Pb/<sup>235</sup>U- and <sup>204</sup>Pb/<sup>238</sup>U-ratios.",
    "UPb_rhoXY_7568": "Error correlation between the <sup>207</sup>Pb/<sup>235</sup>U- and <sup>206</sup>Pb/<sup>238</sup>U-ratios.",
    "UPb_rhoYZ_7646": "Error correlation between the <sup>207</sup>Pb/<sup>206</sup>Pb- and <sup>204</sup>Pb/<sup>206</sup>Pb-ratios.",
    "UPb_82": "Measured <sup>208</sup>Pb/<sup>232</sup>Th-ratios.",
    "UPb_err_82": "Analytical uncertainty of the <sup>208</sup>Pb/<sup>232</sup>Th-ratios",
    "UPb_0806": "Measured <sup>208</sup>Pb/<sup>206</sup>Pb-ratios.",
    "UPb_err_0806": "Analytical uncertainty of the <sup>208</sup>Pb/<sup>206</sup>Pb-ratios",
    "UPb_0807": "Measured <sup>208</sup>Pb/<sup>207</sup>Pb-ratios.",
    "UPb_err_0807": "Analytical uncertainty of the <sup>208</sup>Pb/<sup>207</sup>Pb-ratios",
    "UPb_3238": "Measured <sup>232</sup>Th/<sup>238</sup>U-ratios (optional).",
    "UPb_err_3238": "Analytical uncertainty of the <sup>232</sup>Th/<sup>238</sup>U-ratios",
    "UPb_rhoWX_7568": "Error correlation between the <sup>207</sup>Pb/<sup>235</sup>U- and <sup>206</sup>Pb/<sup>238</sup>U-ratios.",
    "UPb_rhoWY_7582": "Error correlation between the <sup>207</sup>Pb/<sup>235</sup>U- and <sup>208</sup>Pb/<sup>232</sup>Th-ratios.",
    "UPb_rhoWZ_753238": "Error correlation between the <sup>207</sup>Pb/<sup>235</sup>U- and <sup>232</sup>Th/<sup>238</sup>U-ratios.",
    "UPb_rhoXY_680832": "Error correlation between the <sup>206</sup>Pb/<sup>238</sup>U- and <sup>208</sup>Pb/<sup>232</sup>Th-ratios.",
    "UPb_rhoXZ_683238": "Error correlation between the <sup>206</sup>Pb/<sup>238</sup>U- and <sup>232</sup>Th/<sup>238</sup>U-ratios.",
    "UPb_rhoYZ_08323238": "Error correlation between the <sup>208</sup>Pb/<sup>232</sup>Th- and <sup>232</sup>Th/<sup>238</sup>U-ratios.",
    "UPb_rhoWX_8676": "Error correlation between the <sup>238</sup>U/<sup>206</sup>Pb- and <sup>207</sup>Pb/<sup>206</sup>Pb-ratios (optional).",
    "UPb_rhoWY_38060806": "Error correlation between the <sup>238</sup>U/<sup>206</sup>Pb- and <sup>208</sup>Pb/<sup>206</sup>Pb-ratios (optional).",
    "UPb_rhoWZ_38063238": "Error correlation between the <sup>238</sup>U/<sup>206</sup>Pb- and <sup>232</sup>Th/<sup>238</sup>U-ratios (optional).",
    "UPb_rhoXY_7686": "Error correlation between the <sup>207</sup>Pb/<sup>206</sup>Pb- and <sup>208</sup>Pb/<sup>206</sup>Pb-ratios (optional).",
    "UPb_rhoXZ_763238": "Error correlation between the <sup>207</sup>Pb/<sup>206</sup>Pb- and <sup>232</sup>Th/<sup>238</sup>U-ratios (optional).",
    "UPb_rhoYZ_08063238": "Error correlation between the <sup>208</sup>Pb/<sup>206</sup>Pb- and <sup>232</sup>Th/<sup>238</sup>U-ratios (optional).",
    "UPb_rhoXY_38060406": "Error correlation between the <sup>238</sup>U/<sup>206</sup>Pb- and <sup>204</sup>Pb/<sup>206</sup>Pb-ratios (optional).",
    "UPb_rhoXY_35070407": "Error correlation between the <sup>235</sup>U/<sup>207</sup>Pb- and <sup>204</sup>Pb/<sup>207</sup>Pb-ratios (optional).",
    "UPb_rhoXY_38060806": "Error correlation between the <sup>238</sup>U/<sup>206</sup>Pb- and <sup>208</sup>Pb/<sup>206</sup>Pb-ratios (optional).",
    "UPb_rhoXZ_38063238": "Error correlation between the <sup>238</sup>U/<sup>206</sup>Pb- and <sup>232</sup>Th/<sup>238</sup>U-ratios (optional).",
    "UPb_rhoYZ_08063238": "Error correlation between the <sup>208</sup>Pb/<sup>206</sup>Pb- and <sup>232</sup>Th/<sup>238</sup>U-ratios (optional).",
    "UPb_rhoXY_35070807": "Error correlation between the <sup>235</sup>U/<sup>207</sup>Pb- and <sup>208</sup>Pb/<sup>207</sup>Pb-ratios (optional).",
    "UPb_rhoXZ_35073238": "Error correlation between the <sup>235</sup>U/<sup>207</sup>Pb- and <sup>232</sup>Th/<sup>238</sup>U-ratios (optional).",
    "UPb_rhoYZ_08073238": "Error correlation between the <sup>208</sup>Pb/<sup>207</sup>Pb- and <sup>232</sup>Th/<sup>238</sup>U-ratios (optional).",
    "UPb_C": "Optional variable to be used as fill colours in concordia and radial plots.",
    "UPb_redundancy": "If <tt>rXY</tt>, <tt>rXZ</tt> or <tt>rYZ</tt> are omitted, then their value will be inferred from the redundancy between the three sets of uncertainties (<tt>err[X]</tt>, <tt>err[Y]</tt> and <tt>err[Z]</tt>). This inference assumes that these errors are based on the same number of data points. If some data has been rejected from one ratio but not another, because of isobaric interferences, instrument issues, outlier rejection, or any other reason, then this method will not work.",
    "UPb_rhoXY_8676": "Error correlation between the <sup>238</sup>U/<sup>206</sup>Pb- and <sup>207</sup>Pb/<sup>206</sup>Pb-ratios.",
    "IsoplotR_version": "This is IsoplotR version",
    "reference": "Citable reference:",
    "ages_err": "The estimated uncertainty of the <span class='hidden show4PbPb'> Pb-Pb </span> <span class='hidden show4ArAr'> Ar-Ar </span> <span class='hidden show4RbSr'> Rb-Sr </span> <span class='hidden show4SmNd'> Sm-Nd </span> <span class='hidden show4ReOs'> Re-Os </span> <span class='hidden show4LuHf'> Lu-Hf </span> <span class='hidden show4UThHe'> U-Th-He </span> <span class='hidden show4fissiontracks'> fission track </span> <span class='hidden show4ThU1 show4ThU2'> <sup>230</sup>Th-<sup>234</sup>U-<sup>238</sup>U</span> <span class='hidden show4ThU3 show4ThU4'> <sup>230</sup>Th-<sup>238</sup>U</span> ages",
    "ages_err_75": "The estimated uncertainty of the <sup>207</sup>Pb/<sup>235</sup>U-ages",
    "ages_68": "The <sup>206</sup>Pb/<sup>238</sup>U-ages.",
    "ages_err_68": "The estimated uncertainty of the <sup>206</sup>Pb/<sup>238</sup>U-ages",
    "ages_76": "The <sup>207</sup>Pb/<sup>206</sup>Pb-ages.",
    "ages_err_76": "The estimated uncertainty of the <sup>207</sup>Pb/<sup>206</sup>Pb-ages",
    "ages_82": "The <sup>208</sup>Pb/<sup>232</sup>Th-ages.",
    "ages_err_82": "The estimated uncertainty of the <sup>208</sup>Pb/<sup>232</sup>Th-ages",
    "ages_tconc": "The single-grain concordia age. This is the maximum likelihood intersection between the (Wetherill) concordia line and the (<sup>207</sup>Pb/<sup>235</sup>U-<sup>206</sup>Pb/<sup>238</sup>U) error ellipse.",
    "ages_err_tconc": "The estimated uncertainty of the single-grain concordia age",
    "ages_pconc": "The p-value for concordance. Note: it would be unwise to use the p-value value as a concordance filter. Doing so would 'punish' high precision measurements, which are more likely to fail the chi-square test than low precision measurements. The latter would therefore be 'rewarded' by such a criterion.",
    "ages_disc": "Depending on the chosen discordance option, either the absolute age difference (Ma) between the <sup>206</sup>Pb/<sup>238</sup>U and <sup>207</sup>Pb/<sup>206</sup>Pb ages; the relative age difference (%) between the <sup>206</sup>Pb/<sup>238</sup>U and <sup>207</sup>Pb/<sup>206</sup>Pb ages; the percentage of common Pb measured along a mixing line connecting the measured composition and the Stacey-Kramers mantle composition in Tera-Wasserburg space; the logratio distance (%) measured along a perpendicular line connecting Tera-Wasserburg concordia and the measured composition; or the logratio distance (%) measured along a line connecting the measured composition and the corresponding single grain concordia age composition.",
    "ages_err_48_0": "Estimated uncertainty of the initial <sup>234</sup>U/<sup>238</sup>U-ratio",
    "ages_corr_t_48_0": "Correlation coefficient between the <sup>230</sup>Th-<sup>234</sup>U-<sup>238</sup>U age and the initial <sup>234</sup>U/<sup>238</sup>U-ratio uncertainties.",
    "ArAr_J": "Irradiation constant and its analytical uncertainty",
    "ArAr_39": "Amount of <sup>39</sup>Ar in each heating step, which will be normalised to form the X-axis of the age spectrum (optional).",
    "ArAr_3940": "Measured <sup>39</sup>Ar/<sup>40</sup>Ar-ratios.",
    "ArAr_err_3940": "Analytical uncertainty of the <sup>39</sup>Ar/<sup>40</sup>Ar-ratios",
    "ArAr_3640": "Measured <sup>36</sup>Ar/<sup>40</sup>Ar-ratios.",
    "ArAr_err_3640": "Analytical uncertainty of the <sup>36</sup>Ar/<sup>40</sup>Ar-ratios",
    "ArAr_3936": "Measured <sup>39</sup>Ar/<sup>36</sup>Ar-ratios.",
    "ArAr_err_3936": "Analytical uncertainty of the <sup>39</sup>Ar/<sup>36</sup>Ar-ratios",
    "ArAr_4036": "Measured <sup>40</sup>Ar/<sup>36</sup>Ar-ratios.",
    "ArAr_err_4036": "Analytical uncertainty of the <sup>40</sup>Ar/<sup>36</sup>Ar-ratios",
    "ArAr_rho_0696": "Error correlation between the <sup>40</sup>Ar/<sup>36</sup>Ar- and <sup>39</sup>Ar/<sup>36</sup>Ar-ratios.",
    "ArAr_rho_6090": "Error correlation between the <sup>36</sup>Ar/<sup>40</sup>Ar- and <sup>39</sup>Ar/<sup>40</sup>Ar-ratios (optional).",
    "ArAr_redundancy": "<tt>IsoplotR</tt> uses the redundancy of the three ratios to calculate the correlation between their respective analytical uncertainties.",
    "average_intro": "Let t = {t<sub>1</sub>, ..., t<sub>n</sub>} be a set of n age estimates determined on different aliquots of the same sample, and let {s[t<sub>1</sub>], ..., s[t<sub>n</sub>]} be their analytical uncertainties (standard errors). <tt>IsoplotR</tt> implements two ways to compute the average of these data:  <ol> <li> A random effects model with two sources of variance:<p>log[t<sub>i</sub>] ~ <i>N</i>( log[&mu;], &sigma;<sup>2</sup> = (s[t<sub>i</sub>]/t<sub>i</sub>)<sup>2</sup> + &omega;<sup>2</sup> ) <span class='alignright'>(eq. 1a)</span></p>where &mu; is the mean, &sigma;<sup>2</sup> is the total variance and &omega; is the 'overdispersion'. Equation 1a can be solved for &mu; and &omega; by the method of maximum likelihood. </li><li> A weighted mean algorithm that assumes that any dispersion between the different aliquots is only due to the analytical uncertainty: <p>&mu; = &Sigma;(t<sub>i</sub>/s[t<sub>i</sub>]<sup>2</sup>)/&Sigma;(1/s[t<sub>i</sub>]<sup>2</sup>)<span class='alignright'>(eq. 1b)</span></p></li></ol><tt>IsoplotR</tt> uses a modified version of Chauvenet's criterion for outlier detection:  <ol> <li>Compute the error-weighted mean of the n age determinations t<sub>i</sub> using their analytical uncertainties s[t<sub>i</sub>] using one of the aforementioned two approaches. </li><li> For each t<sub>i</sub>, compute the probability p<sub>i</sub> that that |t-&mu;|>|t<sub>i</sub>-&mu;| under eq. 1a for the random effects model, or under <p> t ~ <i>N</i>(&mu;,&sigma;<sup>2</sup>=s[t<sub>i</sub>]<sup>2</sup>MSWD) <span class='alignright'>(eq. 2)</span></p><p>if the ordinary weighted mean is used.</p></li> <li> Let p<sub>j</sub> &equiv; min(p<sub>1</sub>,&hellip;,p<sub>n</sub>). If p<sub>j</sub><0.05/n, then reject the j<sup>th</sup> date, reduce n by one (i.e., n &rarr; (n-1) and repeat steps 1 through 3 until the surviving dates pass the third step.</li> </ol>If the analytical uncertainties are small compared to the scatter between the dates, then this generalised algorithm reduces to the conventional Chauvenet criterion. If the analytical uncertainties are large and the data do not exhibit any overdispersion, then the heuristic outlier detection method is equivalent to Ludwig (2003)'s 'modified 2-sigma' method.",
    "average_caveat": "An asterisk is added to the plot title if the initial daughter correction is done by isochron regression, to mark the circularity of using an isochron to compute a weighted mean. Also note that the uncertainty budget of the weighted mean does not include the uncertainty of the initial daughter correction (if any). This uncertainty is neither purely systematic nor purely random and cannot easily be propagated with conventional geochronological data processing algorithms. In this case the isochron errors are more meaningful, and the weighted mean plot should just be used to inspect the residuals of the data around the isochron.",
    "average_mu": "the weighted mean age.",
    "mu_err": "the width of the confidence interval for &mu; (at <span class=\"hidden show4oerr1 show4oerr2 show4oerr3\">absolute</span><span class=\"hidden show4oerr4 show4oerr5 show4oerr6\">relative</span> <span class=\"hidden show4oerr1 show4oerr4\">1&sigma;</span><span class=\"hidden show4oerr2 show4oerr5\">2&sigma;</span><span class=\"hidden show4oerr3 show4oerr6\">100(1-&alpha;)%</span> confidence). This is also shown as a grey band on the plot. The uncertainty associated with the random errors is shown in dark grey, whereas the systematic uncertainties (i.e. J-factor and decay constant) are shown in light grey.",
    "mu_err_disp": "the confidence interval for &mu; with overdispersion, calculated as y = x &radic;MSWD (only reported if the p-value of the chi-square test is < &alpha;, not reported for random effects models).",
    "average_mswd_x": "the Mean Square of the Weighted Deviates (MSWD) for age homogeneity. MSWD values >> 1 indicate that the ages are overdispersed with respect to the stated analytical uncertainties.",
    "average_mswd_y": "the chi-squared p-value for the age homogeneity test. p-values << 0.05 indicate that the ages are overdispersed with respect to the stated analytical uncertainties.",
    "average_omega": "the standard deviation of the true ages after removal of the analytical uncertainties. The dispersion is significantly greater than zero if the p-value of the chi-square test is < &alpha;. The 100(1-&alpha;)% Normal confidence region for the dispersion (e.g., 1.96 &times; &omega; if &alpha; = 0.05) is shown as a set of dashed lines.",
    "output": "Output:",
    "CAD_intro": "Empirical cumulative distribution functions or cumulative age distributions CADs (Vermeesch, 2007) are the most straightforward way to visualise the probability distribution of multiple dates. A CAD is a step function that sets out the rank order of the dates against their numerical value:<p></p>CAD(t) = &sum;<sub>i</sub> 1(t &lt; t<sub>i</sub>)/n <span class='alignright'>(eq. 1)</span> <p></p>where 1(*) = 1 if * is true and 1(*) = 0 if * is false. CADs have two desirable properties. First, they do not require any pre-treatment or smoothing of the data. This is not the case for histograms or kernel density estimates. Second, it is easy to superimpose several CADs on the same plot. This facilitates the intercomparison of multiple samples. The interpretation of CADs is straightforward but not very intuitive. The prominence of individual age components is proportional to the steepness of the CAD. This is different from probability density estimates such as histograms, in which such components stand out as peaks. It is arguably easier to identify peaks than inflection points and this probably why CADs are not as widely used as probability density estimates. But the ease of interpretation of density estimates comes at a cost, as they require smoothing and cannot as easily be combined as CADs.",
