On the principles of the U-trend method for dating quaternary sediments, I: Model, experimental procedures and data

QuaternaryScienceReviews(QuaternaryGeochronology),Vol. 14, pp. 409-420, 1995.

Pergamon

Copyright © 1995 Elsevier Science Ltd. Printed in Great Britain. All rights reserved. 0277-3791/95 $29.00

0277-3791(95)00034--8

ON THE PRINCIPLES OF THE U-TREND METHOD FOR DATING QUATERNARY SEDIMENTS, h MODEL, EXPERIMENTAL PROCEDURES AND DATA A.G. LATHAM Archaeological Sciences, Hartley Building, Liverpool University, Liverpool L69 3BX, U.K.

Abstract - - The U-trend method for dating a wide range of Quaternary sediments was first presented by John Rosholt in a series of U.S. Geological Survey Open File Reports. The thinking was that upon fluviation uranium, filtering down through the unit, left behind a trail of daughter products in a systematic fashion - - a trend. The exponential decrease of this U flux was defined by a flux factor the significance of which was not known exactly. Equivalently, the flux of U could be characterized by a 'half-period', which appeared to act analogously to a radioactive decay half-life. By using leaching techniques, the loosely bound isotopes would define a trend when plotted on a 'U-trend isochron' diagram. This trend was characterized in the plot by a gradient and intercept which could be referred to calibration diagrams in order to recover the half-period and the age of the unit. Such age estimates have now appeared in the more fully-refereed literature, though without the fuller descriptions found in the USGS publications. The assumptions of the method are examined here, together with the details of the method from the earlier publications. Various problems with the method stand out, among which are: (i) it is not clear how s-recoil effects are included in the empirical equations; (ii) the use of independently-dated sediments as calibration units has not been fully justified; (iii) the leaching techniques appear to be too strong to select only the loosely bound isotopes and no others; and (iv) several of the key data-sets do not show a sufficiently strong variation of isotope ratios with depth to warrant being described as a trend. Despite these and other difficulties and because of its potential importance to Quaternary chronology, it is felt that the continuing study of U-trend type methods is worth the effort.

INTRODUCTION

QG

where L230 and ~'234 are the decay constants of 23°Th and 234O .

Uranium-series methods, principally those using the isotopes 238U, 234U and 23°Th, have been used successfully to date secondary precipitates such as speleothems, caliche and lacustrine evaporites (see various chapters in Ivanovich and Harmon, 1992). U-series mass-spectrometry on aragonitic corals has provided increasingly precise dates on interglacial high sea-level stands. The possibility of dating these precipitates arises from the fact that U is soluble in groundwater and seawater, and it becomes incorporated into the precipitate upon the formation of the latter; thorium (23ffrh and 232Th), being insoluble, is not carried in the groundwater. The moment of precipitation thus defines t = 0, with 23°Tho = 0; 23°Th subsequently begins to grow toward equilibrium with its parent 234U and grandparent 238U. The isotope activity ratios (ARs) of 234U/238U and 23°Th/234U relating to initial deposition of the precipitate are input into the age equation to find t, by iteration;

23°Th/234U=

e )~230t

1 ) + (1 --

(1 234 U/238 U

(

~3o

Hot-spring deposits, dirty cave deposits and caliche, w h i c h are o f t e n c o n t a m i n a t e d b y U and T h - b e a r i n g detritus, are also p r o v i n g a m e n a b l e to dating. Several coeval samples are totally dissolved (total sample dissolution method, TSD; Bischoff and Fitzpatrick, 1991; Luo and Ku, 1991), if the sample-to-sample contamination is s u f f i c i e n t l y varied; or they are l e a c h e d in w e a k a c i d ( l e a c h a t e - r e s i d u e and l e a c h a t e - l e a c h a t e methods, L - R and L - L ; Ku and Liang, 1984; Schwarcz and Latham, 1989), if sample-to-sample contamination is of uniform distribution. These a p p r o a c h e s use s o - c a l l e d isochron diagrams in which 232Th is used as an index for allogenic 238U, 234U and 23°Th in the samples. The gradients of these plots, giving the isotope ARs of the precipitate fraction, are then input into the age equation as before in order to estimate the age. Such samples are amenable to U - T h dating, providing that they have remained closed to further transport of U or Th into or out of the sample. It is sometimes possible to date bone and peat that has taken up U soon after burial, if they have subsequently remained a closed system. However, if U is taken up long after formation or is lost through subsequent leaching, then it is not possible to e s t i m a t e ages for the s a m p l e w i t h o u t m a k i n g further

)× 234 U/238 U

)

( 1 - e-(~3~z-234 t))

(1)

(~230 - ~234 )

409

410

Quaternary. Science Reviews (Quaternary Geochronology): Volume 14

assumptions about the rate of loss or gain of U. Loss of U, a common effect in chemically open systems, is usually severe enough that it is detectable by 23°Th]234UARs that exceed unity. Up to the dating limit of 200 ka, the 235U-23~pa method could be used for concordance checking with the U-Th method, and this is sometimes done for bone, for example, where there is often sufficiently high U content (Chen and Yuan, 1988). Rosholt (1967), Szabo and Rosholt (1969), Hille (1979) and others have attempted to construct open-system models for dating molluscs and other fossil shells by adopting further assumptions about the rate of uptake of U. In connection with the ESR dating of tooth enamel, Grtin et al. (1988) have also used similar continuous linear uptake models for the overall dose and have compared the ages so derived with their early U uptake model. All such ages appear to require reference to stratigraphy, or a modelled age sensitivity analysis and/or concordance checks with another method in order to elicit acceptance. Having great potential importance for Quaternary studies, and the most unusual and innovative of these open-system methods is that used by Rosholt and coworkers on a variety of sediments and known as the uranium-trend dating method (Rosholt, 1980, 1985; Szabo and Rosholt, 1989; Rosholt et al., 1985a, b, 1991; Muhs et al., 1989). As above, it uses 23°Th/Z34U and 234U/23~U ARs with a calibration from known-age sediments and a 'U-trend' curve, in order to find the age of the major filtration of water through the deposit. In many cases this age will be the same age as that of the deposit itself. The principal assumption upon which the method is founded is that after a sediment layer has been laid down, water filtering through carries an attenuating flux of U which leaves a trail of daughter products in a systematic fashion through the lower layers. The flux isotopes are 238U and 234U; the daughter products are 234U and 23°Th. In the U-trend method, age calibration curves have been constructed using sediments whose U-Th systematics are measured and whose ages are known independently, and the claim is that the isotope ratios from the target sediment can be used with these calibration curves to find its age. From the first publication of the U-trend dating method (Rosholt, 1980), the methodology and presentation has hardly varied. This is despite the continued admission that the significance of the main U-flux parameter is not known for certain. Moreover, the quoted Bateman-like equations have never been derived or their terms explained, as far as this author is aware. If a sufficient linear spread of points is obtained on the U-trend plot, and if the invariance of 232Th content is established to confirm the same depositional unit, then this appears to be sufficient to yield an age, independent of the sediment type. Of great significance is the claim that the method should work on such diverse sediments as lacustrine and fluvial sediments, weathered tuffs, alluvial, glacial and aeolian deposits (Rosholt, 1980, 1985; Rosholt et al., 1985a, b; Szabo and Rosholt, 1989). The

