Strontium isotope stratigraphy

warth and G.A. Shields Chapter 7
J.M. McArthur, R.J. Ho
The Geologic Time Scale 2012. DOI: 10.1016/B978-0-444-59425-9.00007-X

Copyright � 2012 Felix M. Gradstein, James G. Ogg, Mark Schmitz and Gabi Ogg. Published by Elsevier B.V. All rights reserved.

Strontium Isotope Stratigraphy

Abstract: The 87Sr/86Sr value of Sr dissolved in the world’soceans varied though time in a known way, facts that allow87Sr/86Sr to be used to date and to correlate marine

sedimentary rocks worldwide. In this work, the variation in87Sr/86Sr is displayed graphically and the theory and practiceof the methodology is discussed.

Chapter Outline

7.1. Introduction 127

7.2. Materials for Strontium Isotope Stratigraphy 128

7.3. The Databases Used for this Volume 129

7.4. Numerical Ages 129

7.5. Fitting the Lowess Database 130

7.6. The Quality of the Fit 134

7.6.1. Standards and Inter-Laboratory Bias 134

7.6.2. Confidence Limits on the LOWESS Fit 134

7.6.3. Confidence Limits on Measured 87Sr/86Sr 135

7.6.4. Numerical Resolution of the Fitted Curve 136

7.7. Rubidium Contamination 136

7.8. Comments on the Lowess Fit 136

7.9. Sr-Isotope Stratigraphy for Pre-Ordovician Time 139

References 141

7.1. INTRODUCTION

The ability to date and correlate sediments using Sr(strontium) isotope ratios (invariably 87Sr/86Sr) relies on thefact that the 87Sr/86Sr value of Sr dissolved in the world’soceans has varied over time. In Figure 7.1, this variation isshown plotted using the time scale given in this volume.More detailed plots are given in Figure 7.2, and Table 7.1tabulates the sources of the 4119 data-pairs used to plot thecurves in Figures 7.1 and 7.2. Comparison of the measured87Sr/86Sr of Sr in a marine mineral with these calibrationcurves can yield a numerical age for the mineral. Thedegree to which numerical dating with strontium isotopestratigraphy (SIS) can be accomplished rests, in part, onhow well the trend in marine-87Sr/86Sr through rock can beturned into a trend through time. For reviews of SIS, thereader is referred to McArthur (1994) and Veizer et al.(1997, 1999).

Correlation can be accomplished by comparison of the87Sr/86Sr trends in samples from more than one section(Figure 7.3). Correlation avoids the need for a calibrationcurve of 87Sr/86Sr against numerical age, but when corre-lating with 87Sr/86Sr it is useful to know that at least someparts of each section overlap in age in order to avoidmiscorrelation. Knowing the approximate age of a sectionalso avoids wasting time and money trying to date orcorrelate with 87Sr/86Sr during times when marine-87Sr/86Sr

was changing little, or not at all (e.g., in Middle Devoniantimes; van Geldern et al., 2006). Other uses for SIS includeestimating the duration of stratigraphic gaps (Miller et al.,1988; Brasier et al., 1996), biozones (McArthur et al., 1993,2000a) and Stages (Weedon and Jenkyns, 1999), andrevealing changes in sedimentation rate (McArthur et al.,2000, 2007; Figure 7.4).

The method works only for marine minerals. It rests on theassumption that the world’s oceans are homogeneous withrespect to 87Sr/86Sr and always have been so. Such uniformity of87Sr/86Sr is expected, because the residence time of Sr in theoceans today (z 106 years) is far longer than the time it takescurrents to mix the oceans (z 103 years), so the oceans arethoroughly mixed on time scales that are short relative to therates of gain and loss of strontium. The degree towhich this wastrue in past times is not known. Measured values of 87Sr/86Sr inmodern open oceans, and some large but restricted seawayssuch as Hudson’s Bay and the Baltic Sea, are indeed uniformfor salinities down to 20 psu (DePaolo and Ingram, 1985;Andersson et al., 1992; Paytan et al., 1993)whenmeasured at ananalytical precision of � 0.000 020. Today, values of 87Sr/86Srcan be measured to a precision of� 0.000 003 (for the mean ofreplicate analyses), so a further test is overdue of the assumptionof oceanic uniformity in 87Sr/86Sr.

When rivers locally lower the salinity of seawater,marine-87Sr/86Sr is rarely altered at salinities above 20 psu,a salinity at which a moderately diverse marine invertebrate

127

Cenozoic Cretaceous Jura Trias Perm Carb Devon Sil Ord Camb Ediacaran Cryogenian

0.7095

0.7085

0.7080

0.7075

0.7070

0.7065

0.7060

0.7055

0.7050

0.7090

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850

87Sr

/ 86

Sr

Numerical Age, Ma

Red = Table 7.1Black = Table 7.2

FIGURE 7.1 Variation of 87Sr/86Sr through time: LOWESS fit to data sources in Table 7.1 for Phanerozoic (post-Cambrian) time, trend from data in

Table 7.2 for pre-Ordovician time.

128 The Geologic Time Scale 2012

fauna may live (Bryant et al., 1995). Nevertheless, whendating coastal and shallow water faunas, it is wise to establishthat the local riverine inputs did not alter the 87Sr/86Sr ofseawater in the depositional environment.

Before being reported, measured isotopic ratiosfor 87Sr/86Sr are normalized to a standard value of 0.1194 for86Sr/88Sr. This procedure corrects for the large isotopicfractionations between 84Sr, 86Sr, 87Sr and 88Sr that occurduring mass-spectrometric measurement and, coincidentally,removes any natural fractionation. Nevertheless, the frac-tionations can be measured using (presently) non-standardtechniques (e.g., Fietzke and Eisenhauer, 2006) and theresulting un-normalized isotopic data have application insome research fields (e.g., Krabbenhoft et al., 2010).