    "concordia_intro": "The concordia diagram is a graphical means of assessing the internal consistency of U-Pb data. It sets out the measured <sup>206</sup>Pb/<sup>238</sup>U- and <sup>207</sup>Pb/<sup>235</sup>U-ratios against each other ('Wetherill' diagram) or, equivalently, the <sup>207</sup>Pb/<sup>206</sup>Pb- and <sup>238</sup>U/<sup>206</sup>Pb-ratios ('Tera-Wasserburg' diagram). The space of concordant isotopic compositions is marked by a curve, the 'concordia line'. Isotopic ratio measurements are shown as confidence ellipses (at <span class=\"hidden show4oerr1 show4oerr4\">1&sigma;</span><span class=\"hidden show4oerr2 show4oerr5\">2&sigma;</span><span class=\"hidden show4oerr3 show4oerr6\">100(1-&alpha;)%</span> confidence). Concordant samples plot near to, or overlap with, the concordia line. They represent the pinnacle of geochronological robustness. Samples that plot away from the concordia line but are aligned along a linear trend form an isochron (or 'discordia' line) that can be used to infer the composition of the non-radiogenic ('common') lead or to constrain the timing of prior lead loss.",
    "conc_t": "the Maximum Likelihood estimate of the age using the algorithm of Ludwig (1998).",
    "conc_mswd_u": "the Mean Square of the Weighted Deviates (MSWD) for concordance.",
    "conc_mswd_v": "the MSWD for equivalence.",
    "conc_mswd_w": "the MSWD for concordance + equivalence.",
    "conc_mswd_x": "the chi-squared p-value for concordance.",
    "conc_mswd_y": "the chi-squared p-value for equivalence.",
    "conc_mswd_z": "the chi-squared p-value for concordance + equivalence.",
    "lowint": "lower intercept",
    "upint": "upper intercept",
    "disc_t": "the <span class='hidden show4model1 hide4model2 show4model3'>Maximum Likelihood</span> <span class='hidden hide4model1 show4model2 hide4model3'>least squares</span> estimate of the age or initial Pb-ratio <span class='hidden show4model1 hide4model2 show4model3'> using the algorithm of Ludwig (1998)</span>.",
    "disc_u": "the Mean Square of the Weighted Deviates (MSWD) for the isochron fit.",
    "disc_v": "the chi-squared p-value for the isochron fit.",
    "disc_omega": "the estimated standard deviation of the assumedly Gaussian geological scatter of the true intercept ages.",
    "detritals_info": "The detrital ages arranged in columns which may have unequal lengths. Sample names may be provided in the first row. If they are omitted, then please untick the 'Sample names on first row?' box in the Options menu.",
    "evolution_x": "the initial <span class='hidden show4ThU1 show4ThU2'>(<sup>234</sup>U/<sup>238</sup>U)</span> <span class='hidden show4ThU3 show4ThU4'> (<sup>230</sup>Th/<sup>232</sup>Th)</span>-ratio.",
    "evolution_info_ThU12": "The Th-U evolution diagram is a scatter plot that sets out the <sup>234</sup>U/<sup>238</sup>U-activity ratios against the <sup>230</sup>Th/<sup>238</sup>U-activity ratios as error ellipses (drawn at 100[1-&alpha;]% confidence level), and displays the initial <sup>234</sup>U/<sup>238</sup>U-activity ratios and ages as a set of intersecting lines. The Th-U evolution diagram has a similar and purpose and appearance as the U-Pb concordia diagram, which also displays compositions and dates simultaneously. An alternative way of doing so is to plot the <sup>234</sup>U/<sup>238</sup>U-ratios against the <sup>230</sup>Th/<sup>234</sup>U-<sup>238</sup>U-ages. In both types of evolution diagrams, <tt>IsoplotR</tt> provides the option to project the raw measurements along the best fitting isochron line and thereby remove the detrital <sup>230</sup>Th-component. This procedure allows a visual assessment of the degree of homogeneity within a dataset, as is quantified by the MSWD.",
    "evolution_info_ThU34": "The Th-U evolution diagram has a similar and purpose and appearance as the U-Pb concordia diagram, which also displays compositions and dates simultaneously. For igneous datasets, in which <sup>234</sup>U and <sup>238</sup>U are in secular equilibrium, <tt>IsoplotR</tt> produces an (Osmond-style) isochron plot that is decorated with a fanning set of isochrone lines.",
    "evolution_t": "the isochron age.",
    "evolution_mswd_x": "the Mean Square of the Weighted Deviates (MSWD) for the linear fit. MSWD values >> 1 indicate that the ages are overdispersed with respect to the stated analytical uncertainties.",
    "evolution_mswd_y": "the chi-squared p-value for the linear fit. p-values << 0.05 indicate that the ages are overdispersed with respect to the stated analytical uncertainties.",
    "evolution_omega": "the excess ('geological') dispersion of the data, i.e. the standard deviation of the assumedly Gaussian distribution that describes the true age or authigenic composition.",
    "FT_tstand": "Standard age and its standard error.",
    "FT_zeta": "Zeta calibration constant and its analytical uncertainty",
    "FT_rho": "Induced track density in a co-irradiated dosimeter glass and its analytical uncertainty",
    "FT_spot_size": "The diameter of the LA-ICP-MS laser spot, in &mu;m",
    "FT_Ns": "Number of spontaneous tracks",
    "FT_Ni": "Number of induced tracks",
    "FT_A": "Counting area, in &mu;m<sup>2</sup>",
    "FT_U": "Uranium concentration (in ppm, for both the &zeta;-calibration and absolute methods), or U/Ca-ratios (for the &zeta;-calibration method only) measured by LA-ICP-MS",
    "FT_err_U_a": "Analytical uncertainty",
    "FT_err_U_b": "of U1, U2, ... . These should <i>exclude</i> any external sources of uncertainty for the calculation of radial plots or weighted means.",
    "FT_C": "Optional variable to be used as fill colours in radial plots.",
    "helioplot_intro": "The space of all possible U-Th-He compositions fits within the constraints of a ternary diagram or 'helioplot' (Vermeesch, 2008, 2010). If Sm is included as well, then this expands to a three-dimensional tetrahaedral space (Vermeesch, 2008). Conventional statistical analysis of data that fit within these constrained spaces is fraught with theoretical and practical problems that can be solved by applying a simple logratio transformation (Aitchison, 1982, 1986)<p></p>u &equiv; ln[U/He], &nbsp; v &equiv; ln[Th/He] &nbsp; (, w &equiv; ln[Sm/He]) <span class='alignright'>(eq. 1)</span><p></p>and then performing the desired statistical analysis (averaging, uncertainty propagation, ...) on the transformed data (Vermeesch, 2008, 2010). Upon completion of these mathematical operations, the results can then be mapped back to U-Th-(Sm)/He space using an inverse logratio transformation:  <p></p> [He] = 1/[e<sup>u</sup>+e<sup>v</sup>+(e<sup>w</sup>)+1]; &nbsp; [U] = e<sup>u</sup>/[e<sup>u</sup>+e<sup>v</sup>+(e<sup>w</sup>)+1]; &nbsp;<br> [Th] = e<sup>v</sup>/[e<sup>u</sup>+e<sup>v</sup>+(e<sup>w</sup>)+1]; &nbsp; ([Sm] = e<sup>w</sup>/[e<sup>u</sup>+e<sup>v</sup>+(e<sup>w</sup>)+1]; &nbsp;) <span class='alignright'>(eq. 2)</span><p></p>where [He] + [U] + [Th] (+ [Sm]) = 1. The <i>barycentric</i> age (which is equivalent to the 'central' age of Vermeesch, 2008) is defined as the age that corresponds to the arithmetic mean composition in logratio space, which is equivalent to the logratio mean in compositional dataspace. The <tt>helioplot</tt> function visualises U-Th-(Sm)-He data on either a ternary diagram or a bivariate ln[Th/U] vs. ln[U/He] contour plot. These diagrams provide a convenient way to simultaneously display the isotopic composition of samples as well as their chronological meaning. In this respect, they fulfil the same purpose as the U-Pb concordia diagram and the U-series evolution plot.",