method can work independently of sediment type, since it depends on a water born U-flux any time after deposition Using U-trend analyses of seven profiles consisting of loess, weathered tuff, paleosols and river terrace deposits, from Germany, Atkins (1986) was unable to recover the age of two of these deposits, two profiles produced ages that were too old in comparison with the established chronostratigraphy, and three profiles gave U-trend ages in reasonable agreement with the established chronostratigraphy. Generally, the estimated age errors tended to be uncomfortably high, making dates 'little more than order of magnitude' estimates. This paper (paper I) examines the assumptions of the U-trend method, its experimental procedures and some of the data from which U-trend ages have been estimated. The model itself is empirical and it is not clear whether it was intended to fit all open-system sediments or only those which have experience regular U-fluxing. Therefore, in paper II, three other models have been presented to highlight the necessity of being more precise about these basic assumptions. Although the two papers were written to stand alone, some cross referencing has been added to aid comparison; the U-trend model is referred to as model A and the others as models B, C and D. There is little doubt that the validation of any 'U-trend' type dating model, even if it fits only some s e d i m e n t s , w o u l d be a very useful aid in Quaternary chronological studies. U-TREND DATING

The Basic Assumptions The basis, testing and application of the U-trend dating method has been presented in Rosholt (1980, 1985), Szabo and Rosholt (1989), Rosholt et al. (1985a, b) and Patton et al. (1991). A fuller evaluation of problems associated with different sediments is given in Muhs et al. (1989). Some practical problems have been discussed by Ku (1988) and I v a n o v i c h et al. (1992). Before any evaluation of any sediment-specific data is examined, several questions stand out even at the philosophical and methodological stages. These questions are presented after discussion of each stage of methodology of the U-trend model. Wherever possible, the original wording in smaller print of the U-trend presentation has been retained. For surfical deposits, the starting point for the uranium-trend clock is the initiation of movement of water through the sediment rather than initiation of soil development, although both of these processes may start at essentially the same time (Rosholt, 1985). The water movement introduces a flux of U (238U and z34U) that is measurably above that of the fixed U, and which leaves behind a trail of z34U and 23°Th in a systematic way - - a trend. This trend can be illustrated on a plot of (234U-z38U)/z38u vs. (238U-23°Th)/23~U (Fig. 1). Initially, in the depositional stratum, the 234U/238Uratio is constant because of mixing during transport.

A.G. Latham: Principles of the U-Trend Method, I Divergence of the 23°Tb/238U ratio from uniformity [from unit sample to sample ?] would not affect the development of the uranium trend line because such divergence, coupled with uniform 234U/238Uratios in the sediment initially would define a line with a slope of zero. Figure l illustrates hypothetical isotope development over time in a sediment using samples taken at three depths (Rosholt, 1985). As R o s h o l t (1980, 1985) d i s c u s s e s here and e l s e where, it appears that there is frequently an excess of U over that contained within the resistate minerals of the sediment. It occurs (a) because o f the ease with which U can be weathered from primary sources and (b) because of its great mobility in oxidizing water filtering through the deposit (e.g. Szabo and Rosholt, 1969). In the sediment, a distinction can thus be made between a tightly bound component o f U and the fluxed U that is loosely bound to gain surfaces. At the time of deposition, large volumes of water pass through the alluvium. However, after compaction and during subsequent soil development, the volumes of water passing through the alluvium are reduced significantly (Rosholt, 1985). Or, the U in the water is reduced as the overlying sediment becomes leached (B. Szabo, pers. commun.). It is assumed that cyclical variation of the flux caused by climatic changes can be approximated by an average flux. Both the quantity of water passing through and affecting a deposit, and the concentration of uranium in this water are components of the flux; the magnitude of the flux is a function of the concentration of uranium in the mobile phase relative to the concentration of uranium in the fixed phase. Best results should come from materials initially low in uranium content as the uranium-trend signal will override the signal from structural uranium.

411

the results obtained from several alluvial, colluvial, glacial, and eolian deposits of different ages is constructed for solution of uranium-trend ages. The model requires calibration of both the trend slope and the uranium flux factor based on results from deposits of known age. U n d e r the U - f l u x a s s u m p t i o n s , therefore, it w o u l d appear that all we need to find is the ~0 particular to the time-averaged U-flux, and we can then find t. The starti n g c o n d i t i o n s a r e k n o w n ; t h a t is, p r e s u m a b l y , (23°Th/234U)t = 0 = 0, ( n o 23°Th in f l u x w a t e r ) a n d (234U/238U)t =0 -- a constant, or nearly so. Rosholt chose to find ~ and t by means of a gradient and intercept method, as follows: The isotopic composition of several samples from the same depositional unit expressed in activity units, is required for solution of the model. The value from which ages are calculated is the slope (of U-trend; Fig. 1) of the line representing (234 U --

238U)

(234 U _ 238U) or

(234 U _

230Th)

(238U - 230Th)

Changes in isotopic composition with time ideally should follow a complex radioactive growth and decay curve; the Utrend slope for the three samples is represented by the tangent to this curve. The model is based on the empirical assumptions that ( 2 3 4 U - 238U) = -

~"234 -

e ~- -

(~234 -- ~'0)

~'234 -

e ~-234t-t- e ~234t

(2a)

()t'234 -- )~"0)

- 3X~4X~3o ( 2 3 4 U - 23°Th) =

e z0'-

(~234- ~ ) ( ~ 3 0 - Xo) 3~234)~230 e-~.234t _ (t~"0-- ~234)(~230 - ~'234)

In the a b o v e , ' a v e r a g e f l u x ' p r e s u m a b l y m e a n s that repeating fluxes do not vary greatly in U concentration (and, similarly so, with initial 234U/C238UARs at the sediment surface).

DEVELOPMENT OF THE MODEL (MODEL A) The empirical model incorporates a component called uranium flux, F(0). The actual physical significance of F(0) is not well understood; however, the flux varies exponentially with time in a deposit but the half period of F(0) is represented by a constant [given later to be ln2/L0, where ~ is the exponential 'decay constant' of F(0)] for a discrete depositional unit. It is related to the migration of mobile-phase uranium through a deposit. The process of c~-recoil, with time, of 234U (via 234Th) from resistate minerals into the loosely bound component of U and the reverse process of recoil into the resistate phase is d i s c u s s e d in R o s h o l t (1985) and M u h s et al. (1989). It is s t a t e d that " T h e e m p i r i c a l m o d e l u s e d includes these parameters o f daughter emplacement, 234U displacement, and uranium flux factor". Because of the large number of variables in a system that is completely open with regard to migration of uranium, a rigorous mathematical model based on simple equations for radioactive growth and decay of daughter products cannot be constructed. Instead, an empirical model tested against

3 Jk-234)L230

e ~a30~- 2e ~234t + e ~230t

(2b)

(Zo- ~ 0 ) ( ~ 3 4 - ~.230) where ~ is the decay constant of F(0), )~234 is the decay constant of 234U ( 0 . 2 8 0 X 10-5/yr), and ~230 is the decay constant of 23°Th (0.922 x lfkS/yr). For samples of the same age, the rate of change between parent~zlaughter activities would be represented by the first derivatives of the above equations: and these are given, finishing up with Y X

(234 U __ 238U)/238 U (234U -

23°Th)/238U

Cle-~ot+ C2e L234t

(3) C3e ~

+ C4e-L234 t -t- C5e-Yt230 t

where C1-C5 are functions of ~ , )k,234 and L230. It is then stated that: These are empirical model equations and the numerical constants in the coefficients preceding the exponential terms were determined by computer synthesis to provide a model with the best fits for deposits of known age. As mentioned earlier, the ratio Y

( 2 3 4 U _ 238U)

X-Y ( 2 3 8 U - 23°Th) is used for computer solution of the age.

(4)

Quaternary Science Reviews (Quaternary Geochronology): Volume 14

412

C O M M E N T S ON THE M O D E L

Second, the only adjustable parameter in the above equations is Xo, the decay constant for the U flux. All other parameters are fixed and each term has a definite functional magnitude related to ~ . It is therefore wrong to adjust the pre-exponential terms, C~-C5, in the above equations as though the terms were independent of one another, by fitting them to the data, since the exponential terms themselves also contain X0. If o~-recoil is included, however, it is true that U-flux terms (together) and c~-recoil terms would contribute independently of one another. Third, despite the idea or assumption of having no initial 23°Th, Rosholt (1980) seems to abandon this assumption when he writes, as above, that,

First, F(0) is not used as a parameter in subsequent equations; only X0 and ln2/X 0 are used. The reason for having the brackets and the enclosed zero in F(0) has not been presented; it may mean F(t = 0); i.e. the flux at time zero, although it is stated that, "the flux varies exponentially with time in a deposit". The statement, noted here and above, that, "isotopic data f r o m d e p o s i t s o f k n o w n age indicate that (U) migration decreases exponentially with time" is very important. It is about what might be expected, but it is never anywhere demonstrated explicitly. It is supported by: (1) sediments tend to compact after deposition;

Divergence of 23°Th]Z34Ufrom uniformity would not affect the development of the uranium trend line because such divergence, coupled with uniform 234U/23~U ratios in the sediment (which is seen to mean, 'constant initial ratios throughout the unit') initially would define a line with a slope of zero.

(2) pedogenic clay accumulates over time in soil B horizons; (3) secondary CaCO3 accumulates over time. All of these decrease pore space with time and may be e x p e c t e d t h e r e b y to d e c r e a s e U flux ( M u h s , pers.

commun. ).

Hence, the initial 23°Th/234Umust be a third unknown, that is, in addition to Xo and t. As is seen below, it is the experimental condition of 23°Th extraction, following a laboratory technique that involves strong acid dissolution, that appears to force recognition of the presence of initial 23°Th. Also, despite the mixing that produces

It is also stated above that, "The actual physical significance of F(0) is not well understood". Even so, some kind of exponential behaviour with time appears to be implicitly modelled in the equations. What is clear is that F(0) and )~ are constant for a particular depositional unit.

234U

excess

~>10 yr

/-

/

/ Tangent

/

--7

/ -3 O0

I

/

c u r v eei2d s Ip~pt

of

/ Equilibrium

<

23°Th

excess

f..,,,._~ J

¢N

to

T

i me ~

"""" /

increases J

J

f

Sample at

point

profile in

time

J

( ( 230Th

_ 2 3 8 U ) / 238 U

FIG. 1. The U-trend plot constructed by J.N. Rosholt to show the hypothetical development of 238U-234U-23°Thdisequilibria with time (after Fig. 1, Rosholt, 1985). Three (or more) data points (circles) are required to represent the disequilibria of the sedimentary U-flux unit at some point in time and three of these are presented to show U-trend at three different depths. Once the U-trend curve itself has been calibrated, the slope and intercept on the X-axis of the tangent at the data points thus define the age of the sample.

A.G. Latham: Principles of the U-Trend Method, I uniform 234U/238U,the resulting age must also depend upon its initial value, that is upon (234U/238U)0.It may be that it is not necessary to find what (234U/238U)0is in order to estimate t, as is the case for m a n y c l o s e d - s y s t e m s i t u a t i o n s (e.g. see A p p e n d i x A, o f I v a n o v i c h and Harmon, 1992). Fourth, no derivation is given for these Bateman-like equations having, as they do, such a precise form. They are empirical in that they consist of several exponential terms added to each other, reflecting the various source terms. That is, they appear to have been constructed by analogy with other three-member decay relations. One might hazard a guess that, as claimed, there is an attempt to i n c o r p o r a t e cz-recoil d a u g h t e r e m p l a c e m e n t and displacement. Which terms represent them is not stated, and it is therefore not immediately obvious how these processes have been included in the equation. In reality, the concentration of d a u g h t e r e m p l a c e m e n t must be related, inter alia, to the concentration of U in the resistate phase. However, this is not discussed, nor is there a source term incorporating the U concentration of the resistate phase. In Fig. 1 the 'hypothetical' attentuation-decay curve acquires a 234U/238U ratio with time that diverges from its initially 234Udepleted state to one that has a 234U excess and, although it is not stated, this presumably does reflect the recoil and leaching e n h a n c e m e n t of 234U into the mobile phase. Subsequently, the rate of recoil excess must eventually come into equilibrium with its decay, by

1

I

I

z

413

which time the previously depleted 23°Th will have grown into secular equilibrium with 238U. But this is not shown in Fig. 1. Instead, unsatisfactorily, a dashed line is drawn from a break point to illustrate the loss (decay?) of the excess 234U after 106 years. Though not presented here, it can be shown by computer simulations that it is impossible to derive a time-trend resembling Fig. 1 from these equations, especially if it is to have a reasonable value of the half-period, ln2/~.0, say, from 100 ka to 1 Ma. The trend must go to zero on both axes (the unsupported daughter excesses decay away), as t goes to infinity (say, greater than about 1.5 Ma, since the half-life of 234U is 245,000 year). Moreover, it seems that in order to maintain a disequilibrium of the magnitude illustrated in Fig. 1 (as repeated in all publications), at the higher-age end of the trend line, the unit would require an increasing i n p u t o f e x c e s s 234U and e x c e s s 23°Th f r o m r e c o i l processes. Thus Fig. 1 is a misleading representation of U-trend (compare Fig. 2a,b, paper II). C A L I B R A T I O N OF H A L F - P E R I O D S AND ESTIMATION OF t Samples are taken throughout the unit, top to bottom, to achieve as wide a spread of data points as possible in order to define as good a U-trend gradient as possible. The best-fit line to any three or more points on a U-trend plot may be represented by y = m x + b and by xi = b/m, w h e r e m is the m e a s u r e d U - t r e n d g r a d i e n t o f the

I

,

I

,

,

0"8

0'6

£ 0.4

"5 GO

o)

0.2

'

'*

o

"-J--

-0.2

-0.4

I

-1.6

I

-1.2

i

i

-0.8 (238 U-

i

I

i

-0.4 230Th)/230

I

0

0.4

U

FIG. 2. Actual U-trend isochron from tuff A unit, Lake Tecopa, California, of U-trend age 600 --- 60 ka. After Fig. 20B of Rosholt (1980). (Two points were omitted by JR from the original data, Table 2.)

414

Quaterna~ Science Reviews ( Quaterna~ Geochronology)." Volume 14

I

CO 'V

1

I

I I III]

I

I

t I I Ill

I

i

i

1000

m

0 v

m

v"

LL

0 u~ m

0 "0 0

oo

(ID

,p.

,p

100

° _

w

I~

u3

l

1

m

EL

m

N-CO

"1"

i

10 0"01

I

i i J llJ[

I

I

0'1

X

I I I Ill[

I 1

I 4

I n tercept

FIG. 3. Time-calibration curve for determination of F(0) from X-intercept value. Unit numbers have been omitted from the original plot, but the original ages are shown from, e.g. Fig. 4 of Rosholt (1985).

isochron, b is the intercept on the Y-axis and x~ is the intercept on the X-axis. (An alternative way of estimating m using the so-called T h o r i u m - I n d e x plot is also given.) On Fig. 1 a tangent is drawn at the three sampling points so as to intercept the X-axis, and Fig. 2 is an experimental example taken from Rosholt (1980). Several such X-intercepts, xi, taken from the U-trend diagrams of experimentally analysed sediments, are then plotted against independently determined ages of these sediments in a time-calibration curve, Fig. 3. These calibration points include: (l) the radiocarbon ages ofabout 12 ka for Peoria loess in Minnesota (Frye, 1973); (2) the obsidian hydration age (calibrated by K-Ar ages) of 150 + 15 ka for glacial deposits of Bull Lake age in southwestern Montana and northwestern Wyoming (Pierce, 1979); (3) the K-Ar age of 0.61 Ma for the Lava Creek B ash for the age of the zeolitized ash in Tuff A at Lake Tecopa, California (J.D. Obradovich, pers. commun.); and (4) the K-Ar age of 0.74 +_0.01 Ma for the Bishop ash for the age of Tuff B at Lake Tecopa. In addition, a number of other radiometric ages were also used as secondary calibration points (Rosholt et al., 1985). The calibration is described as follows (Muhs et al., 1989): The value )~ is the decay constant for F(0). It is strictly an empirical value that allowed selection of the proper coefficients (C~, C2, C~, Ca, C5) for the exponential terms in Eq. 4 [Eq. 3 here]. For deposits of unknown age, a method is required to determine the proper ~,0 value to be used in Eq.

4: this is done with a calibration curve that is based on values of ~,~ determined for deposits of known age. For deposits of known age, the quantity x~is plotted against the half period of F(0) on a log-log plot as shown in Fig. 3. The calibration curve was determined by selecting the proper )h~ value that yielded the correct age for independently dated calibration deposits using the model equation. The xi values of known-age deposits are used for calibration (Fig. 3) and these values are plotted against the half periods of F(0) equivalent to their ~,0 values; half periods are plotted instead of ~,os because of their numerical convenience. For deposits whose analyses are included in this report, F(0) is determined from Fig. 3 using the x~ value measured on the uranium-trend plot of the data for each depositional unit. The decay pattern for deposits in different environments varies with different F(0) values.

C O M M E N T S ON C A L I B R A T I O N First, it is possible to have a family of U-trend curves on Figs 1 or 3, each curve representing a different value of ~,0 (or, equivalently, of its half-period). Therefore, it follows that the intercept, x~, is not unique to a given )~0; but x~, depends on both ~,o and t. This is what we would expect i n t u i t i v e l y ; n a m e l y that d i f f e r e n t s e d i m e n t s , though having the same age, generally would have experienced different U fluxes and U flux attenuations. Expressed in the terms presented above, it could be imagined, for example, that two long sediment sequences, having had quite different U fluxes, could be sampled in sub-units so as to give the same x~intercepts but different gradients. The necessity to estimate different ~,~, repre-

A.G. Latham: Principles of the U-Trend Method, I

415

lO0

/ Age

=,oo ,..~

/

/

,oo

/ /

500 J

J

5O

f

100

0

/ Half period of F ( O ) = I O 0 ka Half period of F(O)=6OOka FIG. 4. Variation of U-trend slope with age of deposition for 100,000 and 600,000 year half-periods of F(0) (after Fig. 5 of Rosholt,

1985, with some slopes omitted). It is the combined use of the calibration curve of Fig. 3 and of this figure which allows unique assignment of age to the U-series disequilibrium of the sample. senting different U flux attentuations, only becomes clear when one combines the calibration curve of Fig. 3 with Fig. 4 (Fig. 4 of Rosholt, 1980; Fig. 5 of Rosholt, 1985) where the different gradients are related to the different half-periods. Thus, in order to obtain values of ~ and t one needs calibrations for both the gradient, m, and the

intercept, xi. Expressed mathematically, m and xi map into and t. Second, from the experimental U-trend plots (though not from the hypothetical one) it appears that x i. can take values ranging from negative to positive (Fig. 2 has a negative U-trend gradient, for example). From Fig. 3,

3

/

J

/

-4-

/

t'--

• ¢o

J

r-

Io t~

/

/

J

OIi

O

1

2

3

238U/238Th FIG. 5. Plot of tuff A, Lake Tecopa, California. The thorium-index plot (after Fig. 20A from Rosholt, 1980).

416

Quaternary, Science Reviews (Quaternao' Geochronology): Volume 14

however, the xivalues range from 0.01 to 4; there are no negative values (Muhs et al., 1989). In the calibration Table 1 ( R o s h o l t , 1985; Table 4 o f R o s h o l t et al., 1985a) there are shown all four possible combinations of positive and negative gradients and intercepts. Thus, in Fig. 3, it appears that log Ix,I has been plotted from the tabled values, rather than log (-xi). It could be inferred that the existence of positive xi in the data probably indicates the occurrence either of initial disequilibrium in the s e d i m e n t itself or o f a - r e c o i l d a u g h t e r emplacement, as originally stated, or of other processes such as leaching. Third, the curve of Fig. 3 appears to show that most of the a g e - c a l i b r a t e d sediments have h a l f - p e r i o d s that belong to either of two classes; one of half-period of about 70 ka and the other of between 500 and 700 ka. The middle 'Z' section has no representative calibration, though Rosholt (1985) says that an effort was made to define this region. Moreover, the younger sediments tend to have the younger half-periods and vice versa. Only the lower part of the Pinedale glaciation till has a long hall'period (620 ka) with a young age (60 + 50 ka), and this was one of the units to be omitted from the calibration curve (5b in Table 3, Rosholt, 1985). The chances of this happening from a random choice of known-age sediments must be very low; why should there not be a range of half-periods for different age sediments and different textures? Even low half-period sediments could have high ages, and be dateable, up to the usual dating limit of 350 ka. Thus, one would have expected more of a scattergram appearance to the plot. Fourth, it should be made clear that there is only one independent parameter, )~0, in the U-trend equations. Unless it is explicitly recognized that there can be different strength sources giving different growth and decay terms, from one sediment to the next, C~, C2, C~, Ca, and C5 cannot be determined independently of one another. As was discussed above, however, it is true that U-flux terms (together) and a-recoil terms would contribute independently of one another. It is, therefore, not clear why the calibration ages (equivalent to estimating coefficients C~-C5) are needed at all, since it is a simple matter to recover gradient and intercept from the empirical equations by putting in various values of the age for each value of ~0. The gradient-intercept values can be simulated (as for models in paper II, for example). The form of the empirical equations does not change, and the initial conditions have been prescribed by a constant 2~4U/~3aU AR.

THE THORIUM-INDEX PLOT Different depositional units and their U fluxes will usually represent different depositional or U flux times; that is, there may be significant time gaps between successive units and correspondingly different U fluxes. Therefore, it is necessary to see if succeeding samples belong to the same depositional unit. The methodology to distinguish depositional units is by means of a 'Thorium-Index plot', as follows (Rosholt, 1980; Muhs et al., 1989):

A different plot of the isotopic data can be constructed when the 238U/23?Thratios of the samples are plotted on the X-axis vs. the 2-~°Th/232Thratios plotted on the Y-axis - [Fig. 5 in this paper.] This thorium plot is similar to the isochron plot used by All~gre and Condomines (1976) for dating young volcanic rocks. The plot is used to determine if all the samples included in the uranium-trend line describe a reasonably linear array on the thorium plot, and thus serves as a useful check to determine if all samples belong to the same depositional unit. COMMENTS ON THE THORIUM-INDEX PLOT AND LABORATORY PROCEDURES For the Thorium-Index plot, the samples are dissolved in strong acids (Fig. 5 of Rosholt, 1980), and the U-trend data is produced ]rom the same analyses. The U-trend isotopes are, however, supposed to include only the loosely bound U and its related radiogenic daughters, whereas the :32Th-index data specifically relates to the isotopes of the resistate substrate. Under the same dissolution conditions, these two aims are in conflict. It is evident that since 232Th is not a part of the U-flux process, it being insoluble in groundwater, its presence automatically implies the presence of resistate 238U, 234U and 23°Th in the U-trend data and U-trend plots. Accordingly, these plots will be biased in the direction of the resistate activities by an amount depending on the relative concentrations of the isotopes in the resistate phase to those in the labile phase. One might suppose that recognition of this problem has led to the assumption that initial ARs were the same throughout the unit and, since it is only the gradient of three or more points that is used, adding constant AR values, representing the resistate phases, will make no difference to the gradient. However, (1) U-trend is said to incorporate a term representing recoil displacement of daughters from the resistate phase which affects this a s s u m p t i o n , and (2) for most l e a c h i n g t e c h n i q u e s , Schwarcz and Latham (1989) and Pryzybilowicz et al. (1991) point out the possible existence of differential leaching of different isotopes from resistate into solution. Presumably, in practice, other sedimentary indicators, such as colour and grain size variations and the recognition of disconformities, could also be used to delimit a given unit. There is still a potential problem for, even mild, acid leaching techniques insofar as the loosely bound, authigenic :3°Th can only be brought into solution at pHs less than about 3.5. Isotopic transport and immobilization of U-flux isotopes take place at pH values ranging from about 5 to 8. In some sediments, one could imagine that such light leaching will take up Th and U that is not related to the U-fluxing process. VARIATIONS OF U AND ISOTOPIC ACTIVITY RATIOS WITH DEPTH OF SEDIMENT After fluxing, U-trend model A and the three models meant to approximate U-trend (paper IF) predict that U concentrations will vary monotonically with depth.

A.G. Latham: Principles of the U-Trend Method, I However, it is evident from the data tables of Rosholt (1980, 1985) or Rosholt et al. (1985a, b) that U does not always vary systematically with depth. In order to test for this, the statistics package, MINITAB, was used on a number of the published data of various sedimentary units (the analysis is not exhaustive) f r o m Rosholt (1985), Rosholt et al. (1985a) and Muhs et al. (1989), including two of the age-calibration units, in the following two ways; (1) U was regressed against depth and Th; and (2) U/Th was regressed against depth. For (2), a value for the F-statistic was computed from the mean squares due to linear regression and the mean s q u a r e s due to d e v i a t i o n f r o m the s t r a i g h t line. Comparing this F value against standard table F values gave an F-test which determines if the gradient due to regression was significantly different from zero. Thus, the null hypothesis, H0, was that the regressed gradient, of U/Th vs. depth, was not significantly different from zero, and a 5% level of confidence was chosen beforehand. For (1), most units showed that U was more strongly correlated to Th than to depth, as expected, and the correlation with Th was usually positive. Of 11 units examined, only one showed a negative correlation with Th. In some cases, Th and depth variations explained (R 2 > 90%) most of the variations of U whereas, in others, the R 2 values were down around 20%. For test (2), six units showed no significant variation with depth of U/Th, including the two calibration units, Lake Tecopa A tuff and the Bull Lake end moraine. Three units showed a slight decrease with depth and two s h o w e d a s i g n i f i c a n t U / T h i n c r e a s e with depth. Particularly noteworthy were the marine terrace units, PVH1 and P V H 4 , f r o m Muhs et al. (1989). PVH1 showed U/Th to be highly correlated with depth with a correlation coefficient of 0.971, whereas PVH4 was almost perfectly anticorrelated with depth, with a correlation coefficient of-0.993. Similarly, the U-trend diagram (Fig. 1) strongly implies that ARs should vary systematically with depth since they must vary systematically with time. Therefore, similar statistical analyses, though even more cursory, were used to show that there is very little or no systematic variation in the isotope ARs, 234U/238U and 23°Th/238U, with depth. Thus, for example, units PVH1 and PVH4 showed that the two isotope ratios were invariant with depth, despite the observation that U/Th values were, respectively, strongly correlated and anticorrelated with depth. In order to satisfy the requirements of the U-trend plots, it is necessary, but not sufficient, to show that the two ARs should be correlated with each other. A cursory selection from Muhs et al. (1989) and from Rosholt et al. (1985a), shows that 23°Th/238U and 234U/238U are, usually, either significantly inversely correlated (at a 5% level of confidence) or are not correlated. However, inverse correlation between these two particular AR variables can be explained, not only by systematic U-fluxing, but also by the simple expedient of allowing water to filter through the unit with a more-or-less constant 234U/238Uratio (more

417

strictly, with correlated activities), irrespective of the age of deposition or the time of water movement. This can be seen, as follows: The regression equations for PHV1 and PHV4 are (ignoring analytical errors and the use of YORKFIT, Muhs etal., 1989): 23°Th/238U = 5.2 - 4.4 234U/238U, and 23°Th/Z38U= 4.1 - 3.2 234U/238U, thus showing the inverse correlation. If water moves down through the sediment at about neutral pH then 23°Th is c o m p a r a t i v e l y i m m o b i l e . T h e r e f o r e , for a short t i m e s c a l e , 23°Th = constant, and we can then rearrange a typical regression equation, such as either of the above, to read 234U = KI238U "1- K2, where Kl and K 2 are empirical constants. Thus, the original inverse correlation may only be reflecting a (common?) property of U-flux that 234U and 238U activities are positively correlated with each other. Whether water is present now or has ceased long ago is immaterial to the observation of this derivable positive correlation. There is not necessarily any age information here. Rather, what is more important for age estimation is that the two ARs should be correlated with depth and this does not appear to be the general case for the data so far presented.

DISCUSSION AND C O N C L U S I O N S The two basic ideas behind the open-system U-trend method for dating Quaternary sediments are that the attenuation of a repeating U-flux leaves behind a trail of daughter products in such a way as to hold age information, and that this age information can be recovered by means of independently dated sediments whose U flux attenuation is claimed to reveal the attenuation of the target sediment. If fluxing was continuous over a long period of time and attenuation was low, then the method has the potential of being able to date sedimentary units that are more than a million years old. In attempting to systematize the dating of open-ended systems using the U-trend model, Rosholt and co-workers list various problems that inhibit regularity in either sedimentation, U fluxing or in the subsequent history of the sediment, and these are summarized in Muhs et al. (1989). These include: the mixing of sediments, fixed phase U that is significantly greater than mobile-phase U, deposits with no contact with U-bearing water, sediments approximating closed-system conditions (such as precipitates), sediments with little sorptive capacity for U, too homogeneous mineralogy resulting in similar U - T h abundances and sediments with complex history. These conditions generally are thought to lead to non-linearity in the plots or to bunching of data points making regression meaningless. Muhs (pers. c o m m u n . ) is also concerned to exclude sediments that have experienced U emplacement from groundwater. Before even these problems can be addressed, however, there appear to be flaws in the underlying methodology of the U-trend approach as currently practiced:

418

Quaternary Science Reviews (Quaternary Geochronology): Volume 14

(i) It is not made clear that 'open-system' means regular open system in the sense that the U-trend method can only be used on sediments whose U-flux has continued from some initiation time to the present day in a more-or-less systematic fashion. Several of the data tables of Rosholt (Rosholt, 1980, 1985; Muhs et al., 1989 and others on U-trend) indicate that attempts were made to date superposed units. Although complex histories are ruled out, some of these examples and calibrations would appear to raise the suspicion that accumulation, or significant fluxing, has ceased some time ago. Such sediments would have a two-stage history incorporating a c o n t i n u o u s U-flux f o l l o w e d by normal radioactive decay re-equilibration. Moreover, it is almost certain that the isotope ARs from a two-stage process can mimic those from a single stage process and the data are thus susceptible to non-unique interpretation. This means that other information is needed in order to rule out the possible objection that the observed ARs have resulted, perhaps in part, from ordinary radioactive decay following the cessation of U-fluxing. These considerations are not made sufficiently clear in U-trend publications. (ii) In the general closed-system case, the age information is lost either if we do not know the initial conditions or if there has been some unknowable subsequent disturbance (becomes irregular open-system). What is certain is that we ought to know the exact form of the system equations as for the case of a closed-system, pure, secondary precipitate (see Introduction). In the regular open-system case of the U-trend approach, a major role in these assumptions is assumed by the exact form of the empirical attenuation-decay equations with the necessity to find the attenuation parameter or, equivalently, the half-period. The attenuation parameter, unlike the decay constants which it resembles functionally in the empirical decay equations, however, is a variable that is theoretically, if not practically, unique to each sediment. This means that each sediment has its own attenuation-decay line (Utrend curve) which is determined by both the value of the parameter and the initial conditions. A different sedimentary unit of the same age would, in general, have a different attenuation-decay line, either because the initial conditions had been different or because the half-period was different or both. The first part of the problem in the U-trend model is accommodated by assuming some of the initial conditions, such as: (1) No initial fluxed 23°Th. This is probably safe in many cases but Muhs (pers. commun.) points out that clay formation in many soils might be expected to carry sorbed colloidal 23°Th. (2) No 'hard' 23°Th leached from the sediment in the laboratory preparation. This is unsafe; it is violated by the apparent necessity to produce Thorium-Index plots. However, it is potentially solvable by analysing twin aliquots in weak and strong acids separately; and (3) Fluxed 23au/238U ratios that are initially the same from subunit to subunit within the same sediment. For the latter, it is not clear if it has been assumed that

initial 234U/238Uratios are the same from one sediment to another, or are assumed to have been the same from the target sediment to the calibration units. Considerations from Models B and C (paper II), for example, indicate that, even if all the above are satisfied, the attenuation-decay lines of the target sediment may still be different from any of those from the calibrations because the initial 234U/238U ratios were probably different. All that the U-trend methodology assumes is that initial 234U/23sU ratios were the same throughout a set of roughly co-eval sublayers. The empirical equations of U-trend contain terms that are said to take into account the amount of m-recoiled 234U/23°Th. However, in order to do this, no reference is given to the amount of resistate or source 23sU in the sediment, nor is there any discussion as to how this can possibly be allowed for using calibrated known-age sediments whose fluxed U to resistate U is likely to have been different In the continuing development of the m e t h o d o l o g y , this a p p r o x i m a t i o n has r e m a i n e d unassessed. Because of its largely intractable nature, it is also omitted from the (first approximation) models of paper II. (iii) It is not clear why it is necessary to have to use known-age sediments in order to find the age of the target sediment. Simulations made by substituting in values of age and )~0, from a model or from the empirical equations, can provide the calibrations for us since the form of the equations remain the same from one to the other. If it is in order to estimate how long ago Ufluxing ceased, so that an allowance be made for whole system decay to re-equilibration, then this is never mentioned. If it is in order to assess the ratio of fluxed to recoiled daughters, then this is also not pointed out. The gradient and intercept are both needed to make the estimate of the attenuation parameter (half-period) and age. The oft-presented calibration curve, Fig. 3, in isolation, tends to obscure this double requirement. Thus, the reverse sigmoidal-shaped line is only one of many lines that can exist; either a third axis is needed with gradient plotted along it, or the gradient-age nomogram for various half-periods is also needed, as in Fig. 4 of Rosholt (1980). From the experimental procedures used in U-trend and from some of the resulting published data, the following problems have been identified. A major part of the U-trend methodology has to do with identifying discrete units by means of linear Thorium-Index plots, and this is achieved in the same experiments that are used to produce the U-trend isotope ratios. 23~Th is clearly neither a fluxed isotope nor a recoiled one. It can only be concluded that the analysed 'fluxed' isotopes must also contain concomitant amounts of resistate 23sU, 234U and 23°Th. No attempt seems to have bene made to correct for this using, say, 232Th as an index for subtracting off resistate amounts of the U-trend isotopes. The overall effect must be to make fluxing and sedimentation appear older than they really are because, in general, the sediment materials may be expected to be

A.G. Latham: Principles of the U-Trend Method, I much older than the later fluxing. This same problem has been tackled in the age estimation o f c o n t a m i n a t e d calcites (see Introduction). If U-fluxing is a natural systematic process, it should be possible to observe a systematic trend in 23su concentration with sediment depth. As examined here from the published work, this was not statistically apparent in five units, including two o f the calibration units, out o f a selection of l 1. Some units show that U increases while o t h e r s s h o w that U d e c r e a s e s with d e p t h and this apparently indicates that divergent U transport processes operated. By contrast, the U-trend model A and models in paper II predict systematic variation of U with depth. These models and the statistical analyses of the data place in perspective Rosholt's (1980, 1985) claim that modern deposits show an exponentially decreasing U-flux with time. The evidence used for this observation has not been presented (explicitly, at any rate). Similarly, the U-trend Fig. 1 indicates that regularity in U-fluxing over some period of time must have led to a s y s t e m a t i c v a r i a t i o n in i s o t o p e A R s w i t h d e p t h . Unfortunately, many of the published units apparently show AR data points scattered along the regression lines without any order related to depth, and these impressions were confirmed by statistical tests in some cases. It is notable that the U-trend publications, though talking about attenuation, which is strictly a thickness-related fall-off in concentration, disregard any depth variations of the data or parameters, aside from in the introductions. It may be that z need not appear in the age equations (paper II), but the A R data points must, at least, be ordered with depth. (iv) In order to obtain age information, a straight line through pairs of isotope ARs is not a sufficient guarantee of the present methodology, as it can be shown that correlation between A R pairs can also result simply from transport of regularly correlated ~34U and 238U at any time and in any way (filtration, leaching, chemical changes, rising groundwater etc.). A great deal of work has been published by Rosholt and co-workers in order to test the feasibility of the Utrend method in the hope that upper Quaternary sedimentary units could be amenable to dating. Evidently, the empirical approach was adopted in the belief that formal regular open-system models might never be forthcoming or sufficiently widely applicable and that the sediment thickness had to be eliminated from the equations. It has, apparently, yielded realistic age estimates for some sedimentary units and is therefore worth pursuing further. If "the proof of the pudding is in the eating" at least some of the U-trend results have been palatable. So, despite the formidable problems with the current methodology, is the U-flux concept still feasible? To answer this, perhaps a more systematic approach would be: (1) to investigate the isotopic concentration and AR variations in much longer uniform units, preferably with as complete a history as possible; (2) to test for lateral variations within the same unit; (3) then to look at different sedimentary source units; and (4) to look at the

419

same source units, but having different climatic histories. In the laboratory, the task is to be able to isolate only the U-flux isotopes without having to spend too much time doing leaching experiments on individual samples. The advantage of knowing that only the U-fluxed isotopes have been isolated is that only these are supposed to contain any potential age information. U-flux disequilibrium is simply diluted by resistate phase isotopes that are usually close to equilibrium, and finding the point at which leaching changes over from attacking one phase to the other is no small task. In the case of uniformly contaminated calcites it was found necessary to use isochron plots from multiple leachates with 232Th as a resistate phase index (Ivanovich et al., 1992). If similar procedures have to be adopted here the overall methodology could be quite long.