7.2. MATERIALS FOR STRONTIUMISOTOPE STRATIGRAPHY

Most of the Neogene Sr-calibration curve is based on analysisof foraminiferal calcite, largely from DSDP/ODP sites(e.g., works by Farrell 1995; Hodell 1991,1994; and Millerand their collaborators 1988, 1991; Table 7.1). For Mesozoicand Paleozoic sedimentary rocks, the most useful sample

media have proven to be belemnite guards (Jones et al.,1994a,b) and brachiopod shells (Veizer et al., 1999), becauseboth materials resist diagenesis well. Acid-leached nanno-fossil ooze (McArthur et al., 1993), ammonoid aragonite(McArthur et al., 1994), atoll carbonates (Jenkyns et al.,1995) and inoceramid prisms (Bralower et al., 1997) have allyielded good data in the middle to late Mesozoic. Attempts touse barite met with mixed success (Paytan et al., 1993; Martinet al., 1995; Mearon et al., 2003). The use of conodonts forPaleozoic studies has proven problematic; some samples witha low color-alteration index (around 1), where minimalalteration is implied (Martin and Macdougall, 1995), appearto be abnormally high in 87Sr/86Sr, whilst others appear morein line with expected results (e.g., Ruppel et al., 1996).

For strata of Cambrian age and older, when biogeniccalcite and apatitewere all but absent, samples comprise eitherbulk micrite or early-diagenetic marine cement (the latterrarely used in the Phanerozoic, but see Carpenter et al., 1991).Trilobite calcite is largely untested as a medium, but may havepotential for Cambrian studies. The heterogeneous nature ofpre-Ordovician bulk carbonate means that diageneticscreening is less diagnostic of alteration than it is for Phan-erozoic biogenic calcite. Few studies report multiple 87Sr/86Sr

87

Sr / 86

Sr

87

Sr / 86

Sr

0.70750

0.70800

0.70850

0.70900

0 10 20 30 40 50 60 70 80 90 100 110 120 130

0.70680

0.70700

0.70720

0.70740

0.70760

0.70780

0.70800

140 150 160 170 180 190 200 210 220 230 240 250 260

Ol In C Wu Capit

Numerical age, Ma

Cretaceous (part)

Quat

Neogene

Jurassic

Triassic

Cret

(part)

Perm

(part)

Paleogene

FIGURE 7.2 Details of 87Sr/86Sr through time for data listed in Table 7.1, together with the mean LOWESS fitted line through the data.

129Chapter | 7 Strontium Isotope Stratigraphy

from a single stratigraphic horizon so as to allow a thoroughanalysis of diagenetic alteration. Bulk rock also alwayscontains impurities that affect measured 87Sr/86Sr. Preleachingthe sample with, for example, ammonium acetate, mayremove some of the Rb and radiogenic Sr in non-carbonatephases; for example, that on easily exchangeable sites in clayminerals. As a consequence of these problems, assessments ofdiagenetic alteration are made on a sample-by-sample basis,and the assumption made that trends of 87Sr/86Sr may beextrapolated from what are assessed to be the least-alteredsamples. As a consequence, secular trends can sometimes notbe distinguished from post-depositional effects.

7.3. THE DATABASES USED FOR THISVOLUME

Data for post-Cambrian time, used for the LOWESS fit that isshown in Figure 7.1 and diagrams for Phanerozoic time, werecompiled by J.M. McArthur from the sources tabulated in

Table 7.1. The database is updated from McArthur andHowarth (2004) and uses 4119 data pairs. The fitted trendthrough that data, together with fitted 95% confidence inter-vals on the fitted line, is available in electronic format [email protected]. A separate database (the Bochum-Ottawa Database; Veizer et al., 1999; Shields and Veizer,2002; Prokoph et al., 2008) details over 5000 87Sr/86Sr resultsfor Phanerozoic and Precambrian time and, updated usingreferences in Table 7.1, was used to plot 87Sr/86Sr against timefor pre-Ordovician times.

7.4. NUMERICAL AGES

The calibration curve given here (Figures 7.1 and 7.2) usesthe GTS2012 time scale of this volume. Where original datawere reported to other time scales, the original ages havebeen converted to the current time scale by appropriate(usually linear) scaling between the nearest pair of numer-ically dated stratigraphic tie points. The tie points are

87

Sr / 86

Sr

87

Sr / 86

Sr

260 270 280 290 300 310 320 330 340 350 360 370 380 390

Cap W R Kung Artinkian Sak As Gz Ka Mosco Bashk Serpuk Visean Tournasian Famennian Frasnain Giv Eifel

0.70770

0.70800

0.70830

0.70890

0.70920

400 420 440 460 480 500Numerical age, Ma

0.70860

EmsianEif Pr Loch P L G H S Tel A Rh H Katian Sand Darriwil Dap Floian Tremad 10 Jiang Pa Gu Dru 5

Gor

stia

n

0.70680

0.70700

0.70720

0.70740

0.70760

0.70780

0.70800

0.70820 Permian

(part)

Carboniferous

Silurian Ordovician

Cambrian

(part)

Devonian

(part)

Devonian

(part)

FIGURE 7.2 (Continued).


mostly period, epoch or stage/substage boundaries for theMesozoic and Paleozoic, supplemented by zone and chronboundaries in the Cenozoic. In some instances, where thelocal or regional stratigraphy has been revised sincethe publication of a source of data, we have updated thebiostratigraphic and numerical age model used in originalpublications.

The calibration curve shown in Figures 7.1 and 7.2 isbased on the measurement of 87Sr/86Sr in samples dated bybiostratigraphy, magnetostratigraphy and astrochronology.Assigning numerical ages to sedimentary rocks by thesemethods is not straightforward. In Figure 7.4, we illustrategraphically how sedimentation rate links to the rate of changein marine-87Sr/86Sr through time. It is the rate of change of87Sr/86Sr with stratigraphic level in a section that is measured.Turning that into a rate of change of 87Sr/86Sr through time isseldom easy.

The calibration curve incorporates all the uncertainties onthe original numerical ages for the data used, including theproblems inherent in the interpolation, extrapolation andindirect stratigraphic correlations necessary for age assign-ment. These include problems of boundary recognition (bothbio- and magnetostratigraphic), diachroneity, and assump-tions concerning sedimentation rate. Furthermore, mostMesozoic and Paleozoic age models are still based onradiometric dates and are no more accurate than those dates.

7.5. FITTING THE LOWESS DATABASE

For the post-Ordovician data, we fitted the calibration line todata using the statistical non-parametric regression methodLOWESS (LOcally WEighted Scatterplot Smoother ofCleveland, 1979; Chambers et al., 1983; Thisted, 1988;Cleveland et al., 1992) to obtain a best-fit curve for the

TABLE 7.1 Data for the Phanerozoic Interval: 4119 Data-Pairs

Author Normalizer (�106) Age Range Ma Interval

Ando et al. (2011): ODP 1120 �2 7 19 Miocene

Azmy et al. (1999) 30 420 443 Silurian

Bralower et al. (1997): DSDP 511 inoceramids 0 94 117 Aptian & Albian

Brand and Brenckle (2001): some 0 317 319 Miss. / Penn. Bdy.

Bruckschen et al. (1999): not USA data 30 332 353 Carboniferous

Callomon and Dietl (2000) 0 166.0 166.2 Callov. / Bathonian Bdy.

Carpenter et al. (1991) 3 372.2 Devonian tie-point

Clemens et al. (1993, 1995) �6 0 0.2 Recent

Cramer et al. (2011) �2 424 432 Silurian

Cummins and Elderfield (1994): brachiopods 11 331 334 Carboniferous

Denison et al. (1993) 102 43 64 Paleogene

Denison et al. (1994) 102 251 358 Carb. & Permian

Denison et al. (1997) 102 360 440 Silurian & Devonian

Denison et al. (1998) 102 445 488 Ordovician

DePaolo and Ingram (1985) �59 39 64 Paleogene

Ebneth et al. (2001): Texas and Australia 33 484 490 Cambrian / Ord. Bdy.

M. Engkilde, pers. comm. (1998) 0 144 176 Early Jurassic

Farrell et al. (1995): ODP 758 (part) �9 0 7 Neogene

Gao and Land (1991): new age model 108 470 491 Cambrian & Ordovician

Henderson et al. (1994) 17 0 0.4 Recent

Hesselbo et al. (2000) 0 190.8 Sinemur. / Pliensbach. Bdy.

Hodell et al. (1991): DSDP 588 and 588A 18 7 18 Miocene

Hodell and Woodruff (1994): DSDP 289 18 11 23 Miocene

Jenkyns et al. (1995) �12 102 126 Aptian & Albian

Jones et al. (1994a, b): UK; some 22 100 204 Jurassic

Koepnick et al. (1990) 102 203 251 Triassic

Korte et al. (2003) 25 204 252 Triassic

Korte et al. (2004) 25 250 254 PermoeTriassic Bdy.

Korte et al. (2006) 25 254 299 Permian

Martin and Macdougall (1995) �12 249 300 Permian

Martin et al. (1999): <13.8 Ma. ODP 926(part)

22 5 14 Miocene

McArthur and Kennedy (unpub. data) 0 97 112 Cenomanian & Albian

McArthur et al. (1994): US Western Interior 0 70 84 Campanian & Maastr.

McArthur et al. (1998): Denmark & Antarctica 0 65 69 Cret / Paleogene. Bdy.

McArthur et al. (2000a, unpub. data): UK. 0 174 185 Pliensbachian & Toarcian

(Continued)


TABLE 7.1 Data for the Phanerozoic Interval: 4119 Data-Pairsdcont’d

Author Normalizer (�106) Age Range Ma Interval

McArthur et al. (2000b): Skye, UK. 0 169 173 Aalenian / Bajocian Bdy.

McArthur et al. (2004): Speeton, UK 0 126 134 Hauterivian & Barremian

McArthur et al. (2006): Sicily 0 2.6 3.6 Pliocene

McArthur et al. (2007): France 0 131 143 BerriasianeHauterivian

Mead and Hodell (1995): ODP 689B 18 19 45 Cenozoic

Miller et al. (1991): ODP 608 �14 9 24 Miocene

Oslick et al. (1994): ODP 747A >16 Ma �14 16 25 Miocene

Page et al. (2009) �3 163 164 Callovian / Oxford. Bdy.

Qing et al. (1998): <463 Ma 5 424 441 Silurian

Reilly et al. (2002): DSDP 522 �14 23 34 Oligocene

Ruppel et al. (1996) �7 420 442 Silurian

Sugarman et al. (1995): ODP 525A �14 66 73 Maastrichtian

Young et al. (2009) 6 445 469 Ordovician

Zachos et al. (1992, 1999) 0 23 42 Paleogene

Section A

Stratigraphic Level

Meters above datum

Section B

Unconformity

0.7068 0.7072 0.7074 0.7068 0.7072 0.7074 0

20

40

60

80

100

120

0

10

20

30

40

50

60

70

Correla

tive L

evel

FIGURE 7.3 Correlation with 87Sr/86Sr. Values of 87Sr/86Sr are matched between 87Sr/86Sr profiles constructed for separate sections.


87Sr/86Sr data as a function of time. Details of the fittingprocedure are given in Howarth andMcArthur (1997). Becauseof the complex shape of the fit, and the very uneven density ofdata points through time, the curve was optimized by beingfitted in numerous overlapping local segments. These were

then joined using splines at segment junctions. To obtaina table for predicting age from 87Sr/86Sr, and the lower andupper confidence limits on the age, we used inverse interpo-lation of the fitted curve of 87Sr/86Sr and its 95% confidenceintervals (CIs) on the fitted line as a function of age.

A constant rate of increase in 87Sr/ 86Sr through time, dR/dt, appears in a sequence of rock as :

A varying rate of increase in 87Sr/ 86Sr through time, dR/dt, appears in a sequence of rock as :

87Sr

/ 86 S

r87

Sr / 8

6 Sr

2. a jump-up, if

sedimentation

stopped, or strata

are faulted out

3. a steeper interval,

if the sedimentation

rate slowed

4. a shallower interval,

if the sedimentation

rate increased

5. a plateau, if sedimentation

was instantaneous

(slump, turbidite)

6. a jump-down

if faulting repeats

the sequence

1. unchanged, if

sedimentation rate

is constant (judged

independently, e.g. by

cyclostratigraphy)

Time

Time

7. A complex pattern, where

structure and sedimentation

rate are complex

1. u

nchanged, if s

edim

enta

tion ra

te is

consta

nt

87Sr

/ 86 Sr

It is difficult to isolate the effects of changing sedimentation rate from changing dR/dt.

Strat Level e.g. meters

FIGURE 7.4 How the rate of change of 87Sr/86Sr with stratigraphic level through a section (dR/dl) can be interpreted in terms of the rate of change of87Sr/86Sr with time (dR/dt).


TABLE 7.2 Sources of Pre-Ordovician Data Used in the

Construction of Figure 7.1

Author Time Interval

Age Range,

(Ma)

Alvarenga et al. (2008) Ediacaran 635 580

Brasier et al. (1996) Ediacaran/Cambrian 670 520

Burns et al. (1994) Ediacaran 600 550

Calver (2000) Ediacaran 630 550

Derry et al. (1994) Cambrian 530 510

Ebneth et al. (2001) Cambrian 530 485

Fairchild et al. (2000) Cryogenian 800 720

Gorokhov et al. (1995) Tonian/Cryogenian 900 750

Halverson et al. (2007) Neoproterozoic 850 540

James et al. (2001) Cryogenian 670 540

Jiang et al. (2007) Ediacaran 630 545

Kaufman et al. (1996) Cambrian 545 525

Kouchinsky et al. (2008) Cambrian 530 495

McKirdy et al. (2001) Cambrian 670 640

Melezhik et al. (2009) Ediacaran 620 550

Miller et al. (2009) Tonian/Cryogenian 850 720

Misi et al. (2007) Ediacaran 630 600

Montanez et al. (1996) Cambrian 515 495

Nicholas (1996) Cambrian 545 525

Noguiera et al. (2007) Ediacaran 630 550

Pokrovskii et al. (2006) Ediacaran 620 550

Saltzman et al. (1995) Cambrian 495 490

Shields (1999) Neoproterozoic 850 500

Shields and Veizer (2002) Precambrian 3000 500

Shields et al. (2002) Cryogenian 670 600

Shields et al. (2007) Ediacaran 635 630

Valledares et al. (2006) Ediacaran 550 545

Walter et al. (2000) Neoproterozoic 850 550

Wotte et al. (2007) Cambrian 515 505

Yoshioka et al. (2003) Cryogenian 670 650


7.6. THE QUALITY OF THE FIT

7.6.1. Standards and Inter-Laboratory Bias

Measurements of 87Sr/86Sr are affected by inter-laboratorybias. To correct for this, standards are run alongside samples

and the value of the standard is reported. Values of 87Sr/86Srare then adjusted by addition or subtraction to either standardor sample values, by the amount needed to bring the standardto the preferred value. Here, we correct data to a value of0.710 248 for standard reference material NIST-987 (formerlyknown as SRM-987), which is equivalent to correcting toa value of 0.709 174 for EN-1, a modern Tridacna clam fromEniwetok Atoll (prepared by the USGS). Some older work isnormalized to a SrCO3 standard, known as “E and A”, thatwas prepared by the Eimer and Amend company. The87Sr/86Sr value of E and A is 0.708 022 � 4 (2 s.e.,n ¼ 34) relative to a value for NIST-987 of 0.710 248 (Joneset al., 1994a). In a few cases, the magnitude of our normal-ization differs from that used in the original source of data.

As replication of 87Sr/86Sr measurement can give meanvalues precise to � 0.000 003 (Jones et al., 1994a; McArthuret al., 2006), standards and interlaboratory bias should bequantified to this precision, but this is seldom done. Fewlaboratories have reported a comparison of 87Sr/86Sr inNIST-987 and EN-1, the two common standards, at a preci-sion of less than � 0.000 005. Interlaboratory bias, especiallyfor pre-1990 data, is as high as 0.000 020, so the uncertaintyin dating such bias introduces is the time-equivalent of �0.000 020 in 87Sr/86Sr.

7.6.2. Confidence Limits on the LOWESS Fit

Fitting gives a best-fit curve of estimated 87Sr/86Sr as a func-tion of age, and two-sided, 95% CIs on the fitted line(Figure 7.5). These confidence intervals are included in theLOWESS table available from the authors. These CIs areanalogous to the standard error of a mean ( � s/n). They aresmaller than, and should not be confused with, measures ofstandard deviation, which quantifies the scatter of data abouta mean line (� s); the CIs give a confidence with which theposition of the mean line is known and say little about thedistribution of data about the mean line.

The width of the CI varies with numerical age, and isdependent on both the density and spread of the calibrationdata. For substantial segments of the Mesozoic, CI half-widthvalues approach � 0.000 005 and are seldom more than� 0.000 010. Where data are abundant and samples wellpreserved, e.g., 0e7 Ma, the half-width CI is around� 0.000 003. Where data are few, e.g., early Devonian(sensu lato), the uncertainty is much greater. Well-preservedsamples become rarer with increasing age so the uncertaintyenvelope increases with age as sample quality deteriorates;nevertheless, achieving a precision of � 0.000 015 for theentire Paleozoic is not an unrealistic goal.

Assuming that the half-widths of the upper and lowerconfidence intervals are about equal, then the total uncer-tainty on an 87Sr/86Sr to be used to derive an age fromthe curve can be computed by combining the uncertainty onthe measurement (sm, for example, � 0.000 020) with the

0

5

10

15

20

25

-150

-100

-50

0

50

100

150

200

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

Numerical Age, Ma

Numerical Age, Ma

Pote

ntia

l str

atig

raph

ic

reso

lutio

n, m

yrs

Cen Cretaceous Jurassic Triassic Perm Carb Devon Sil Ord Cam

0.50.5

0.1

0.1

0.05

0.05

Hal

f-wid

th C

I as

87Sr

/ 86

Sr x

106

of

fitte

d m

ean

line

Rat

e-of

-cha

nge

in 87

Sr /

86Sr

x 1

06

(A)

(B)

FIGURE 7.5 Half-width of the 95% confidence intervals on the LOWESS fit (A), and rate of change with time of 87Sr/86Sr through the Phanerozoic, showing

the potential resolution in dating for any given rate of change (B).


uncertainty of the fitted curve (sc, for example, � 0.000 010)as follows:

stotal ¼�s2m þ s2c

�1=2; so stotal ¼ � 0:000023 (7.1)

The mean age is then derived from the mean 87Sr/86Sr of thesample and the mean line of the calibration curve, whilst theCIs on the age are given at the points on the calibration curvethat are 0.000 023 above and below the mean 87Sr/86Sr. The

CIs are mostly equal about the mean line but, in the fewplaces where they are not, it may be preferable independentlyto calculate upper and lower bounds on ages.

7.6.3. Confidence Limits onMeasured 87Sr/86Sr

The uncertainty with which the mean (m) 87Sr/86Sr ofa sample is known, from n independent determinations of


87Sr/86Sr, may be quantified if one assumes that themeasurement errors are normally distributed and so a two-sided confidence interval applies:

Uncertainty ¼ � t1�a=2; n�1ðs=n1=2Þ; (7.2)

where s is the standard deviation of n observed 87Sr/86Srvalues, and t1�a/2, n�1 is the 100(1�a/2)th percentile ofStudent’s t-statistic with (n � 1) degrees of freedom; a is therisk (specified as a proportion) that the true (but unknown)value of 87Sr/86Sr in the mineral, which is estimated by m,will fall outside the specified confidence interval. Thus, a iscommonly set to 0.05 (5%) in order to obtain two-sided 95%confidence limits on m. The t-statistic is used for this purpose,rather than the 100(1�a/2)th percentile of the cumulativenormal distribution in order to correct for the fact that thenumber of replicate determinations of 87Sr/86Sr is finite.Increasing n decreases the uncertainty in m. For example, themultipliers for two-sided 95% confidence limits when n ¼ 2,3, 4, 5, and 10 are 12.71, 4.30, 3.18, 2.78, and 2.26,respectively.

It may be possible to obtain only a single determination of87Sr/86Sr (x) for a given mineral sample. If, for some reasonthere exists a prior estimate of the expected value of87Sr/86Sr (a), e.g., from measurements previously made onpresumed similar material, or the ratio has been estimatedfrom the 87Sr/86Sr curve and a knowledge of the sample’sstratigraphic position, then, assuming x is the centre ofa normal distribution, Blachman and Machol (1987) showedthat a two-sided 100(1�a)% confidence interval on x isgiven by:

x� ð1þ 0:484=aÞjx� aj (7.3)

If a is 0.05, the multiplier equals 9.68. Less conservativebounds are obtained by inverting the prediction interval fora single future observation. This gives:

x� z1�a=2 ð1þ 1=n0Þ1=2s0 (7.4)

In this case, s0 is a prior estimate of the standard deviation ofthe distribution (assumed normal) from which x is drawn,e.g., the pooled standard deviation based on n0 sets ofprevious determinations of similar samples, and z1�a/2 is the100(1�a/2)th percentile of the cumulative normal distribu-tion. If a is 0.05, the multiplier equals 1.96.

7.6.4. Numerical Resolutionof the Fitted Curve

The uncertainty of an estimated numerical age obtained usingthe calibration curve (Figures 7.1 and 7.2) depends on:

(i) the width of the 95% CI on the calibration curve,(ii) the uncertainty on the measured 87Sr/86Sr,(iii) the rate of change with time of marine-87Sr/86Sr (dR/dt).

Given that the best-defined parts of the calibration curvehave half-width CIs no better than � 0.000 003, and that thisis also the best-attainable precision on measurement of87Sr/86Sr, application of Equation 7.1 above givesa minimum total uncertainty in dating of around 0.000 004.Given that the slope of the calibration curve (Figure 7.5)rarely exceeds a value of 0.000 060 per myr, it follows thatthe precision in dating with 87Sr/86Sr will not be better thanabout � 0.1 myr. Correlation with 87Sr/86Sr avoids theuncertainty involved in assigning numerical ages and theaccuracy with which that task can be accomplished dependsupon the rate at which 87Sr/86Sr changes through a section.

Under optimum conditions, e.g., with well-preservedmaterial and where dR/dt is steep, the precision with whichSIS can date and/or correlate marine strata can surpass fora-miniferal biostratigraphy in the Cenozoic and ammonitebiostratigraphy in the Mesozoic. The utility and accuracy ofSIS declines with increasing sample age, because the methodrelies on analysis of well-preserved samples, mostly ofbiogenic calcite, and such samples become less common withincreasing age.

7.7. RUBIDIUM CONTAMINATION

Because 87Rb decays to 87Sr with the passage of time, the87Sr/86Sr of even a perfectly preserved sample will increasewith age if it contains Rb. Luckily, most marine calcitecontains too little for this problem to arise, because Rb doesnot easily substitute for Ca in calcite, and the concentrationof Rb in seawater is low (around 0.1 mg/L). Furthermore,the decay rate of Rb is low, so the problem is rare even incalcites of Paleozoic age. The larger cation site in arago-nite, however, can incorporate more Rb than does calcite,so corrections for radiogenic 87Sr/86Sr derived from Rbmay therefore be needed for aragonite. Corrections towhole rock 87Sr/86Sr are more necessary and also moreproblematic, as bulk rock invariably contains clay mineralsthat incorporate Rb in concentrations of tens to hundreds ofppm. Correcting for in situ Rb decay in such materialmay yield unrealistically low original values of 87Sr/86Sr(Gorokhov et al., 1995). As a rule of thumb, a Rb correctionmay be needed if a sample contains more than 0.1 ppm ofRb and is older than 50 Ma, but the presence of even thatamount of Rb in calcite (but not aragonite, which maycontain more) may signal alteration of the sample. A tablefor making such Rb corrections can be found in McArthur(1994).

7.8. COMMENTS ON THE LOWESS FIT

Some details of the GTS2012 database and fit requirecomments.

Pliocene to Recent: For the period from 0 to 7 Ma, werely mostly on the data of Farrell et al. (1995) except


between 2.6 and 3.6 Ma, where, to remove cyclic-likeartefacts in the data of those authors, we substituted that ofMcArthur et al. (2006) obtained by analysis of Orbulinauniversa from the Pliocene type-section at Punta Piccola,Sicily, which is astronomically calibrated.

Oligocene / Early Miocene: From the data of Hodell et al.(1991) we exclude that for Site 588C, which has an uncertainage model; age models for DSDP/ODP Sites 588 and 588Awere updated for McArthur and Howarth (2004) and areretained here. For Site 289 (Hodell and Woodruff, 1994), weuse a revised age model that includes breaks in the sequencebetween 522 and 544 meters below seafloor. The update ofMiller et al. (1988) given in Reilly et al. (2002) is nowincluded for Site 522, as is the recent data of Ando et al.(2011) but with a modified, shipboard, age model, rather thanthe chemostratigraphic age model of those authors.

Paleogene: The 87Sr/86Sr curve for the Paleogene showssufficient slope for it to be potentially useful for dating(Figure 7.2). From the KeP boundary (65.5 Ma) value of0.707 830 � 0.000 008 (McArthur et al., 1998), 87Sr/86Srdeclines to 0.707 72 in the Ypresian (51 Ma) before risingsharply to a maximum of 0.707 78 in the early Lutetian(47 Ma) and then declining again to a second minimum of0.707 73 in the earliest Bartonian (41 Ma). Thereafter, theratio increases steeply until modern times. For the Paleocene,the low rate of decrease in 87Sr/86Sr, of around 0.000 08 permyr, may allow a resolution in dating no better than 1 myrwhen the curve for the interval is better defined.

Maastrichtian: For the Late Maastrichtian interval, we usethe data of Sugarman et al. (1995) and Barrera et al. (1997)for DSDP Site 463, the latter after recalibration to the agemodel of Li and Keller (1999). The results appear to agreewell with an independent assessment of the 87Sr/86Sr trendgiven in Huber et al. (2008).

CampanianeCenomanian: The trend for Campanian timeis defined well by a combination of data from the ammonite-zoned strata of the US western interior, and data from theEnglish chalk. The latter comprises mostly analysis of soft,semi-indurated, acid-leached, white chalk and the data agreewell with data for belemnites from the same sections. Theinterval Turonian-to-Cenomanian is poorly defined owing toa scarcity of well-preserved samples in this interval, but theavailable data suggest that the curve reaches a minimum of0.707 280 in the later part of Turonian time.

AptianeAlbian: Of Bralower et al.’s (1997) data, we useonly that for inoceramids. As in GTS2004, we have adjustedthe Albian boundary ages of Bralower et al. (1997) to those inthis volume, but retain those authors’ apportionment of timebetween them.

Jurassic: The interval is based on data from Jones et al.(1994a,b), with replacement of the data as follows: forPliensbachian and Toarcian time, we use data in McArthuret al. (2000a); for Berriasian, Valanginian, and Hauteriviantime, we use McArthur et al. (2007). In both publications,

numerical ages were assigned to biostratigraphic boundarieson the basis of composited linear fits of 87Sr/86Sr to strati-graphic level for successive short stratigraphic intervals. ForHettangian and Sinemurian time, we use the belemnite data ofJones et al. (1994a; see McArthur, 2007 for reasons) togetherwith those authors original age models, recomputed to the timescale used here. The value of 87Sr/86Sr for the Sinemurian/Pliensbachian boundary is based on Hesselbo et al. (2000).

TriassiceJurassic Boundary: We discard as incorrect theage models and Sr-isotope curve for this boundary intervalgiven in McArthur and Howarth (2004), preferring theinterpretation of McArthur (2007; Figure 7.6) which excludesthe oyster data of Jones et al. (1994a) as reflecting alteration.This new interpretation minimizes the inflection in 87Sr/86Sracross the boundary.

Triassic: Two data for Rhaetian time are from Jones et al.(1994a). The rest are from Korte et al. (2003). Peaks inearliest and latest Triassic time are defined by analysis ofconodonts. Conodonts do not preserve 87Sr/86Sr well, so thepeak amplitudes have been reduced by omission of the higherconodont values of 87Sr/86Sr, which may reflect alteration.The steepness of the rise in 87Sr/86Sr in the very earliestTriassic (Figure 7.2) might be revealing an undue compres-sion of the time scale in the early Triassic, when the rate ofincrease in marine-87Sr/86Sr was, on the present time scale,around 0.000 110 per myr, nearly twice that of the steepestrate during Cenozoic time, and more than the late Permianrate of 0.000 097 per myr estimated by Martin and Macdou-gall (1995).

Permian: We use a combination of data from Korte et al.(2006) for the whole Permian, Denison et al. (1994) forOchoan time, and Martin and Macdougall (1995) for the latestPermian time. These data sets differ and the differencesdecrease the precision of the fit. Data from all three authors aredifficult to reconcile; further analysis is needed to define theSr-isotope curve through this interval. For example, the P/Tboundary value from Korte et al. (2004) appears to be around0.707 24, whilst that for Martin and Macdougall (1995) isaround 0.707 40. Unpublished data of the authors confirm thatthe Capitanian minimum in 87Sr/86Sr was around 0.706 850.

The durations given in this volume for earlier stages ofthe Permian are markedly different to those in GTS2004. Theduration of the Sakmarian is reduced by 50% (from 10.2 myrto 5.5 myr), that of the Artinskian is increased by 20%(8.8 to 10.7 myr) and the duration of Kungurian is alsoincreased by 20% (5.0 to 6.0 myr). These changes introducemore sinuosity to the 87Sr/86Sr curve than was apparent inKorte et al. (2006) and this in itself may be revealing thatthe new apportionment of time for this interval requiresre-examination.

Carboniferous: Data for Carboniferous time are mostlyfrom Bruckschen et al. (1999), but exclude data for samplesfrom the USA, owing to difficulty in correlation; it might bebetter to use the Sr data to integrate US and European

Brachiopods

Conodonts

(b)

(a)

Brachiopods &bivalvesBelemnites

H

H

Sinemurian

Sinemur

Rhaetian

Rhaetian

87Sr

/ 86

Sr

Numerical Age, Ma

190 192 194 196 198 200 202 204

190 192 194 196 198 200 202 204

Jurassic Triassic

Undifferentiated samples of

Korte et al. 2003

Jones et al. 1994

Koepnick et al. 1990

Differentiated samples of

Korte et al. 2003

Jones et al. 1994

0.7080

0.7079

0.7078

0.7077

0.7076

0.7075

87Sr

/ 86

Sr

0.7080

0.7079

0.7078

0.7077

0.7076

0.7075

FIGURE 7.6 Interpretations of the variation in 87Sr/86Sr through the Triassic / Jurassic boundary interval. In (a) we show the model used for GTS2004, which

did not differentiate on the basis of sample type; in (b) we show an alternative fit that rejects conodont and oyster samples because of their propensity to alter on

burial. In this volume model (b) was adopted and configured to its timescale: GTS12’s longer Rhaetian (8.2 myrs v. 4.0 myrs) and shorter Hettangian (2.0 v. 3.1

myrs), compared to GTS04, nearly equalizes the Jurassic and Triassic slopes of the curve for model (b) as used in this volume.



stratigraphies. The data show a large spread, especially forSerpukhovian and Visean times: values of 87Sr/86Sr around332 Ma range from 0.707 637 to 0.707 805 even if extremeoutliers are ignored. Data from Germany group more tightlythan do data from Belgium, and are mostly higher (by about0.000 070). The spread leads to high CIs on the fitted cali-bration in this interval. Values of 87Sr/86Sr for tie-points atspecific times are provided by Cummins and Elderfield(1994) for Dinantian time and by Brand and Brenckle (2001)for the Mississippian/Pennsylvanian boundary interval atArrow Canyon, Nevada, USA.

Devonian: The curve for much of the Devonian derivesfrom van Geldern et al. (2006). This data defines the cali-bration curve more tightly than did previous data for theinterval, and clearly show the breaks in slope of the curve atthe boundaries of the Middle Devonian. These points arepresent in the data of Diener et al. (1996) but are obscured byscattering of the data. The late Devonian data of van Geldernet al. (2006) coincides with the time tie-point provided by thedata of Carpenter et al. (1991) for the A. triangularis con-odont zone of the late Devonian Golden Spike and Neviscarbonate reefs in Alberta, Canada. The SilurianeDevonianboundary interval is fixed by the data of Fryda et al. (2002).

Silurian: The conodont data of Ruppel et al. (1996) agreewith later data of Azmy et al. (1999) and Cramer et al. (2011).Successive time scales have shortened the duration of theGorstian, which has the effect of steepening the 87Sr/86Srcurve in that interval, and introducing breaks in slope at thestage boundaries. The original near linear increase throughtime in 87Sr/86Sr reported by Ruppel et al. (1996) is therebymade sinuous. The matter is well explained by Cramer et al.(2011) and alluded to in Chapter 21 of this volume. That therate of change in 87Sr/86Sr with time changes sharply at stageboundaries is strong evidence for a problem in this intervalwith the assignment of numerical ages to stage boundaries.

Ordovician: The trend in 87Sr/86Sr across the CambrianeOrdovician boundary differs markedly between data sets. Wehave chosen to use Ebneth et al. (2001) for the Cam-brianeOrdovician boundary interval and continue the Earlyand Middle Ordovician trend using the data of Denison et al.(1998) and Shields et al. (2003). The differences betweenthese authors are likely caused by artefacts of diagenesis, asthe data scatter considerably. As the apparent high rate ofdecline through the Ordovician has prompted discussion aboutits cause (Shields et al., 2003; Young et al., 2009), furtheranalysis, and better stratigraphy, are required to refine thecurve in this interval.Where unusually steep rates of change of87Sr/86Srwith time have been noted before in a number of partsof the geological record, they have diminished with improvedcorrelation, improved age models, or further analysis of bettersamples.

Data gaps: Finally, Figure 7.2 reveals a paucity of reliabledata for many intervals of time (the late Albian to Turonian,most of the Kimmeridgian and Tithonian, the early Devonian

and the DevonianeCarboniferous transition). This lack isreflected in the large (> 0.000 015) half-width of the confi-dence interval on the mean for the LOWESS fit (Figure 7.5)for many intervals; to reduce this uncertainty substantiallywill require some three to five accurate and precise 87Sr/86Srvalues per biozone.

7.9. Sr-ISOTOPE STRATIGRAPHY FORPRE-ORDOVICIAN TIME

Reconstruction of the seawater 87Sr/86Sr curve before theOrdovician Period must overcome particular difficulties ontwo fronts: poor age constraints and a lack of suitably well-preserved materials for analysis. Both the relative and abso-lute ages of older strata remain poorly constrained. Markerfossils of the lower Cambrian tend to be endemic to specificregions and facies, while Precambrian biostratigraphy is in itsinfancy. The lack of a global stratigraphic framework hasnecessitated the use of calibration schemes, which integrateSr- and C-isotope trends, geochronology, chemo-oceano-graphic marker beds and sequence stratigraphy with theemerging biostratigraphy (Shields, 1999; Robb et al., 2004).

In the absence of sufficiently large sets of well-constrained 87Sr/86Sr data, we approach the reconstruction ofthe seawater 87Sr/86Sr curve by first delimiting seawater87Sr/86Sr at established chronostratigraphic tie-points usingthe mutual agreement of multiple studies. Longer ranging Sr-isotope studies are then used to trace broad trends betweentie-points, primarily using d13C features for global calibrationin the Precambrian. 87Sr/86Sr values are generally reportedhere only to the fifth significant figure in recognition of thepoor resolution of the Precambrian and Cambrian 87Sr/86Srrecord. There are currently no adequate tie-points forpre-800 Ma strata (Shields and Veizer, 2002).

Despite acknowledged difficulties, the use of Sr isotopestratigraphy to correlate Neoproterozoic and Cambrian strataremains promising due to the major increase in seawater87Sr/86Sr from 0.705 to 0.709, which occurred between about850 and 500Ma. Chronostratigraphic tie-point ages below arecurrently accepted estimates based on the new geologicaltime scale given in this book.

1) 497 Ma: Late Cambrian SPICE interval e published dataare consistent with a rising trend through the mid-lateCambrian from 0.70893 � 2 (latest Mayan stage inSiberia) through the Epoch 3/4 boundary to the SPICEinterval across which least altered values are constrainedto 0.709 10 � 1 (Montanez et al., 2000; Kouchinskyet al., 2008). Internally consistent data for the Elvinia-Taenicephalus biozone boundary (the SteptoaneSunwaptan boundary in Laurentia) indicate that seawater87Sr/86Sr rose to its highest ever value after the SPICEexcursion, before falling from 0.709 25 to 0.709 14through the upper Steptoan to 0.709 10 to 0.709 11 in the


Sunwaptan (Saltzman et al., 1995). The conodont study ofEbneth et al. (2001) traces this decrease further to0.709 00 at the CambrianeOrdovician boundary.

2) 509 Ma: Cambrian Epoch 2/3 boundary e three studiesprovide data across this boundary from Siberia, USA,France and Spain. Least altered values in Montanez et al.(2000) and Wotte et al. (2007) are mutually consistent,while high Mg/Ca ratios indicate that the lower values ofDerry et al. (1994) arose during dolomitization. Leastaltered values of 0.708 94� 3 imply that the 87Sr/86Sr riseleveled off during Epoch 3 (Kouchinsky et al., 2008).

