Thermal annealing of fission tracks in apatite 4. Quantitative modelling techniques and extension to geological timescales

Chemical Geology (Isotope Geoscience Section), 79 (1989) 155-182 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

155

Thermal annealing of fission tracks in apatite 4. Quantitative

P.F. GREENl,*‘,

modelling techniques and extension timescales

I.R. DUDDY2,

G.M. LASLETT3, K.A. HEGARTY2, J.F. LOVERING

to geological

A.J.W. GLEADOW’T*~

and

‘Department of Geology, University of Melbourne, Parkville, Vie. 3052 (Australia) ‘Geotrack International, P.O. Box 4120, Melbourne University, Vie. 3052 (Australia) “C.S.Z.R.O. Division of Mathematics and Statistics, Clayton, Vie. 3168 (Australia) 4School of Earth Sciences, Flinders University, Bedford Park, S.A. 5042 (Australia) (Received June 27,1988; accepted for publication

January

10,1989)

Abstract Green, P.F., Duddy, I.R., Laslett, G.M., Hegarty, K.A., Gleadow, A.J.W. and Lovering, J.F., 1989. Thermal annealing of fission tracks in apatite, 4. Quantitative modelling techniques and extension to geological timescales. Chem. Geol. (Isot. Geosci. Sect.), 79: 155-182. A methodology is presented for the prediction of fission-track parameters in geological situations from a laboratorybased description of annealing kinetics. To test the validity of extrapolation from laboratory to geological timescales, the approach is applied to a number of geological situations for which apatite fission-track analysis (AFTA) data are available and where thermal history is known with some confidence. Predicted fission-track parameters agree well with observation in all cases, giving confidence in the validity of the extrapolation, and suggesting that fission-track annealing takes place by a single pathway in both laboratory and geological conditions. The precision of predicted track lengths is considered in some detail. Typical levels of precision are - + 0.5 pm for mean lengths 5 10 pm, and - ? 0.3 pm for length 2 10 pm. Precision is largely independent of thermal history for any reasonable geological thermal history. Accuracy of prediction is limited principally by the effect of apatite composition on annealing kinetics. The development of fission-track parameters is illustrated through a series of notional thermal histories to emphasise various key aspects of the response of the system. Temperature dominates over time in determining final fissiontrack parameters, with an order of magnitude increase in time being equivalent to a - 10°C increase in temperature. The final length of a track is determined predominantly by the maximum temperature to which it is subjected. Aspects of AFTA response are further highlighted by prediction of patterns of AFTA parameters as a function of depth and temperature from a series of notional burial histories embodying a variety of thermal history styles. The quantitative understanding of AFTA response not only affords the basis of rigorous paleotemperature estimation, but also allows a better understanding of the situations in which AFTA can be applied to yield useful information.

1. Introduction In previous papers (Green et al., 1986; Laslett et al., 1987), we have described the behaviour of fission tracks in apatite during isotherma1 laboratory annealing, and developed an empirical quantitative description of the pro0168-9622/89/$03.50

0 1989 Elsevier Science Publishers

cess, in terms of the rate of decrease of the mean confined track length of induced tracks in Durr’sPresent addresses: *‘Department of Geology, La Trobe University, Bundoora, Vie. 3083, Australia. *‘Geotrack International, P.O. Box 4120, Melbourne University, Vie. 3052, Australia.

B.V.

156

ango apatite (Mexico). We then adapted this isothermal treatment to describe annealing under variable temperature conditions (Duddy et al., 1988). These studies are designed to develop a quantitative understanding of annealing behaviour, capable of accurately predicting fission-track parameters in geological situations, and thereby providing estimates of paleotemperatures in natural samples. Studies of natural annealing of fission tracks in apatites from borehole sequences have established that in most circumstances such effects are observed in the temperature range 20-150°C (Naeser, 1979; Gleadow and Duddy, 1981; Gleadow et al., 1983; Hammerschmidt et al., 1984; Green et al., 1989). It is worth noting that our basic laboratory annealing data (Green et al., 1986) cover the temperature range 40095°C and so the field of experimental control on the annealing description developed by Laslett et al. (1987) actually overlaps the geological field. The extrapolation in terms of time, however, is still severe, over several orders of magnitude from laboratory timescales of up to 500 days to geological times of the order of millions of years. For confident use, the validity of such extrapolation should be demonstrated rather than assumed. In this paper, after developing the methodology required to model the evolution of fission-track parameters through geological thermal histories, we discuss geological constraints on fission-track annealing behaviour which provide tests of the extrapolation of the laboratory description. After showing that predicted fission-track parameters are consistent with observations in a variety of geological situations, we illustrate the response of fission tracks in apatite through a variety of notional but geologically reasonable thermal histories, in order to establish the general pattern of behaviour, and to highlight those situations in which apatite fission-track analysis (AFTA) can be employed to best advantage as a means of paleotemperature estimation.

