FACTORS IMPACTING THE ACCURACY OF APATITE(U-TH)/HE DATING

doi:10.3969/j.issn.0253-4967.2016.04.024

Abstract

Abstract:

Apatite (U-Th)/He dating has gained popularity since its rejuvenation as geochronometry and thermochronometry applied in the deduction of the geological processes of the upper-three-km crust.However,this irreplaceable method,which has the lowest known closure temperature (~70℃),sometimes is suffering from large dispersion and deviation because of its dating theory,its analytical method,and its diffusion process.In this paper,we summarized ten factors impacting the accuracy of (U-Th)/He dating.They are grain size,fluid and mineral inclusions,α-particle ejection,α-particle implantation,U-Th zonation,radiation damage,chemical composition,samarium concentration,multiple thermal events,and U-series disequilibrium.We discussed how these ten factors would affect the (U-Th)/He ages and how to reduce and/or avoid the deviation caused by them.The factors of grain size (different size,different diffusion domain) and inclusions (parentless ⁴He) can be suppressed in the procedure of grain selection under binocular.It is the precise measurement of a homogenous crystal that endows the (U-Th)/He dating method credible due to the correction of α-particle ejection based on the dimension of crystals.The possible implantation of α-particles can be evaluated by the negative correlation of age and eU (eU=[U]+0.235[Th]).U-Th zonation,a heterogeneous distribution of parent nuclides,makes the correction of α-particle ejection inaccurate;besides,this factor also amplifies the side effects of radiation damage and grain size.LA-ICP-MS can detect this phenomenon.Radiation damage outstands when the samples experience reheating or long residence time in partial retention zone (40~70℃),indicated by the positive correlation between age and eU/[⁴He].Apatite (U-Th)/He age can be entangled by higher Cl content,with which the crystal accumulates more radiation damage,leading to a larger age,meanwhile this factor needs more investigation.Having larger half-life than U-series nuclides,the ¹⁴⁷Sm is not a big problem in the dating of a large timescale,while more precise event needs the data of ¹⁴⁷Sm in the age calculation.The multiple thermal events should be evaluated to exclude thermal perturbation,when applying the (U-Th)/He geo/thermochronology to the deduction of a particular thermal event.U-series disequilibrium has an impact on the ages smaller than 1Ma,making the age results larger than the true one.U-series disequilibrium method and mineral couples can solve this problem.Inclusion,α-particle ejection and implantation,and U-Th zonation are at the mercy of analytical methods.The factors stemming from helium diffusion in the crystals are grain size,radiation damage,Cl content,multiple thermal events.The dating theory of (U-Th)/He method renders U-series disequilibrium and ¹⁴⁷Sm outstand as side effects in some specific conditions.It would be our pleasure if this paper could provide some useful information for the works relevant to this dating method.

Key words: apatite, (U-Th)/He dating, accuracy, effects

摘要：

磷灰石（U-Th）/He体系因具有已知最低的放射性同位素体系封闭温度（70℃，约3km深度），而被广泛应用于浅地表构造变形及地貌演化研究，是近20a来发展较为迅速的1种热年代学方法。但由于定年原理、测试方法和⁴He扩散特点等诸多因素的限制，该同位素年龄体系的准确度受到了一定程度的制约。文中归纳了现有文献中常见的10类磷灰石（U-Th）/He定年准确度的影响因素，即粒径、包裹体、α粒子射出效应、α粒子植入效应、U-Th成分环带、辐射损伤、磷灰石化学成分、钐含量、多期热事件和铀系不平衡等，并初步探讨了造成偏差的原因和解决方法，用以抛砖引玉，引起相关研究者的考虑和重视。

关键词: 磷灰石, (U-Th)/He年代学, 准确度, 影响因素

CLC Number:

P597

ZHANG Wei-bin, WU Lin, WANG Fei. FACTORS IMPACTING THE ACCURACY OF APATITE(U-TH)/HE DATING[J]. SEISMOLOGY AND GEOLOGY, 2016, 38(4): 1107-1123.

张炜斌, 吴林, 王非. 磷灰石(U-Th)/He年龄准确度的影响因素[J]. 地震地质, 2016, 38(4): 1107-1123.