    "helioplot_t": "the barycentric age, which is defined as the U-Th-He age corresponding to the weighted mean composition in log(U/He)-log(Th/He) space.",
    "helioplot_mswd_x": "the Mean Square of the Weighted Deviates (MSWD) of compositional equivalence for the U-Th-He measurements. MSWD values >> 1 indicate that the ages are overdispersed with respect to the stated analytical uncertainties.",
    "helioplot_mswd_y": "the chi-squared p-value of equivalence for the geometric mean composition. p-values << 0.05 indicate that the ages are overdispersed with respect to the stated analytical uncertainties.",
    "helioplot_omega": "the estimated standard deviation of the 'geological scatter' of the U/He, Th/He (and Sm/He) logratios required to explain the overdispersion of the U-Th-(Sm)-He compositions with respect to the stated analytical uncertainties.",
    "isochron_i": "the <span class='hidden show4PbPb'>initial (<sup>207</sup>Pb/<sup>204</sup>Pb)</span><span class='hidden show4ArAr'>initial (<sup>40</sup>Ar/<sup>36</sup>Ar)</span><span class='hidden show4UPby0option1'>common Pb</span><span class='hidden show4ThUy0option1'>authigenic (<sup>234</sup>U/<sup>238</sup>U)</span><span class='hidden show4ThUy0option2'>detrital (<sup>230</sup>Th/<sup>232</sup>Th)</span><span class='hidden show4ThU3 show4ThU4'>initial (<sup>230</sup>Th/<sup>232</sup>Th)</span><span class='hidden show4ThUy0option3'>authigenic (<sup>230</sup>Th/<sup>238</sup>U)</span><span class='hidden show4UPby0option2 show4ThUy0option4'>initial (<sup>234</sup>U/<sup>238</sup>U)</span><span class='hidden show4UPby0option2'>initial (<sup>230</sup>Th/<sup>238</sup>U)</span><span class='hide3PbPb hide4ArAr hide4ThU'> isotope</span>-ratio.",
    "isochron_intro": "Isochrons are an important instrument of high precision, high accuracy geochronology. Given several aliquots from a single sample, they allow the non-radiogenic component of the daughter nuclide to be quantified and separated from the radiogenic component. In its simplest form, the isochron is obtrained by setting out the radiogenic daughter isotope against the radioactive parent isotope, both normalised to a non-radiogenic isotope of the daughter element, and fitting a straight line through these points by least squares regression Nicolaysen (1961). The slope and intercept then yield the radiogenic daughter-parent ratio and the non-radiogenic daughter composition, respectively. <tt>IsoplotR</tt> offers three ways to fit an isochron:<ol><li>Model-1: maximum Likelihood regression, using the <span class='hide4ThU1 hide4ThU2 hide4UPb'> modified error weighted least squares algorithm of York et al. (2004)</span><span class='hidden show4UPb'>Maximum Likelihood formulation of Ludwig (1998, for formats 1 through 6) or Vermeesch (2020, for formats 7 and 8)</span><span class='hidden show4ThU1 show4ThU2'> Maximum Likelihood formulation of Ludwig and Titterington (1994)</span>.  This algorithm takes into account the analytical uncertainties and error correlations, under the assumption that the scatter between the data points is solely caused by the analytical uncertainty. If the assumption is correct, then the MSWD value should be approximately equal to one. If the p-value of the chi-square test is < &alpha;, then model-1 regression assumes that the analytical uncertainties have been underestimated by a factor &radic;MSWD. </li><li>Model-2: total least squares regression, ignoring the analytical uncertainties. </li> <li>Model-3: maximum likelihood regression with overdispersion. Instead of attributing any overdispersion to underestimated analytical uncertainties, one can also attribute it to the presence of geological uncertainty, which manifests itself as an added (co)variance term. </li> </ol>",
    "isochron_t": "the isochron age.",
    "isochron_mswd_x": "the Mean Square of the Weighted Deviates (MSWD) for the linear fit. MSWD values >> 1 indicate that the ages are overdispersed with respect to the stated analytical uncertainties.",
    "isochron_mswd_y": "the chi-squared p-value for the linear fit. p-values << 0.05 indicate that the ages are overdispersed with respect to the stated analytical uncertainties.",
    "isochron_omega_a": "the excess ('geological') dispersion, i.e. the standard deviation of the assumedly Gaussian distribution that describes the authigenic component.",
    "isochron_omega_b": "the excess ('geological') dispersion of the isochron age, i.e. the standard deviation of the assumedly Gaussian distribution that describes the variability of the <span class='hidden show4UPb'>age</span> intercept.",
    "KCa_K40Ca44": "Measured <sup>40</sup>K/<sup>44</sup>Ca-ratios.",
    "KCa_err_K40Ca44": "Analytical uncertainty of the <sup>40</sup>K/<sup>44</sup>Ca-ratios",
    "KCa_Ca40Ca44": "Measured <sup>40</sup>Ca/<sup>44</sup>Ca-ratios.",
    "KCa_err_Ca40Ca44": "Analytical uncertainty of the <sup>40</sup>Ca/<sup>44</sup>Ca-ratios",
    "KCa_rho": "Error correlations between the <sup>40</sup>K/<sup>44</sup>Ca and <sup>40</sup>Ca/<sup>44</sup>Ca-ratios.",
    "KCa_K40K44": "Measured <sup>40</sup>K/<sup>40</sup>Ca-ratios.",
    "KCa_err_K40Ca40": "Analytical uncertainty of the <sup>40</sup>K/<sup>40</sup>Ca-ratios",
    "KCa_redundancy": "<p></p><tt>IsoplotR</tt> uses the redundancy of the three ratios to calculate the correlation between their respective analytical uncertainties.",
    "KDE_intro": "Histograms smooth data by binning. <tt>IsoplotR</tt> uses Sturges' Rule (log<sub>2</sub>[n]+1, where n is the number of data points) as the default number of histogram bins, but this can be changed to any other natural number by the user. Alternatively, kernel density estimates KDEs (Vermeesch, 2012) smooth data by applying a (Gaussian) kernel:  <p></p>KDE(t) = &sum;<sub>i</sub><i>N</i> (t | &mu;=t<sub>i</sub>, &sigma;=h[t]) <span class='alignright'>(eq. 1)</span> <p></p>where <i>N</i>(&mu;,&sigma;) is the probability of observing a value t under a Normal distribution with mean &mu; and standard deviation &sigma;. h[t] is the smoothing parameter or 'bandwidth' of the kernel density estimate which may or may not depend on the age t. If h[t] depends on t, then KDE(t) is known as an 'adaptive' KDE. The default bandwidth used by <tt>IsoplotR</tt> is calculated using the algorithm of Botev et al. (2010) and modulated by the adaptive smoothing approach of Abramson (1982). The rationale behind adaptive kernel density estimation is to use a narrower bandwidth near the peaks of the sampling distribution (where the ordered dates are closely spaced in time), and a wider bandwidth in the distribution's sparsely sampled troughs. Thus, the resolution of the density estimate is optimised according to data availability. Kernel density estimates are not to be confused with <tt>Isoplot</tt>'s 'probability density plots' (PDPs). The mathematical definition of a PDP closely resembles that of the KDE, the only difference being the substitution of the bandwidth h[t] by the analytical uncertainty s[t<sub>i</sub>] in Equation 1. This similarity in appearance and definition is the source of much confusion. PDPs do not stand up to further statistical scrutiny (see counter-examples provided by Vermeesch, 2012), and are not implemented in <tt>IsoplotR</tt>.",
    "LuHf_Lu": "Lu concentration, in ppm.",
    "LuHf_err_Lu": "Analytical uncertainty of the Lu concentration, in ppm",
    "LuHf_Hf": "Hf concentration, in ppm.",
    "LuHf_err_Hf": "Analytical uncertainty of the Hf concentration, in ppm",
    "LuHf_Lu176Hf177": "Measured <sup>176</sup>Lu/<sup>177</sup>Hf-ratios.",
    "LuHf_err_Lu176Hf177": "Analytical uncertainty of the <sup>176</sup>Lu/<sup>177</sup>Hf-ratios",
    "LuHf_Hf176Hf177": "Measured <sup>176</sup>Hf/<sup>177</sup>Hf-ratios.",
    "LuHf_err_Hf176Hf177": "Analytical uncertainty of the <sup>176</sup>Hf/<sup>177</sup>Hf-ratios",
    "LuHf_rho_Lu6Hf7Hf6Hf7": "Error correlations between the <sup>176</sup>Lu/<sup>177</sup>Hf and <sup>176</sup>Hf/<sup>177</sup>Hf-ratios (optional).",
    "LuHf_redundancy": "<p></p><tt>IsoplotR</tt> uses these data to calculate the <sup>176</sup>Lu/<sup>177</sup>Hf-ratios and the correlation between the <sup>176</sup>Hf/<sup>177</sup>Hf- and the <sup>176</sup>Lu/<sup>177</sup>Hf-uncertainties.",
    "MDS_intro": "Multidimensional Scaling (MDS) is a dimension-reducting technique that takes a matrix of pairwise 'dissimilarities' between objects (e.g., detrital age distributions) as input and produces a configuration of two (or higher-) coordinates as output, so that the Euclidean distance between these coordinates approximates the dissimilarities of the input matrix. Thus, an MDS-configuration serves as a 'map' in which similar samples cluster closely together and dissimilar samples plot far apart. In the context of detrital geochronology, the dissimilarity between samples is given by the statistical distance between age distributions. There are many ways to define this statistical distance. <tt>IsoplotR</tt> uses the Kolmogorov-Smirnov (KS) statistic for this purpose due to its simplicity and the fact that it behaves like a true distance in the mathematical sense of the word (Vermeesch, 2013, 2018). The KS-distance is closely related to the CAD-plot. It is given by the maximum vertical distance between two CAD step functions. Thus, the KS-distance takes on values between zero (perfect match between two age distributions) and one (no overlap between two distributions). Calculating the KS-distance between samples two at a time populates a symmetric dissimilarity matrix with positive values and a zero diagonal. <tt>IsoplotR</tt> implements two algorithms to convert this matrix into a configuration. The first ('classical' MDS) approach uses a sequence of basic matrix manipulations to achieve a linear fit between the KS-distances and the fittted distances on the MDS configuration. The second, more sophisticated ('nonmetric' MDS) approach subjects the input distances to a transformation f prior to fitting a configuration:<p></p>&delta;<sub>i,j</sub> = f(KS<sub>i,j</sub>)<p></p>where KS<sub>i,j</sub> is the KS-distance between samples i and j (for 1 &le; i &ne; j &le; n) and &delta;<sub>i,j</sub> is the 'disparity'. Fitting an MDS configuration then involves finding the disparity transformation that maximises the goodness of fit (or minimises the 'stress') between the disparities and the fitted distances. The latter two quantities can also be plotted against each other as a 'Shepard plot'. Additional options and higher order alternatives to these MDS algorithms are provided in a separate <tt>R</tt>-package called <a href='http://provenance-london-geochron.com'>provenance</a> (Vermeesch et al., 2016).",
    "other_radial_t": "A column of numerical values (e.g. ages)",
    "other_radial_err_t": "The analytical uncertainty of these values",
    "other_radial_C": "Optional variable to be used as fill colour.",
    "other_radial_omit": "Optional variable used to hide or ignore aliquots. Aliquots marked as (lowercase) '<tt>x</tt>' are plotted but ignored for central age and mixture modelling calculations; Aliquots marked as (uppercase) '<tt>X</tt>' are removed from both plots and calculations.",
    "other_regression_X": "A column of numerical values (e.g., isotope ratios)",
    "other_regression_err_X": "The analytical uncertainty of these values",
    "other_regression_Y": "A second column of numerical values (e.g., isotope ratios)",
    "other_regression_err_Y": "The analytical uncertainty of these values",
    "other_regression_rXY": "The error correlation of X and Y",
    "other_regression_XZ": "A column of ratio data",
    "other_regression_err_XZ": "The analytical uncertainty of these values",
    "other_regression_YZ": "A second column of ratio data",
    "other_regression_err_YZ": "The analytical uncertainty of this second set of ratios",
    "other_regression_XY": "A third column of (redundant) ratio data",
    "other_regression_err_XY": "The analytical uncertainty of the third set of ratios, whose redundancy is used to estimate the correlation coefficient of X/Z and Y/Z",
    "other_regression_X_Y": "A column of with X-values on top of the corresponding Y-values",
    "other_regression_Xi": "The (co)variances of X<sub>i</sub> with Y<sub>j</sub> for (1&le;j&le;n), where n is the number of aliquots and 1&le;j&le;n",
    "other_regression_Yi": "The (co)variances of Y<sub>i</sub> with X<sub>j</sub> for (1&le;j&le;n), where n is the number of aliquots and 1&le;j&le;n",
    "other_regression_C": "Optional variable to be used as fill colour in error ellipses. <span class='hidden show4other6'>Note: only the first half of the column is used.</span>",
    "other_regression_omit": "Optional variable used to hide or ignore aliquots. Aliquots marked as (lowercase) '<tt>x</tt>' are plotted but ignored for the regression analysis; Aliquots marked as (uppercase) '<tt>X</tt>' are removed from both plots and calculations. <span class='hidden show4other6'>Note: only the first half of the column is used.</span>",
    "other_spectrum_f": "The fraction of 'stuff' in each column, which will be normalised to form the X-axis of the spectrum",
    "other_spectrum_X": "Numerical values, which will form the Y-axis of the spectrum",
    "other_spectrum_err_X": "The analytical uncertainty of these values",
    "other_spectrum_omit": "Optional variable used to hide or ignore aliquots. Aliquots marked as (lowercase) '<tt>x</tt>' are plotted but ignored for the plateau calculation; Aliquots marked as (uppercase) '<tt>X</tt>' are removed from both plots and calculations.",
    "other_average_X": "A column of numerical values",
    "other_average_err_X": "The analytical uncertainty of these values",
    "other_average_omit": "Optional variable used to hide or ignore aliquots. Aliquots marked as (lowercase) '<tt>x</tt>' are plotted but ignored for the weighted mean calculation; Aliquots marked as (uppercase) '<tt>X</tt>' are removed from both plots and calculations.",
    "other_kde_cad": "A column of numerical values",
    "other_omit": "Optional variable used to ignore aliquots. Aliquots marked as '<tt>x</tt>' or '<tt>X</tt>' are removed from the plot.",
    "PbPb_64": "Measured <sup>206</sup>Pb/<sup>204</sup>Pb-ratios.",
    "PbPb_err_64": "Analytical uncertainty of the <sup>206</sup>Pb/<sup>204</sup>Pb-ratios",
    "PbPb_74": "Measured <sup>207</sup>Pb/<sup>204</sup>Pb-ratios.",
    "PbPb_err_74": "Analytical uncertainty of the <sup>207</sup>Pb/<sup>204</sup>Pb-ratios",
    "PbPb_46": "Measured <sup>204</sup>Pb/<sup>206</sup>Pb-ratios.",
    "PbPb_err_46": "Analytical uncertainty of the <sup>204</sup>Pb/<sup>206</sup>Pb-ratios",
    "PbPb_76": "Measured <sup>207</sup>Pb/<sup>206</sup>Pb-ratios.",
    "PbPb_err_76": "Analytical uncertainty of the <sup>207</sup>Pb/<sup>206</sup>Pb-ratios",
    "PbPb_rho_6474": "Error correlation between the <sup>206</sup>Pb/<sup>204</sup>Pb- and <sup>207</sup>Pb/<sup>204</sup>Pb-ratios.",
    "PbPb_rho_4676": "Error correlation between the <sup>204</sup>Pb/<sup>206</sup>Pb- and <sup>207</sup>Pb/<sup>206</sup>Pb-ratios.",
    "radial_intro": "Radial plots are bivariate (x<sub>i</sub>,y<sub>i</sub>) scatterplots where:<p></p>x<sub>i</sub> = 1∕&sigma;(z<sub>i</sub>) and y<sub>i</sub> = (z<sub>i</sub> - z<sub>o</sub>)∕&sigma;(z<sub>i</sub>) (for 1 &le; i &le; n)<p></p>with z<sub>i</sub> a transformation of some data and &sigma;(z<sub>i</sub>) the corresponding measurement uncertainty. For example, if z<sub>i</sub> = log(t<sub>i</sub>) then &sigma;(z<sub>i</sub>) = &sigma;(t<sub>i</sub>)∕t<sub>i</sub>. z<sub>o</sub> is a convenient central value such as the weighted mean. The slope of a line connecting the origin (x=0,y=0) of a radial plot with a data point (x<sub>i</sub>,y<sub>i</sub>) equals z<sub>i</sub>, and the horizontal distance along x-axis is a measure if its precision. Thus, the radial plot simultaneously visualises a measurement’s value and precision. No other graphical method achieves this goal with the same elegance (Galbraith, 1988). This makes the radial plot the method of choice for visualising heteroscedastic data, i.e. data with variable measurement uncertainties. Traditional applications in the Earth Sciences are fission track and luminescence dating (e.g., Galbraith, 1990; Galbraith et al., 1999). <tt>IsoplotR</tt> generalises it to all other geochronometers as well.",
    "radial_caveat": "An asterisk is added to the plot title if the initial daughter correction is done by isochron regression, to mark the circularity of using an isochron to compute a central age. Also note that the uncertainty budget of the central age does not include the uncertainty of the initial daughter correction (if any). This uncertainty is neither purely systematic nor purely random and cannot easily be propagated with conventional geochronological data processing algorithms. In this case the isochron errors are more meaningful, and the radial plot should just be used to inspect the residuals of the data around the isochron.",
    "radial_t": "the central age, which is defined as e<sup>&mu;</sup> where &mu; is the mean of the following log-normal distribution:  <p></p>log[t<sub>i</sub>] ~ Norm(&mu;, (s[t<sub>i</sub>]/t<sub>i</sub>)<sup>2</sup> + &omega;<sup>2</sup>) <span class='alignright'>(eq. 1)</span><p></p>with s[t<sub>i</sub>] the standard error of the i<sup>th</sup> (out of n) measurements, and &omega; the <i>overdispersion</i>.",
    "radial_m": "the Mean Square of the Weighted Deviates a.k.a. the reduced chi-squared statistic. p-values less than &alpha; suggest that the dataset under consideration is overdispersed with respect to the analyical uncertainties.",
    "radial_p": "the p-value of a chi-square probability for homogeneity. High values of p (>0.05, say) indicate that there is not enough evidence for overdispersion.",
    "radial_omega": "the dispersion defined by eq. 1.",
    "pooled_age": "the pooled age, obtained by taking the sum of all the spontaneous tracks and combining it with the sum of all the induced tracks (for the EDM), or the area-weighted average of the uranium-concentrations (for ICP-MS data).",
    "RbSr_Rb": "Rb concentration, in ppm.",
    "RbSr_err_Rb": "Analytical uncertainty of the Rb concentration, in ppm",
    "RbSr_Sr": "Sr concentration, in ppm.",
    "RbSr_err_Sr": "Analytical uncertainty of the Sr concentration, in ppm",
    "RbSr_Rb87Sr86": "Measured <sup>87</sup>Rb/<sup>86</sup>Sr-ratios.",
    "RbSr_redundancy": "<p></p> <tt>IsoplotR</tt> uses these data to calculate the <sup>87</sup>Rb/<sup>86</sup>Sr-ratios and the correlation between the <sup>87</sup>Sr/<sup>86</sup>Sr- and the <sup>87</sup>Rb/<sup>86</sup>Sr-uncertainties.",
    "RbSr_Sr87Sr86": "Measured <sup>87</sup>Sr/<sup>86</sup>Sr-ratios.",
    "RbSr_err_Sr87Sr86": "Analytical uncertainty of the <sup>87</sup>Sr/<sup>86</sup>Sr-ratios",
    "RbSr_rho_Rb87Sr86_Sr87Sr86": "Error correlations between the <sup>87</sup>Rb/<sup>86</sup>Sr and <sup>87</sup>Sr/<sup>86</sup>Sr-ratios (optional).",
    "RbSr_Rb87Sr87": "Measured <sup>87</sup>Rb/<sup>87</sup>Sr-ratios.",
    "RbSr_err_Rb87Sr87": "Analytical uncertainty of the <sup>87</sup>Rb/<sup>87</sup>Sr-ratios",
    "RbSr_Sr86Sr87": "Measured <sup>86</sup>Sr/<sup>87</sup>Sr-ratios.",
    "RbSr_err_Sr86Sr87": "Analytical uncertainty of the <sup>87</sup>Sr/<sup>86</sup>Sr-ratios",
    "RbSr_rho_Rb87Sr87_Sr86Sr87": "Error correlations between the <sup>87</sup>Rb/<sup>87</sup>Sr and <sup>86</sup>Sr/<sup>87</sup>Sr-ratios (optional).",
    "RbSr_8786": "Measured <sup>87</sup>Sr/<sup>86</sup>Sr-ratios.",
    "RbSr_err_8786": "Analytical uncertainty of the <sup>87</sup>Sr/<sup>86</sup>Sr-ratios",
    "regression_i": "the y-intercept.",
    "regression_i_x": "the estimated uncertainty (&sigma;) of i.",
    "regression_i_y": "the 100(1-&alpha;)% confidence interval for i using the appropriate number of degrees of freedom.",
    "regression_i_z": "the approximate 100(1-&alpha;)% confidence interval for i with overdispersion, calculated as z = y&radic;MSWD (only reported if the p-value of the chi-square test is < &alpha;).",
    "regression_intro": "<tt>IsoplotR</tt> offers three ways to fit a straight line through 2-dimensional data with measurement uncertainties:<ol><li>Model-1: maximum likelihood regression, either using the modified error weighted least squares algorithm of York et al. (2004) for input formats 1 and 2; or by the Omnivariant Generalised Least Squares (OGLS) algorithm of Da&euml;ron and Vermeesch (2023) for input format 3. These algorithms take into account the analytical uncertainties and error correlations, under the assumption that the scatter between the data points is solely caused by the analytical uncertainty. If the assumption is correct, then the MSWD value should be approximately equal to one. If the p-value of the chi-square test is < &alpha;, then model-1 regression assumes that the analytical uncertainties have been underestimated by a factor &radic;MSWD. </li><li>Model-2: ordinary least squares regression, ignoring the analytical uncertainties. </li> <li>Model-3: maximum likelihood regression with overdispersion. Instead of attributing any overdispersion to underestimated analytical uncertainties, one can also attribute it to the presence of geological uncertainty, which manifests itself as an added (co)variance term. </li></ol>",
    "regression_s": "the slope of the best fit line.",
    "regression_s_x": "the estimated uncertainty (&sigma;) of s.",
    "regression_s_y": "the 100(1-&alpha;)% confidence interval for s using the appropriate number of degrees of freedom.",
    "regression_s_z": "the approximate 100(1-&alpha;)% confidence interval for s with overdispersion, calculated as z = y&radic;MSWD (only reported if the p-value of the chi-square test is < &alpha;).",
    "regression_mswd_x": "the Mean Square of the Weighted Deviates (MSWD) for the linear fit. MSWD values >> 1 indicate that the data are overdispersed with respect to the stated analytical uncertainties.",
    "regression_mswd_y": "the chi-squared p-value for the linear fit. p-values << 0.05 indicate that the data are overdispersed with respect to the stated analytical uncertainties.",
    "ReOs_Re": "Re concentration, in ppm.",
    "ReOs_err_Re": "Analytical uncertainty of the Re concentration, in ppm",
    "ReOs_Os": "Os concentration, in ppm.",
    "ReOs_err_Os": "Analytical uncertainty of the Os concentration, in ppm",
    "ReOs_redundancy": "<p></p> <tt>IsoplotR</tt> uses these data to calculate the <sup>187</sup>Re/<sup>188</sup>Os-ratios and the correlation between the <sup>187</sup>Os/<sup>188</sup>Os- and the <sup>187</sup>Re/<sup>188</sup>Os-uncertainties.",
    "ReOs_Re187Os188": "Measured <sup>187</sup>Re/<sup>188</sup>Os-ratios.",
    "ReOs_err_Re187Os188": "Analytical uncertainty of the <sup>187</sup>Re/<sup>188</sup>Os-ratios",
    "ReOs_Os187Os188": "Measured <sup>187</sup>Os/<sup>188</sup>Os-ratios.",
    "ReOs_err_Os187Os188": "Analytical uncertainty of the <sup>187</sup>Os/<sup>188</sup>Os-ratios",
    "ReOs_rho_Re187Os188Os187Os188": "Error correlations between the <sup>187</sup>Re/<sup>188</sup>Os and <sup>187</sup>Os/<sup>188</sup>Os-ratios (optional).",
    "zeta": "The fission track age is given by:  <p></p> t = ln[1 + {2 N<sub>s</sub>&lambda;<sub>238</sub>&lambda;<sub>f</sub>}/ {[<sup>238</sup>U]A<sub>s</sub>L}] / &lambda;<sub>238</sub> <span class='alignright'>(eq. 1)</span> <p></p>  where N<sub>s</sub> is the number of spontaneous fission tracks measured over an area A<sub>s</sub>, [<sup>238</sup>U] is the <sup>238</sup>U-concentration in atoms per unit volume, &lambda;<sub>f</sub> is the fission decay constant, L is the etchable fission track length, and the factor 2 is a geometric factor accounting for the fact that etching reveals tracks from both above and below the internal crystal surface.  <p></p>  <div class='show4EDM hide4absolute hide4ICP'> [<sup>238</sup>U] can be measured indirectly using the induced fission of neutron-irradiated <sup>235</sup>U as a proxy for the <sup>238</sup>U. In the most common implementation of this approach, the induced fission tracks are recorded by an external detector made of mica or plastic that is attached to the polished grain surface (Fleischer and Hart, 1972; Hurford and Green, 1983). The fission track age equation then becomes:  <p></p> t = ln[ 1 + {&lambda;<sub>238</sub>&zeta;&rho;<sub>d</sub>N<sub>s</sub>}/ {2 N<sub>i</sub>}] / &lambda;<sub>238</sub> <span class='alignright'>(eq. 2)</span> <p></p>  where N<sub>i</sub> is the number of induced fission tracks counted in the external detector over the same area as the spontaneous tracks, &zeta; is a 'zeta'-calibration factor that incorporates both the fission decay constant and the etchable fission track length, and &rho;<sub>d</sub> is the number of induced fission tracks per unit area counted in a co-irradiated glass of known U-concentration. &rho;<sub>d</sub> allows the &zeta;-factor to be 'recycled' between irradiations. </div> <div class='hide4EDM hide4absolute show4ICP'> The <sup>238</sup>U-concentration can also be measured directly by LAICPMS. Unfortunately the accuracy of LAICPMS-based age estimates is compromised by the absence of matrix-matched concentrations standards, and uncertainies associated with the fission track decay constant and the etching and counting efficiencies. These systematic errors can be removed by normalising to a standard of known fission track age and defining a new 'zeta' calibration constant &zeta;<sub>icp</sub>:  <p></p> t = ln( 1 + {2 &zeta;<sub>icp</sub> &lambda;<sub>238</sub>N<sub>2</sub>}/ {[<sub>238</sub>U] A<sub>s</sub>})/ &lambda;<sub>238</sub> <span class='alignright'>(eq. 2)</span> <p></p>  where [<sup>238</sup>U] may either stand for the <sup>238</sup>U-concentration (in ppm) <i>or</i> for the U/Ca (for apatite) or U/Si (for zircon) ratio measurement, and A<sub>s</sub> is the spontaneous track counting area, which may either correspond to one laser spot or to a larger area (if multiple U-measurements were made). </div>",
    "SmNd_Sm": "Sm concentration, in ppm.",
    "SmNd_err_Sm": "Analytical uncertainty of the Sm concentration, in ppm",
    "SmNd_Nd": "Nd concentration, in ppm.",
    "SmNd_err_Nd": "Analytical uncertainty of the Nd concentration, in ppm",
    "SmNd_redundancy": "<p></p> <tt>IsoplotR</tt> uses these data to calculate the <sup>147</sup>Sm/<sup>144</sup>Nd-ratios and the correlation between the <sup>147</sup>Sm/<sup>144</sup>Nd- and the <sup>143</sup>Nd/<sup>144</sup>Nd-uncertainties.",
    "SmNd_Sm147Nd144": "Measured <sup>147</sup>Sm/<sup>144</sup>Nd-ratios.",
    "SmNd_err_Sm147Nd144": "Analytical uncertainty of the <sup>147</sup>Sm/<sup>144</sup>Nd-ratios",
    "SmNd_Nd143Nd144": "Measured <sup>143</sup>Nd/<sup>144</sup>Nd-ratios.",
    "SmNd_err_Nd143Nd144": "Analytical uncertainty of the <sup>143</sup>Nd/<sup>144</sup>Nd-ratios",
    "SmNd_rho_Sm147Nd144Nd143Nd144": "Error correlations between the <sup>147</sup>Sm/<sup>144</sup>Nd and <sup>143</sup>Nd/<sup>144</sup>Nd-ratios (optional).",
    "SmNd_Sm147Nd143": "Measured <sup>147</sup>Sm/<sup>143</sup>Nd-ratios.",
    "spectrum_intro": "The <sup>40</sup>Ar/<sup>39</sup>Ar-age spectrum is a useful tool to visualise stepwise heating measurements. Its appearance is based on the weighted mean plot with the different heating steps arranged in order of increasing temperature along the horizontal axis, and the width of the different sample boxes proportional to the corresponding amounts of <sup>39</sup>Ar. <tt>IsoplotR</tt> defines the 'plateau age' as the weighted mean age of the longest sequence (in terms of cumulative <sup>39</sup>Ar content) of consecutive heating steps that pass a modified Chauvenet criterion. This definition is different (and simpler) than the one used by <tt>Isoplot</tt> (Ludwig, 2003). However, it is important to mention that all definitions of an age plateau are heuristic by nature and should therefore not be used for quantitative inference. It is possible (and likely) that the plateau exhibits significant overdispersion. This overdispersion can be manually reduced by removing individual heating steps using the optional <tt>omit</tt> column.",
    "spectrum_t": "the plateau age, which is defined as the weighted mean age of the largest consecutive set of steps that survive the modified Chauvenet's Criterion used for the ordinary weighted mean.",
    "spectrum_mswd_x": "the mean square of the weighted deviates (aka 'reduced chi-square statistic') of the plateau. <tt>IsoplotR</tt>'s plateau definition allows the p-value of the chi-square test to be < &alpha;, as long as the overdispersion does not violate Chauvenet's outlier criterion.",
    "spectrum_mswd_y": "p-value of a chi-square test of homogeneity. <tt>IsoplotR</tt>'s plateau definition allow the p-value to fall below the &alpha; cutoff, as long as the overdispersion does not violate Chauvenet's outlier criterion.",
    "spectrum_pct_39": "the sum of all the steps that are included in the plateau.",
    "ThU_82": "Measured <sup>238</sup>U/<sup>232</sup>Th activity ratios.",
    "ThU_err_82": "Analytical uncertainty of the <sup>238</sup>U/<sup>232</sup>Th activity ratios",
    "ThU_42": "Measured <sup>234</sup>U/<sup>232</sup>Th activity ratios.",
    "ThU_err_42": "Analytical uncertainty of the <sup>234</sup>U/<sup>232</sup>Th activity ratios",
    "ThU_02": "Measured <sup>230</sup>Th/<sup>232</sup>Th activity ratios.",
    "ThU_err_02": "Analytical uncertainty of the <sup>230</sup>Th/<sup>232</sup>Th activity ratios",
    "ThU_rho_8242": "Error correlation between the <sup>238</sup>U/<sup>232</sup>Th- and <sup>234</sup>U/<sup>232</sup>Th activity ratios.",
    "ThU_rho_8202": "Error correlation between the <sup>238</sup>U/<sup>232</sup>Th- and <sup>230</sup>Th/<sup>232</sup>Th activity ratios <span class='hidden show4ThU3'>(optional)</span>",
    "ThU_rho_4202": "Error correlation between the <sup>234</sup>U/<sup>232</sup>Th- and <sup>230</sup>Th/<sup>232</sup>Th activity ratios.",
    "ThU_28": "Measured <sup>232</sup>Th/<sup>238</sup>U activity ratios.",
    "ThU_err_28": "Analytical uncertainty of the <sup>232</sup>Th/<sup>238</sup>U activity ratios",
    "ThU_48": "Measured <sup>234</sup>U/<sup>238</sup>U activity ratios.",
    "ThU_err_48": "Analytical uncertainty of the <sup>234</sup>U/<sup>238</sup>U activity ratios",
    "ThU_08": "Measured <sup>230</sup>Th/<sup>238</sup>U activity ratios.",
    "ThU_err_08": "Analytical uncertainty of the <sup>230</sup>Th/<sup>238</sup>U activity ratios",
    "ThU_rho_2808": "Error correlation between the <sup>232</sup>Th/<sup>238</sup>U- and <sup>230</sup>Th/<sup>238</sup>U activity ratios <span class='show4ThU4'>(optional)</span>",
    "ThU_rho_4808": "Error correlation between the <sup>234</sup>U/<sup>238</sup>U- and <sup>230</sup>Th/<sup>238</sup>U activity ratios.",
    "ThU_C": "Optional variable to be used as fill colours in evolution diagrams, isochrons and radial plots.",
    "UThHe": "Measured He, U, Th and (optionally) Sm abundance or concentration, in any kind of atomic units (fmol, mol/g, atoms, ...). Note that any &alpha;-ejection correction must be applied to the data <i>before</i> entry into <tt>IsoplotR</tt>.",
    "UThHe_err": "Analytical uncertainty of the He, U, Th and (optionally) Sm measurements",
    "UThHe_C": "Optional variable to be used as fill colours in radial plots, ternary diagrams and logratio plots.",
    "RbSr_err_Rb87Sr86": "Analytical uncertainty of the <sup>87</sup>Rb/<sup>86</sup>Sr-ratios",
    "ThU_rho_2848": "Error correlation between the <sup>232</sup>Th/<sup>238</sup>U- and <sup>234</sup>U/<sup>238</sup>U-ratios.",
    "SmNd_rho_Sm147Nd143Nd144Nd143": "Error correlations between the <sup>147</sup>Sm/<sup>143</sup>Nd and <sup>144</sup>Nd/<sup>143</sup>Nd-ratios (optional).",
    "SmNd_err_Sm147Nd143": "Analytical uncertainty of the <sup>147</sup>Sm/<sup>143</sup>Nd-ratios",
    "SmNd_err_Nd144Nd143": "Analytical uncertainty of the <sup>144</sup>Nd/<sup>143</sup>Nd-ratios",
    "SmNd_Nd144Nd143": "Measured <sup>143</sup>Nd/<sup>144</sup>Nd-ratios.",
    "ReOs_rho_Re187Os187Os188Os187": "Error correlations between the <sup>187</sup>Re/<sup>187</sup>Os and <sup>188</sup>Os/<sup>187</sup>Os-ratios (optional).",
    "ReOs_err_Re187Os187": "Analytical uncertainty of the <sup>187</sup>Re/<sup>187</sup>Os-ratios",
    "ReOs_err_Os188Os187": "Analytical uncertainty of the <sup>188</sup>Os/<sup>187</sup>Os-ratios",
    "ReOs_Re187Os187": "Measured <sup>188</sup>Re/<sup>187</sup>Os-ratios.",
    "ReOs_Os188Os187": "Measured <sup>188</sup>Os/<sup>187</sup>Os-ratios.",
    "LuHf_rho_Lu6Hf6Hf7Hf6": "Error correlations between the <sup>176</sup>Lu/<sup>176</sup>Hf and <sup>176</sup>Hf/<sup>176</sup>Hf-ratios (optional).",
    "LuHf_err_Lu176Hf176": "Analytical uncertainty of the <sup>176</sup>Lu/<sup>176</sup>Hf-ratios.",
    "LuHf_err_Hf177Hf176": "Analytical uncertainty of the <sup>177</sup>Hf/<sup>176</sup>Hf-ratios",
    "LuHf_Lu177Hf176": "Measured <sup>177</sup>Lu/<sup>176</sup>Hf-ratios.",
    "LuHf_Hf177Hf176": "Measured <sup>177</sup>Hf/<sup>176</sup>Hf-ratios.",
    "regression_omega": "the excess ('geological') dispersion of the y-intercept, i.e. the standard deviation of the assumedly Gaussian distribution that describes the inherited component.",
    "input": "Input:",
    "detrital_correction_none": "none",
    "spotsize": "spot size",
    "ThPb_format_1": "1. Normal",
    "ThPb_format_2": "2. Inverse",
    "ThPb_format_3": "3. Three ratios",
    "help_Pb208Pb204": "Initial <sup>208</sup>Pb/<sup>204</sup>Pb ratio:",
    "ThPb_3204": "Measured <sup>232</sup>Th/<sup>204</sup>Pb-ratios.",
    "ThPb_err_3204": "Analytical uncertainty of the <sup>232</sup>Th/<sup>204</sup>Pb-ratios",
    "ThPb_0804": "Measured <sup>208</sup>Pb/<sup>204</sup>Pb-ratios.",
    "ThPb_err_0804": "Analytical uncertainty of the <sup>208</sup>Pb/<sup>204</sup>Pb-ratios",
    "ThPb_rho_3204_0804": "Error correlations between the <sup>232</sup>Th/<sup>204</sup>Pb and <sup>208</sup>Pb/<sup>204</sup>Pb-ratios.",
    "ThPb_3208": "Measured <sup>232</sup>Th/<sup>204</sup>Pb-ratios.",
    "ThPb_err_3208": "Analytical uncertainty of the <sup>232</sup>Th/<sup>208</sup>Pb-ratios",
    "ThPb_0408": "Measured <sup>204</sup>Pb/<sup>208</sup>Pb-ratios.",
    "ThPb_err_0408": "Analytical uncertainty of the <sup>204</sup>Pb/<sup>208</sup>Pb-ratios",
    "ThPb_rho_3208_0408": "Error correlations between the <sup>232</sup>Th/<sup>208</sup>Pb and <sup>204</sup>Pb/<sup>208</sup>Pb-ratios.",
    "ThPb_redundancy": "<p></p><tt>IsoplotR</tt> uses the redundancy of the three ratios to calculate the correlation between their respective analytical uncertainties.",
    "help_ThPb_i2i": "Use the isochron intercept to estimate the initial <sup>208</sup>Pb/<sup>204</sup>Pb-ratio?",
    "PbPb_67": "Measured <sup>206</sup>Pb/<sup>207</sup>Pb-ratios.",
    "PbPb_err_67": "Analytical uncertainty of the <sup>206</sup>Pb/<sup>207</sup>Pb-ratios",
    "ages_48_0": "The initial <sup>234</sup>U/<sup>238</sup>U-ratio.",
    "translate_button": "<a class='translatelink' href='${LINK}' title='Please follow this link to help translate this text'>TRANSLATE</a>"
}
