Maximum depositional age estimation revisited
-
摘要: In a recent review published in this journal, Coutts et al. (2019) compared nine different ways to estimate the maximum depositional age (MDA) of siliclastic rocks by means of detrital geochronology. Their results show that among these methods three are positively and six negatively biased. This paper investigates the cause of these biases and proposes a solution to it. A simple toy example shows that it is theoretically impossible for the reviewed methods to find the correct depositional age in even a best case scenario: the MDA estimates drift to ever smaller values with increasing sample size. The issue can be solved using a maximum likelihood model that was originally developed for fission track thermochronology by Galbraith and Laslett (1993). This approach parameterises the MDA estimation problem with a binary mixture of discrete and continuous distributions. The ‘Maximum Likelihood Age’ (MLA) algorithm converges to a unique MDA value, unlike the ad hoc methods reviewed by Coutts et al. (2019). It successfully recovers the depositional age for the toy example, and produces sensible results for realistic distributions. This is illustrated with an application to a published dataset of 13 sandstone samples that were analysed by both LA-ICPMS and CA-TIMS U-Pb geochronology. The ad hoc algorithms produce unrealistic MDA estimates that are systematically younger for the LA-ICPMS data than for the CA-TIMS data. The MLA algorithm does not suffer from this negative bias. The MLA method is a purely statistical approach to MDA estimation. Like the ad hoc methods, it does not readily accommodate geological complications such as post-depositional Pb-loss, or analytical issues causing erroneously young outliers. The best approach in such complex cases is to re-analyse the youngest grains using more accurate dating techniques. The results of the MLA method are best visualised on radial plots. Both the model and the plots have applications outside detrital geochronology, for example to determine volcanic eruption ages.
-
关键词:
- Zircon /
- U-Pb /
- Geochronology /
- Statistics /
- Maximum depositional age
Abstract: In a recent review published in this journal, Coutts et al. (2019) compared nine different ways to estimate the maximum depositional age (MDA) of siliclastic rocks by means of detrital geochronology. Their results show that among these methods three are positively and six negatively biased. This paper investigates the cause of these biases and proposes a solution to it. A simple toy example shows that it is theoretically impossible for the reviewed methods to find the correct depositional age in even a best case scenario: the MDA estimates drift to ever smaller values with increasing sample size. The issue can be solved using a maximum likelihood model that was originally developed for fission track thermochronology by Galbraith and Laslett (1993). This approach parameterises the MDA estimation problem with a binary mixture of discrete and continuous distributions. The ‘Maximum Likelihood Age’ (MLA) algorithm converges to a unique MDA value, unlike the ad hoc methods reviewed by Coutts et al. (2019). It successfully recovers the depositional age for the toy example, and produces sensible results for realistic distributions. This is illustrated with an application to a published dataset of 13 sandstone samples that were analysed by both LA-ICPMS and CA-TIMS U-Pb geochronology. The ad hoc algorithms produce unrealistic MDA estimates that are systematically younger for the LA-ICPMS data than for the CA-TIMS data. The MLA algorithm does not suffer from this negative bias. The MLA method is a purely statistical approach to MDA estimation. Like the ad hoc methods, it does not readily accommodate geological complications such as post-depositional Pb-loss, or analytical issues causing erroneously young outliers. The best approach in such complex cases is to re-analyse the youngest grains using more accurate dating techniques. The results of the MLA method are best visualised on radial plots. Both the model and the plots have applications outside detrital geochronology, for example to determine volcanic eruption ages.-
Keywords:
- Zircon /
- U-Pb /
- Geochronology /
- Statistics /
- Maximum depositional age
-
-
[1] Barbeau, L., David, Olivero, E.B., Swanson-Hysell, N.L., Zahid, K.M., Murray, K.E., Gehrels, G.E., 2009. Detrital-zircon geochronology of the eastern Magallanes foreland basin: implications for Eocene kinematics of the northern Scotia Arc and Drake Passage. Earth Planet Sci. Lett. 284 (3-4), 489-503. https://doi.org/10.1016/j.epsl.2009.05.014.
[2] Chen, W.-S., Huang, Y.-C., Liu, C.-H., Feng, H.-T., Chung, S.-L., Lee, Y.-H., 2016. U-Pb zircon geochronology constraints on the ages of the Tananao Schist Belt and timing of orogenic events in Taiwan: implications for a new tectonic evolution of the South China Block during the Mesozoic. Tectonophysics 686, 68-81. https://doi.org/10.1016/j.tecto.2016.07.021.
[3] Cherniak, D., Watson, E., 2001. Pb diffusion in zircon. Chem. Geol. 172 (1-2), 5-24.
[4] Copeland, P., 2020. On the use of geochronology of detrital grains in determining the time of deposition of clastic sedimentary strata. Basin Res. https://doi.org/10.1111/BRE.12441.
[5] Coutts, D.S., Matthews, W.A., Hubbard, S.M., 2019. Assessment of widely used methods to derive depositional ages from detrital zircon populations. Geosci. Front. 10 (4), 1421-1435.
[6] Dickinson, W., Gehrels, G., 2009. U-Pb ages of detrital zircons in Jurassic eolian and associated sandstones of the Colorado Plateau: evidence for transcontinental dispersal and intraregional recycling of sediment. Geol. Soc. Am. Bull. 121, 408-433.https://doi.org/10.1130/B26406.1.
[7] Galbraith, R.F., 1990. The radial plot: graphical assessment of spread in ages. Nucl. Tracks Radiat. Meas. 17, 207-214.
[8] Galbraith, R.F., Green, P.F., 1990. Estimating the component ages in a finite mixture.Nucl. Tracks Radiat. Meas. 17, 197-206.