References

Ault A K, Flowers R M. 2012. Is apatite U-Th zonation information necessary for accurate interpretation of apatite(U-Th)/He thermochronometry data［J］. Geochimica et Cosmochimica Acta, 79:60-78.
Barry P H, Hilton D R, Fischer T P, et al. 2013. Helium and carbon isotope systematics of cold "mazuku" CO₂ vents and hydrothermal gases and fluids from Rungwe Volcanic Province, southern Tanzania［J］. Chemical Geology, 339:141-156.
Belton D X, Lorencak M, Carter T J, et al. 2004. Samarium in apatite:Contributions to radiogenic helium and the effect on(U-Th)/He thermochronology//Andressien P(ed). 10th International Fission Track Dating Conference, Amsterdam. 40.
Blaise T, Barbarand J, Kars M, et al. 2014. Reconstruction of low burial(［M］b［M］<100℃)in sedimentary basins:A comparison of geothermometer sensibility in the intracontinental Paris Basin［J］. Marine and Petroleum Geology, 53:71-87.
Bourdon B, Turner S, Henderson G M, et al. 2003. Introduction to U-series geochemistry［J］. Reviews in Mineralogy and Geochemistry, 52:1-21.
Bourdon B, Zindler A, Woner G. 1994. Evolution of the Laacher See magma chamber:Evidence from SIMS and TIMS measurements of U-Th disequilibria in minerals and glasses［J］. Earth and Planetary Science Letters, 126:75-90.
Boyce J W, Hodges K V, King D, et al. 2009. Improved confidence in(U-Th)/He thermochronology using the laser microprobe:An example from a Pleistocene leucogranite, Nanga Parbat, Pakistan［J］. Geochemistry, Geophysics, Geosystems, 10:10.1029/2009gc002497.
Braun J, Simon-Labric T, Murray K E, et al. 2014. Topographic relief driven by variations in surface rock density［J］. Nature Geoscience, 7:534-540.
Brown R W, Beucher R, Roper S, et al. 2013. Natural age dispersion arising from the analysis of broken crystals. Part I:Theoretical basis and implications for the apatite(U-Th)/He thermochronometer［J］. Geochimica et Cosmochimica Acta, 122:478-497.
Brown S, Fletcher I R. 1999. SHRIMP U-Pb dating of the preeruption growth history of zircons from the 340ka Whakamaru Ignimbrite, New Zealand:Evidence for >250 ky magma residence times［J］. Geology, 27:1035-1038.
Caddick M J, Kohn M J. 2013. Garnet:Witness to the evolution of destructive plate boundaries［J］. Elements, 9:427-432.
Capaccioni B, Vaselli O, Tassi F, et al. 2011. Hydrogeochemistry of the thermal waters from the Sciacca Geothermal Field(Sicily, southern Italy)［J］. Journal of Hydrology, 396:292-301.
Chew D M, Spiking R A. 2015. Geochronology and thermochronology using apatite:Time and temperature, lower crust to surface［J］. Elements, 11:189-194.
Condomines M, Gauthier P-J, Sigmarsson O. 2003. Timescales of magma chamber processes and dating of young volcanic rocks［J］. Reviews in Mineralogy and Geochemistry, 52:125-174.
Condon D J, Schmitz M D. 2013. One hundred years of isotope geochronology, and counting［J］. Elements, 9:15-17.
Crossey L J, Karlstrom K E, Springer A E, et al. 2009. Degassing of mantle-derived CO₂ and He from springs in the southern Colorado Plateau region:Neotectonic connections and implications for groundwater systems［J］. Geological Society of America Bulletin, 121:1034-1053.
Ehlers T A. 2005. Crustal thermal processes and the interpretation of thermochronometer data［J］. Reviews in Mineralogy and Geochemistry, 58:315-350.
Ehlers T A, Farley K A. 2003. Apatite(U-Th)/He thermochronometry:Methods and applications to problems in tectonic and surface processes［J］. Earth and Planetary Science Letters, 26:1-14.
Ehlers T A, Farley K A, Rusmore M E, et al. 2006. Apatite(U-Th)/He signal of large-magnitude accelerated glacial erosion, southwest British Columbia［J］. Geology, 34:765-768.
Evans N J, Byrne J P, Keegan J T, et al. 2005. Determination of uranium and thorium in zircon, apatite and fluorite:Application to laser(U-Th)/He thermochronology［J］. Journal of Analytical Chemistry, 60:1159-1165.
Evans N J, McInnes B I A, McDonald B, et al. 2015. An in situ technique for(U-Th-Sm)/He and U-Pb double dating［J］. Journal of Analytical Atomic Spectrometry, 30:1636-1645.
Farley K A. 2000. Helium diffusion from apatite:General behavior as illustrated by Durango fluorapatite［J］. Journal of Geophysical Research, 15:2903-2914.
Farley K A, Kohn B, Pillans B. 2002. The effects of secular disequilibrium on(U-Th)/He systematics and dating of Quaternary volcanic zircon and apatite［J］. Earth and Planetary Science Letters, 21:117-125.
Farley K A, Shuster D L, Ketcham R A. 2011. U and Th zonation in apatite observed by laser ablation ICPMS, and implications for the(U-Th)/He system［J］. Geochimica et Cosmochimica Acta, 75:4515-4530.
Farley K A, Stockli D F. 2002. (U-Th)/He dating of phosphates:Apatite, monazite, and xenotime［J］. Reviews in Mineralogy and Geochemistry, 15:559-578.
Farley K A, Wolf R A, Silver L T. 1996. The effects of long alpha-stopping distances on(U-Th)/He ages［J］. Geochimica et Cosmochimica Acta, 60:4223-4229.
Faure G. 1986. Principles of Isotope Geology［M］. Wiley, New York. 589.
Fitzgerald P G, Baldwin S L, Webb L E, et al. 2006. Interpretation of(U-Th)/He single grain ages from slowly cooled crustal terranes:A case study from the Transantarctic Mountains of southern Victoria Land［J］. Chemical Geology, 225:91-120.
Flowers R M, Shuster D L, Wernicke B P, et al. 2007. Radiation damage control on apatite(U-Th)/He dates from the Grand Canyon region, Colorado Plateau［J］. Geology, 35:447-450.
Flowers R M. 2009. Exploiting radiation damage control on apatite(U-Th)/He dates in cratonic regions［J］. Earth and Planetary Science Letters, 277:148-155.
Flowers R M, Wernicke B P, Farley K A. 2008. Unroofing, incision, and uplift history of the southwestern Colorado Plateau from apatite(U-Th)/He thermochronometry［J］. Geological Society of America Bulletin, 120:571-587.
Flowers R M, Kelley S A. 2011. Interpreting data dispersion and "inverted" dates in apatite(U-Th)/He and fission-track datasets:An example from the US midcontinent［J］. Geochimica et Cosmochimica Acta, 75:5169-5186.
Flowers R M, Ketcham R A, Shuster D L, et al. 2009. Apatite(U-Th)/He thermochronometry using a radiation damage accumulation and annealing model［J］. Geochimica et Cosmochimica Acta, 73:2347-2365.
Gautheron C, Barbarand J, Ketcham R A, et al. 2013. Chemical influence on α-recoil damage annealing in apatite:Implications for(U-Th)/He dating［J］. Chemical Geology, 351:257-267.
Gautheron C, Tassan-Got L, Barbarand J, et al. 2009. Effect of alpha-damage annealing on apatite(U-Th)/He thermochronology［J］. Chemical Geology, 266:157-170.
Gautheron C, Tassan-Got L, Ketcham R A, et al. 2012. Accounting for long alpha-particle stopping distances in(U-Th-Sm)/He geochronology:3D modeling of diffusion, zoning, implantation, and abrasion［J］. Geochimica et Cosmochimica Acta, 96:44-56.
Gorynski K E, Walker J D, Stockli D F, et al. 2014. Apatite(U-Th)/He thermochronometry as an innovative geothermal exploration tool:A case study from the southern Wassuk Range, Nevada［J］. Journal of Volcanology and Geothermal Research, 270:99-114.
Green P F, Crowhurst P V, Duddy I R, et al. 2006. Conflicting(U-Th)/He and fission track ages in apatite:Enhanced He retention, not anomalous annealing behaviour［J］. Earth and Planetary Science Letters, 250:407-427.
Green P F, Duddy I R, Gleadow A J W, et al. 1986. Thermal annealing of fission tracks in apatite, 1. A qualitative description［J］. Chemical Geology, 59:237-253.
Harlov D E. 2015. Apatite:A fingerprint for metasomatic processes［J］. Elements, 11:171-176.
Hawkesworth C J, Turner S P, McDermott F, et al. 1997. U-Th isotopes in arc magmas:Implications for element transfer from the subducted crust［J］. Science, 276:551-555.
Hendriks B W H, Redfield T F. 2005. Apatite fission track and(U-Th)/He data from Fennoscandia:An example of underestimation of fission track annealing in apatite［J］. Earth and Planetary Science Letters, 236:443-458.
Hodges K V. 2014. Thermochronology in orogenic systems［J］. Treaties on Geochemistry, 2:281-308.
Hourigan J K, Reiners P W, Brandon M T. 2005. U-Th zonation-dependent alpha-ejection in(U-Th)/He chronometry［J］. Geochimica et Cosmochimica Acta, 69:3349-3365.
House M A, Wernicke B P, Farley K A. 1998. Dating topography of the Sierra Nevada, California, using apatite(U-Th)/He ages［J］. Nature, 396:66-69.
Hughes J M, Cameron M, Crowley K D. 1990. Crystal structures of natural ternary apatites:Solid solution in the Ca₅(PO₄)₃X(X=F, OH, Cl)system［J］. American Mineralogist, 75:295-304.
Hughes J M, Rakovan J F. 2015. Structurally robust, chemically diverse:Apatite and apatite supergroup minerals［J］. Elements, 11:165-170.
Italiano F, Sasmaz A, Yuce G, et al. 2013. Thermal fluids along the east Anatolian fault zone(EAFZ):Geochemical features and relationships with the tectonic setting［J］. Chemical Geology, 339:103-114.
Johnstone S, Hourigan J, Gallagher C. 2013. LA-ICP-MS depth profile analysis of apatite:Protocol and implications for(U-Th)/He thermochronometry［J］. Geochimica et Cosmochimica Acta, 19:143-161.
Ketcham R A, Carter A, Donelick R A, et al. 2007. Improved modeling of fission-track annealing in apatite［J］. American Mineralogist, 92:799-810.
Ketcham R A, Gautheron C, Tassan-Got L. 2011. Accounting for long alpha-particle stopping distances in(U-Th-Sm)/He geochronology:Refinement of the baseline case［J］. Geochimica et Cosmochimica Acta, 75:7779-7791.
Manga M. 2001. Using springs to study groundwater flow and active geologic processes［J］. Annual Review of Earth and Planetary Sciences, 29:201-228.
Manighetti I, Campillo M, Bouley S, et al. 2007. Earthquake scaling, fault segmentation, and structural maturity［J］. Earth and Planetary Science Letters, 253:429-438.
Mbongo-Djimbi D, Gautheron C, Roques J, et al. 2015. Impact of apatite chemical composition on(U-Th)/He thermochronometry:An atomistic point of view［J］. Geochimica et Cosmochimica Acta, 167:162-176.
McInnes B I A, Farley K A, Sillitoe R H. 1999. Application of apatite(U-Th)/He thermochronometry to the determination of the sense and amount of vertical fault displacement at the Chuquicamata porphyry copper deposit, Chile［J］. Economic Geology, 94:937-948.
Min K, Reiners P W, Nicolescu S, et al. 2004. Age and temperature of shock metamorphism of Martian meteorite Los Angeles from(U-Th)/He thermochronometry［J］. Geology, 32:677-680.
Mitchell S G, Reiners P W. 2003. Influence of wildfires on apatite and zircon(U-Th)/He ages［J］. Geology, 31:1025-1028.
Murray K E, Orme D A, Reiners P W. 2014. Effects of U-Th-rich grain boundary phases on apatite helium ages［J］. Chemical Geology, 390:135-151.
Newell D L, Jessup M J, Cottle J M, et al. 2008. Aqueous and isotope geochemistry of mineral springs along the southern margin of the Tibetan plateau:Implications for fluid sources and regional degassing of CO₂［J］. Geochemisty Geophysics Geosystems, 9:10.1029/2008gc002021.
Reiners P W, Ehlers T A, Mitchell S G, et al. 2003. Coupled spatial variations in precipitation and long-term erosion rates across the Washington Cascades［J］. Nature, 426:645-647.
Reiners P W, Farley K A. 2001. Influence of crystal size on apatite(U-Th)/He thermochronology:An example from the Bighorn Mountains, Wyoming［J］. Earth and Planetary Science Letters, 188:413-420.
Reiners P W, Farley K A, Hickes H J. 2002. (U-Th)/He thermochronometry of zircon:Initial results from the Gold Butte Block, Nevada and Fish Canyon Tuff［J］. Tectonophysics, 349:297-308.
Reiners P W, Nicolescu S. 2006. Measurement of parent nuclides for(U-Th)/He chronometry by solution sector ICP-MS, ARHDL Report 1. http://www.geo.arizona.edu/~reiners/arhdl/arhdl.htm.
Reiners P W, Thomson S N, McPhillips D, et al. 2007. Wildfire thermochronology and the fate and transport of apatite in hillslope and fluvial environments［J］. Journal of Geophysical Research, 112:F04001. doi:10.1029/2007JF000759.
Rutherford E. 1905. Present problem in radioactivity［J］. Popular Science(May):1-34.
Sano Y, Wakita H. 1985. Geographical distribution of³ He/⁴ He ratios in Japan:Implications for arc tectonics and incipient magmatism［J］. Journal of Geophysical Research, 90:8729-8741.
Schoene B, Condon D J, Morgan L, et al. 2013. Precision and accuracy in geochronology［J］. Elements, 9:19-24.
Shuster D L, Cuffey K M, Sanders J W, et al. 2011. Thermochronometry reveals headward propagation of erosion in an alpine landscape［J］. Science, 332:84-88.
Shuster D L, Farley K A. 2009. The influence of artificial radiation damage and thermal annealing on helium diffusion kinetics in apatite［J］. Geochimica et Cosmochimica Acta, 73:183-196.
Shuster D L, Flowers R M, Farley K A. 2006. The influence of natural radiation damage on helium diffusion kinetics in apatite［J］. Earth and Planetary Science Letters, 249:148-161.
Soulet S, Chaumont J, Krupa J C, et al. 2001. Determination of the defect creation mechanism in fluroroapatite［J］. Journal of Nuclear Materials, 289:194-198.
Spiegel C, Kohn B, Belton D, et al. 2009. Apatite(U-Th-Sm)/He thermochronology of rapidly cooled samples:The effect of He implantation［J］. Earth and Planetary Science Letters, 285:105-114.
Stock G M, Ehlers T A, Farley K A. 2006. Where does sediment come from? Quantifying catchment erosion with detrital apatite(U-Th)/He thermochronometry［J］. Geology, 34:725-728.
Stockli D F, Farley K A, Dumitru T A. 2000. Calibration of the apatite(U-Th)/He thermochronometer on an exhumed fault block, White Mountains, California［J］. Geology, 28:983-986.
Thomson S N, Brandon M T, Tomkin J H, et al. 2010. Glaciation as a destructive and constructive control on mountain building［J］. Nature, 467:313-317.
Tripathy-Lang A, Hodges K V, Monteleone B D, et al. 2013. Laser(U-Th)/He thermochronology of detrital zircons as a tool for studying surface processes in modern catchments［J］. Journal of Geophysical Research:Earth Surface, 118:1333-1341.
Turner M G, Romme W H, Tinker D B. 2003. Surprises and lessons from the 1988 Yellowstone fires［J］. Frontiers in Ecology and the Environment, 1:351-358.
Warnock A C, Zeitler P K, Wolf R A, et al. 1997. An evaluation of low temperature apatite U-Th/He thermochronometry［J］. Geochimica et Cosmochimica Acta, 61:5371-5377.
Vermeesch P. 2010. HelioPlot, and the treatment of overdispersed(U-Th-Sm)/He data［J］. Chemical Geology, 271:108-111.
Vermeesch P, Seward D, Latkoczy C, et al. 2007. α-Emitting mineral inclusions in apatite, their effect on(U-Th)/He ages, and how to reduce it［J］. Geochimica et Cosmochimica Acta, 71:1737-1746.
Wolf R A, Farley K A, Kass D M, 1998. Modeling of the temperature sensitivity of the apatite(U-Th)/He thermochronometer［J］. Chemical Geology, 148:105-114.
Wolf R A, Farley K A, Silver L T, 1996. Helium diffusion and low-temperature thermochronometry of apatite［J］. Geochimica et Cosmochimica Acta, 60:4231-4240.
Ziegler J F. 2008. SRIM-2008 The Stopping Range of Ions in Matter［M］. United States Naval Academy, Annapolis.

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