3) 541 Ma: PrecambrianeCambrian boundary e several87Sr/86Sr studies span the PrecambrianeCambrianboundary, the most comprehensive being that of Brasieret al. (1996). That study and other work (Derry et al., 1994;Kaufman et al., 1996; Nicholas, 1996; Valledares et al.,2006; Jiang et al., 2007) constrain latest Ediacaran andearliest Cambrian 87Sr/86Sr to c. 0.708 45 � 5. Leastaltered samples fromMongolia, Siberia and China (Brasieret al., 1996; Kaufman et al., 1996; Li et al., 2012) definea decreasing trend through Epoch 1, during a globalincrease in d13C, to reach a low of 0.708 05 � 5 after theend of the Fortunian Stage (529 Ma), before rising againthrough Epoch 2 (Derry et al., 1994).

4) c.575ec.550 Ma: Late Ediacaran e a striking feature ofthe Ediacaran Period is a prolonged, highly negative,likely global d13C excursion. Recent studies (Pokrovskiiet al., 2006; Melezhik et al., 2009) indicate that seawater87Sr/86Sr increased from 0.708 02 to 0.708 62 during thisinterval. Although the association with celestite in thesesamples hints at a more restricted marine environment,this rise is broadly consistent with 0.708 45 � 3 towardsthe end of this excursion (Jiang et al., 2007), at a horizondated at 551 Ma (Condon et al., 2005), and with c. 0.7087for least altered samples from Oman (Burns et al., 1994;Brasier et al., 2000) and Australia (Calver, 2000). Itseems likely therefore that seawater 87Sr/86Sr reacheda Precambrian peak at c.550 Ma.

5) c.625ec.580 Ma: Early Ediacaran e there are only fewstudies which can be used to constrain the Early Ediacaranseawater 87Sr/86Sr curve between 630 and 580 Ma, usingthe assumption that the rise to high d13C after end-Cryogenian glaciation can be used as a global correlationtool. High d13C values from Siberia are associated witha rise in 87Sr/86Sr from 0.7072 to 0.7080. By comparison,sparse 87Sr/86Sr data from possibly correlative, EarlyEdiacaran samples of the lower Doushantuo Formation(China) indicate a rise from c.0.7077 to 0.7078 to c.0.7080to 0.7081 (Jiang et al., 2007). Several Brazilian studiesindicate that 87Sr/86Sr had previously decreased fromabout 0.7078 to 0.7074 during the rise to high d13C (Misiet al., 2007), indicating that there were possibly two peaksduring the Early Ediacaran.

6) 635ec.625 Ma: basal Ediacaran e the base of the Edia-caran System is defined within the c.635 Ma post-glacial“cap dolostone” of the Nuccaleena Formation in SouthAustralia. Although cap dolostones are not suitable for87Sr/86Sr studies (e.g., Yoshioka et al., 2003), immediatelyoverlying limestone units have provided consistent data.87Sr/86Sr values for Sr-rich samples (>3000 ppm) of theHayhook Formation (NW Canada) range between0.707 14 � 2 (James et al., 2001) and are consistent withdata from post-glacial limestones of Namibia (Halversonet al., 2007). In Namibia, least altered 87Sr/86Sr values risesubsequently to 0.707 48 and then to c.0.7080 as d13Cvalues recover from�4.4& to 0&. High-Sr samples fromNW Canada define an increase from 0.707 28 to 0.707 53,while least altered 87Sr/86Sr data from South Americaconsistently indicate a rise from c.0.7074 to 0.707 77�2during the d13C recovery (Alvarenga et al., 2008;Nogueira et al., 2007). Identical values (c.0.7077 to0.7078) have been reported for basal Ediacaran baritesamples of NWAfrica at a comparable point in the post-glacial d13C curve (Shields et al., 2007). Taken together,these data indicate a rise in seawater 87Sr/86Sr fromc.0.7071 to c.0.7077 or higher during the post-glacial d13Crecovery to positive values.

7) c.665ec.650 Ma: late Cryogenian ‘Sturtian’e‘Marinoan’non-glacial intervale immediately post-glacial limestonesof the Cryogenian Period reveal a rise in 87Sr/86Sr fromc.0.7067 to 0.7071 during the post-glacial d13C recovery.Four regions of the world boast relevant data: Mongoliafrom 0.706 75 to 0.707 09 (Shields et al., 1997), Namibiafrom 0.706 85 to 0.706 99 (Yoshioka et al., 2003), NWCanada from 0.706 68 to “unconstrained” (Kaufman et al.,1997) and Australia from “unconstrained” to 0.707 06(McKirdy et al., 2001). Extremely high d13C values>10&are characteristic of the upper part of this non-glacialinterval and are associated with 87Sr/86Sr of0.707 13e0.707 35 in Mongolia (Shields et al., 2002),0.707 18e0.707 42 in NW Canada (Halverson et al.,2007), and 0.707 25e0.707 35 in Namibia (Halversonet al., 2007). 87Sr/86Sr values from Australia are generallyhigher at this level and indicate the possibility of a peak atc.0.7076 to 0.7078 (McKirdy et al., 2001).

8) c.750 Ma: early Cryogenian, pre-‘Sturtian’ interval e itis currently unclear to what extent pre-glacial successionscan be considered contemporaneous, and thereforewhether the onset of glaciation can be used as achronostratigraphic tie-point. Nevertheless, 87Sr/86Srtypically ranges between 0.7067 and 0.7069 (Halversonet al., 2007) below glacial units. There is a possibility thatseawater 87Sr/86Sr fell to 0.7063 before glaciation inGreenland (Fairchild et al., 2000; Sawaki et al., 2010).

9) c.800 Ma: Bitter Springs Excursion e age constraints areparticularly poor for the mid-Neoproterozoic; however,


a negative d13C excursion at c.800 Ma in the BitterSprings Formation of central Australia may be of possiblyglobal significance based on least altered 87Sr/86Sr of0.7063 at this level in Svalbard, NW Canada, Australiaand possibly Ethiopia, the presence of characteristicacritarchs, and sequence stratigraphy (Halverson et al.,2007). Below this level, 87Sr/86Sr ratios are even lowerwith 0.7057e61 in the lower Bitter Springs Formation(Walter et al., 2000), 0.7055 in NW Canada, 0.7052 inSiberia (Gorokhov et al., 1995) and 0.7050 in Ethiopia(Miller et al., 2009). The ages of these units are not wellconstrained, but available data suggests 87Sr/86Srincreased in seawater during the early Neoproterozoicfrom 0.705 to 0.707 (Halverson et al., 2007) from c.850 toc.750 Ma.

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