[9] Galbraith, R.F., 2005. Statistics for Fission Track Analysis. CRC Press.Galbraith, R., 1988. Graphical display of estimates having differing standard errors.Technometrics 30 (3), 271-281.
[10] Galbraith, R., Laslett, G., 1993. Statistical models for mixed fission track ages. Nucl.Tracks Radiat. Meas. 21 (4), 459-470.
[11] Gehrels, G., 2003. AgePick. https://sites.google.com/a/laserchron.org/laserchron/home/Last. (Accessed 5 June 2020).
[12] Gehrels, G., Giesler, D., Olsen, P., Kent, D., Marsh, A., Parker, W., Rasmussen, C., Mundil, R., Irmis, R., Geissman, J., Lepre, C., 2020. LA-ICPMS U-Pb geochronology of detrital zircon grains from the Coconino, Moenkopi, and Chinle formations in the Petrified Forest National Park (Arizona). Geochronology 2, 257-282.
[13] Herriott, T.M., Crowley, J.L., Schmitz, M.D., Wartes, M.A., Gillis, R.J., 2019. Exploring the law of detrital zircon: LA-ICP-MS and CA-TIMS geochronology of Jurassic forearc strata, Cook Inlet, Alaska, USA. Geology 47 (11), 1044-1048.
[14] Keller, C.B., Schoene, B., Samperton, K.M., 2018. A stochastic sampling approach to zircon eruption age interpretation. Geochem. Perspect. Lett. 8, 31-35. https://doi.org/10.7185/geochemlet.1826.
[15] Ludwig, K.R., 1998. On the treatment of concordant uranium-lead ages. Geochem.Cosmochim. Acta 62, 665-676. https://doi.org/10.1016/S0016-7037(98)00059-3.
[16] Ludwig, K., Mundil, R., 2002. Extracting reliable U-Pb ages and errors from complex populations of zircons from Phanerozoic tuffs. Geochem. Cosmochim. Acta 66, A463.
[17] Ludwig, K.R., 2003. User’s manual for Isoplot 3.00: A geochronological toolkit for Microsoft Excel, vol. 4. Berkeley Geochronology Center, Special Publication.
[18] Nelson, D.R., 2001. An assessment of the determination of depositional ages for Precambrian clastic sedimentary rocks by U-Pb dating of detrital zircons. Sediment.Geol. 141, 37-60.
[19] Nemchin, A.A., Cawood, P.A., 2005. Discordance of the U-Pb system in detrital zircons:implication for provenance studies of sedimentary rocks. Sediment. Geol. 182, 143-162. https://doi.org/10.1016/j.sedgeo.2005.07.011.
[20] Rasmussen, C., Mundil, R., Irmis, R.B., Geisler, D., Gehrels, G.E., Olsen, P.E., Kent, D.V., Lepre, C., Kinney, S.T., Geissman, J.W., Parker, W.G., 2020. U-Pb zircon geochronology and depositional age models for the Upper Triassic Chinle Formation(Petrified Forest National Park, Arizona, USA): implications for Late Triassic paleoecological and paleoenvironmental change. GSA Bulletin. https://doi.org/10.1130/B35485.1.
[21] Ross, J.B., Ludvigson, G.A., Möller, A., Gonzalez, L.A., Walker, J., 2017. Stable isotope paleohydrology and chemostratigraphy of the Albian Wayan Formation from the wedge-top depozone, North American Western Interior Basin. Sci. China Earth Sci. 60(1), 44-57.
[22] Sambridge, M.S., Compston, W., 1994. Mixture modeling of multi-component data sets with application to ion-probe zircon ages. Earth Planet Sci. Lett. 128, 373-390.https://doi.org/10.1016/0012-821X(94)90157-0.
[23] Titterington, D.M., Halliday, A.N., 1979. On the fitting of parallel isochrons and the method of maximum likelihood. Chem. Geol. 26, 183-195.
[24] Tucker, R.T., Roberts, E.M., Hu, Y., Kemp, A.I., Salisbury, S.W., 2013. Detrital zircon age constraints for the Winton Formation, Queensland: contextualizing Australia’s Late Cretaceous dinosaur faunas. Gondwana Res. 24 (2), 767-779.
[25] van der Touw, J., Galbraith, R., Laslett, G., 1997. A logistic truncated normal mixture model for overdispersed binomial data. J. Stat. Comput. Simulat. 59 (4), 349-373.
[26] Vermeesch, P., 2009. RadialPlotter: a Java application for fission track, luminescence and other radial plots. Radiat. Meas. 44 (4), 409-410.
[27] Vermeesch, P., 2012. On the visualisation of detrital age distributions. Chem. Geol. 312-313, 190-194. https://doi.org/10.1016/j.chemgeo.2012.04.021.
[28] Vermeesch, P., 2018a. Dissimilarity measures in detrital geochronology. Earth Sci. Rev. 178, 310-321. https://doi.org/10.1016/j.earscirev.2017.11.027.
[29] Vermeesch, P., 2018b. IsoplotR: a free and open toolbox for geochronology. Geosci. Front. 9, 1479-1493.
[30] York, D., Evensen, N.M., Martínez, M.L., De Basabe Delgado, J., 2004. Unified equations for the slope, intercept, and standard errors of the best straight line. Am. J. Phys. 72(3), 367-375.
[31] Zhang, X., Pease, V., Skogseid, J., Wohlgemuth-Ueberwasser, C., 2016. Reconstruction of tectonic events on the northern Eurasia margin of the Arctic, from U-Pb detrital zircon provenance investigations of late Paleozoic to Mesozoic sandstones in southern Taimyr Peninsula. GSA Bulletin 128 (1-2), 29-46.
计量
- 文章访问数: 375
- HTML全文浏览量: 99
- PDF下载量: 2
下载:
