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...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.展开更多
In the Lower CretaceousMcMurray-Clearwater succession of the intracontinental Alberta Foreland Basin,Canada,detrital zircon U-Pb geochronology samples(referred to herein as DZ samples)have been used to interpret the s...In the Lower CretaceousMcMurray-Clearwater succession of the intracontinental Alberta Foreland Basin,Canada,detrital zircon U-Pb geochronology samples(referred to herein as DZ samples)have been used to interpret the strata as representing a paleo-continental-scale drainage system.However,the majority of DZ samples are relatively small(n≈90–100),and syndepositional DZ(i.e.,crystallization age<5 Ma older than depositional age)are rare.This has forced a reliance on dinocysts with long stratigraphic ranges to chronostratigraphically subdivide the McMurray-Clearwater succession rather than employing maximum depositional ages(MDAs)derived from DZ samples.Herein,43 DZ samples(taken from20 subsurface cores)are assigned to 1 of 5 stratigraphic intervals,and in each stratigraphic interval all associated DZ samples are combined to produce a grouped DZ sample.Analysis and comparison of individual and grouped DZ samples are used to(1)assess variability in provenance through time and space,and(2)assess the accuracy of chronostratigraphically subdividing the succession using MDAs.Along the main paleo-drainage axis,a comparison of dissimilarity between DZ samples from the same stratigraphic interval,as well as between stratigraphic intervals,reveals increasing average dissimilarity between individual DZ samples and their respective grouped DZ samplewith increasing spatial separation of samples.These data indicate that in the McMurray Depocenter some sediment is sourced from local tributaries,leading to geographical provenance variability.CalculatedMDAs for all 43 DZ samples and groupedMDAs(gMDAs)for the 5 grouped DZ samples are compared to an ash-derived absolute age and existing biostratigraphy.In theMcMurray Formation,comparison of MDAs to gMDAs shows that in basins with rare syndepositional DZ,the gMDA method improved depositional age estimates by transforming low-confidence MDAs(e.g.,youngest single grains)into high-confidence(multi-grain)gMDAs.In the Clearwater Formationwhere syndepositional DZ are plentiful(i.e.,>5%of the total DZ population),calculating maximumlikelihood ages fromgrouped DZ samples avoids negatively biased(i.e.,too young)MDAs.We suggest grouped DZ samples and the gMDA method be used in systems with multiple DZ samples from a well-defined stratigraphic interval as a means of assessing variability in provenancewithin a depositional system and for improving estimates of depositional ages using DZ.展开更多
基金NERC standard grant#NE/T001518/1(‘Beyond Isoplot’).
文摘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.
基金We acknowledge BP plc,Cenovus Energy,Husky Energy,Nexen CNOOC Ltd.,and Woodside Energy Ltd.for funding the McMurray Research Consortium,and GeoLOGIC for providing the GeoScout software used in this study.
文摘In the Lower CretaceousMcMurray-Clearwater succession of the intracontinental Alberta Foreland Basin,Canada,detrital zircon U-Pb geochronology samples(referred to herein as DZ samples)have been used to interpret the strata as representing a paleo-continental-scale drainage system.However,the majority of DZ samples are relatively small(n≈90–100),and syndepositional DZ(i.e.,crystallization age<5 Ma older than depositional age)are rare.This has forced a reliance on dinocysts with long stratigraphic ranges to chronostratigraphically subdivide the McMurray-Clearwater succession rather than employing maximum depositional ages(MDAs)derived from DZ samples.Herein,43 DZ samples(taken from20 subsurface cores)are assigned to 1 of 5 stratigraphic intervals,and in each stratigraphic interval all associated DZ samples are combined to produce a grouped DZ sample.Analysis and comparison of individual and grouped DZ samples are used to(1)assess variability in provenance through time and space,and(2)assess the accuracy of chronostratigraphically subdividing the succession using MDAs.Along the main paleo-drainage axis,a comparison of dissimilarity between DZ samples from the same stratigraphic interval,as well as between stratigraphic intervals,reveals increasing average dissimilarity between individual DZ samples and their respective grouped DZ samplewith increasing spatial separation of samples.These data indicate that in the McMurray Depocenter some sediment is sourced from local tributaries,leading to geographical provenance variability.CalculatedMDAs for all 43 DZ samples and groupedMDAs(gMDAs)for the 5 grouped DZ samples are compared to an ash-derived absolute age and existing biostratigraphy.In theMcMurray Formation,comparison of MDAs to gMDAs shows that in basins with rare syndepositional DZ,the gMDA method improved depositional age estimates by transforming low-confidence MDAs(e.g.,youngest single grains)into high-confidence(multi-grain)gMDAs.In the Clearwater Formationwhere syndepositional DZ are plentiful(i.e.,>5%of the total DZ population),calculating maximumlikelihood ages fromgrouped DZ samples avoids negatively biased(i.e.,too young)MDAs.We suggest grouped DZ samples and the gMDA method be used in systems with multiple DZ samples from a well-defined stratigraphic interval as a means of assessing variability in provenancewithin a depositional system and for improving estimates of depositional ages using DZ.