ACKNOWLEDGMENTS I am grateful to JNR's colleagues, B. Szabo and Dan Muhs (USGS) for advice, comments on the first draft and offprints on method and applications, and to Miro Ivanovich (Harwell) for access to unpublished work. John N, Rosholt, the developer and user of this fascinating U-trend technique for dating sediments, died in 1991 while I was becoming interested in the method. I benefitted from him for his technical help variously over the brief period in which I knew him. To find a way to date sediments was a great challenge to JR and, perhaps, he considered it to be part of the 'gravy' of his life. He once related how his platoon was wiped out in Italy in the Second World War, and how he was the only survivor. "I should've gone with 'era", he said, "So all my life after that I considered to be gravy". This work was supported by SERC (U.K.) grant GR/F80340 to A.G. Latham and J. Shaw.

REFERENCES Allbgre, C.J. and Condomines, M. (1976). Fine chronology of volcanic processes using 238U-Z3°Thsystematics. Earth and Planetary Science Letters, 28, 395-406. Atkins, M. (1986). A geochemical and geochronological study of U and Th radioisotopes in paleosols, loess and tephra: a Middle Rhine case study. Ph.D. thesis, University of Reading, 349 pp. Bischoff, J.L. and Fitzpatrick, J.A. (1991). U-series dating of impure carbonates: An isochron technique using total-sample dissolution. Geochimica et Cosmochimica Acta, 55, 543-554. Chen, T.M. and Yuan S. (1988). Uranium dating of bones and teeth from Chinese Paleolithic sites. Archaeometry, 30, 59-76. Frye, J.C. (1973). Pleistocene succession of the central interior United States. Quaternary Research, 3, 275-283. Grtin, R., Schwarcz, H.P. and Chadam, J. (1988). ESR dating of tooth-enamel: coupled correction for U-uptake and U-series disequilibrium. Nuclear Tracks and Radiation Measurements. 14, 237-241. Hille, P. (1979). An open-system model for uranium series dating. Earth Planet Science Letters 42, 138-142. Ivanovich, M. and Harmon, R.S. (eds) (1992). Uranium-Series Disequilibrium. Applications to Earth, Marine, and Environmental Sciences (2nd edn). Oxford University Press,

Oxford. Ivanovich, M., Latham, A.G. and Ku, T.-L. (1992). Uraniumseries disequilibrium applications in geochronology. In: Ivanovich, M. and Harmon, R.S. (eds), Uranium-Series Disequilibrium. Applications to Earth, Marine, and

420

Quaternary Science Reviews (Quaternary Geochronology): Volume 14

Environmental Sciences (2nd edn). Oxford University Press, Oxford. Ku, T.-L. (1988). Radiometric dating with U- and Th-series isotopes in the Nevada Test Site region - - a review, Appendix D. In: Bell, J. (ed.), Quaternary Evaluation of the Geological Relations and Seismo-Tectonic Stability of the Yucca Mountain Area, Nevada Nuclear Waste Site Investigation (NNWS1). Center for Neotectonic Studies, University of Nevada at Las Vegas, NV. Ku, T.-L. and Liang, Z.C. (1984). The dating of impure carbonates with decay series isotopes. Nuclear Instruments and Methods, 223, 563-571. Luo, S. and Ku, T-L. (1991). U-Series isochron dating: a generalized method e m p l o y i n g total sample dissolution. Geochimica et Cosmochimica Acta, 55, 555-564. Muhs, D.R., Rosholt, J.N. and Bush, C.A. (1989). The uraniumtrend dating method: principles and application for Southern California Marine Terrace deposits. Quaternary International, 1, 19-34. Patton, EC., Biggar, N., Condit, C.D., Gillam, M.L., Love, D.W., Machette, M.N., Mayer, L., Morrison, R.B. and Rosholt, J.N. (1991). Quaternary geology of the Colorado Plateau. In: Morrison, R.B. (ed.) Quaternary Nonglacial Geology; Coterminous U.S., Vol. K-2. The Geology of North America, Geological Society of America, Boulder, CO. Pierce, K.L. (1979). History and dynamics of glaciation in the northern Yellowstone National Park area. U.S. Geological Survey Professional Paper, 729-F. P r y z y b i l o w i c z , W., Schwarcz, H.P. and Latbam, A.G. (1991). Dirty Calcites, II: uranium-series dating of artificial c a l c i t e - d e t r i t u s mixtures. Isotope Geoscience, 86, 161-178. Rosholt, J.N. (1967). Open-system model of uranium-series dating of Pleistocene samples. In: Proc. Symp. Radioactive

Dating and Methods of Low-Level Counting, Monaco, pp. 299-310. Rosholt, J.N. (1980). Uranium-trend systematics for dating Quaternary sediments. U.S. Geological Survey, Open-File Report, 80-1087. Rosholt, J.N. (1985). Uranium-trend systematics for dating Quaternary sediments. U.S. Geological Survey, Open-File Report, 85-298. Rosholt, J.N., Bush, C.A., Shroba, R.R., Pierce, K.L. and Richmond, G.M. (1985a). Uranium-trend dating and calibrations for Quaternary sediments. U.S. Geological Survey, Open-File Report, 85-299. Rosholt, J.N., Bush, C.A., Carr, W.J., Hoover, D.L., Swadley, W.C. and Dooley, J.R., Jr (1985b). Uranium-trend dating of Quaternary deposits in the Nevada Test Site Area, Nevada and California. U.S. Geological Survey, Open-File Report, 85-540. Rosholt, J.N., Colman, S.M., Stuiver, M., Damon, EE., Naeser, C.W., Naeser, N.D., Szabo, B.J., Muhs, D.R., Liddicoat, J.C., Forman, S.L., Machette, M.N. and Pierce, K.L. (1991). Dating methods applicable to the Quaternary. In: Morrison, R.B. (ed.), Quaternary Nonglacial Geology; Coterminous U.S. Vol. K-2. The Geology of North America, Geological Society of America, Boulder, CO. Schwarcz, H.E and Latham, A.G. (1989). Dirty calcites I: uranium series dating of contaminated calcite using leachates alone. Isotope Geoscience,'80, 35-43. Szabo, B.J. and Rosholt, J.N. (1969). Uranium-series dating of Pleistocene molluscan shells from Southern California: an open-system model. Journal of Geophysical Research, 74, 3253-3260. Szabo, B.J. and Rosholt, J.N. (1989). Uranium-series radionuclides in the Golden fault, Colorado, U.S.A.: dating latest fault displacement and measuring recent uptake of radionuclides by fault-zone materials. Applied Geochemistry, 4, 177-182.