P.F. GREEN

2. Quantitative 2.1. Model@ system

modelling

ET AL.

procedures

the response of the AFTA

The basic response variable of the AFTA system is the etchable track length, i.e. the total length over which a latent track is etchable. Studies of newly created induced fission tracks in a variety of apatites suggest that tracks form within a narrow range of etchable lengths (Gleadow et al., 1986). Once formed, the etchable length of a track is reduced at a rate which depends on temperature and the amount of shortening that has already occurred (Laslett et al., 1987 ). New tracks are produced through time, and at the present day an apatite contains a distribution of etchable track lengths which reflects the thermal history. The fission-track age is a reflection of the time over which tracks have been retained in the apatite and the amount of annealing (length reduction) that has taken place. To simulate the response of this system, we divide the thermal history into a series of intervals. Using the variable-temperature annealing description given by Duddy et al. (1988), we then predict the final length of tracks formed during each interval, using the appropriate temperature-time path. The final lengths of tracks produced in each interval are then summed to produce the net distribution of track lengths expected from the entire thermal history. In taking this approach, we are assuming that at the time of formation, spontaneous tracks are essentially identical to induced tracks. Several lines of evidence, reviewed by Green (1988), suggest that this assumption is valid. Note that the treatment outlined by Laslett et al. (1987) and Duddy et al. (1988) is based on observed mean confined track length. Green et al. (1986) showed that the distribution of observed track lengths showed a progressive broadening as the degree of annealing increased. Therefore for each interval the appro-

THERMAL

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4

priate distribution of track lengths about the predicted mean length is summed, after first correcting for the geometrical bias in confined track revelation following the procedures of Laslett et al. (1982). Finally the summed distribution is then re-biased to predict the distribution of confined track lengths that would be observed in the apatite. Note also that although fission-track annealing in apatite is anisotropic (Green and Durrani, 1978; Laslett et al., 1984; Green et al., 1986)) the treatment developed in this paper is based only on the mean confined track length. We have adopted this strategy deliberately, with the intention of pursuing the predictive model based on this simplifying assumption as far as possible. If realistic predictions can be derived from such an approach, it is considered unnecessary to further complicate the treatment by development of a kinetic description as a function of angle to the c-axis. The anisotropy of annealing is still accommodated within our treatment, as this is a major influence on the form of the distribution of confined track lengths as annealing becomes increasingly severe (Green et al., 1986). We will show that the treatment based on mean length alone gives satisfactory predictions, and we therefore feel that further sophistication is unwarranted at present. An estimate of fission-track age can also be derived by adding, for each time interval, a component of age appropriate to the final length of the tracks produced in that interval. In the work discussed in the following, we have used the relationship for mono-compositional apatites presented by Green ( 1988)) assuming that ages are normalised to a mean length of 14.5 pm, as observed in the age standards used to calibrate the apatite fission-track dating system (Green, 1985; Gleadow et al., 1986). This procedure carries the implicit assumption that the processes observed to take place during annealing of tracks in Durango apatite (Green et al., 1986; Laslett et al., 1987; Duddy et al., 1988) are completely general, and can be

assumed to be a property of all apatites. While this may or may not be true, evidence at hand, such as the similarity of the length-density reduction relationship in three different apatites reported by Green ( 1988)) suggests that the assumption is justified. Ongoing annealing studies in a variety of different apatites will throw further light on this question.

2.2. An example of predicted

AFTA response

Fig. la shows shortening trajectories of tracks produced at the beginning of 20 time intervals of equal duration within the thermal history shown in Fig. lb (linear cooling from 100” to 20” C over 200 Ma). Since the sub-history for each interval is also a linear cooling, all trajectories show qualitatively similar shortening behaviour, similar also to that for the cooling case in fig. 3 of Duddy et al. (1988). Such behaviour, with initially rapid shortening followed by a longer period in which further shortening is minimal, is characteristic of cooling and can be understood in terms of the equivalent time concept described by Duddy et al. (1988). The final length of tracks from each interval progressively increases, since later-formed tracks are subjected to lower temperatures than those formed earlier. When the component distributions of track lengths about the final predicted mean values are summed as explained above, the resulting distribution of track lengths is as shown in Fig. lc, and shows a skewed distribution with a standard deviation of - 1.9 pm and a mode in the 13-15-flm region with a tail to shorter lengths of - 10 pm or less. Fig. Id shows the evolution of the fissiontrack age throughout the thermal history shown in Fig. lb. The fission-track age always lags behind elapsed time, because of the length reduction that has occurred early in the history. In l&r stages, however, the fission-track age tends towards a linear increase, as mean lengths of the added components approach 14-15 ,um. Conversely, Fig. 2a shows shortening trajectories of tracks produced throughout the ther-

158

P.F. GREEN

. 160

. 120 TIME

80

(Ma

.

I

40 B.P.)

0

0 6 10 TRACK LENGTH

15

ET AL.

20

(microns)

;200 I ;160 !: 5 2 Ip 120

I 200

. 160

. 120 TIME

. 60 (Ma

40 B.P.)

1 0

iz

120 80 40 0 200160120 TIME

80

(Ma

40 B.P.)

0

Fig. 1. Evolution of the length of tracks (a) produced at various times through the thermal history shown in (b) (linear cooling from 100 ’ to 20 oC over 200 Ma). Each individual shortening trajectory is of the same form as that shown in fig. 3 of Duddy et al. (1988), characteristic of linear cooling, but the final length is different for each track, as the maximum temperature each track experiences is different. When added together in the proportions defined by the bias in revelation of tracks of different lengths (Laslett et al., 1982), the final lengths of the individual trajectories lead to the distribution of confined track lengths shown in (c ) . In (d), the evolution of fission-track age is plotted against elapsed time. The fissiontrack age increases only slowly at first, where annealing is pronounced, but as temperature decreases, and new tracks are shortened only to m 14-15 e, the age increases more or less linearly.

ma1 history shown in Fig. 2b, comprising a linear heating between the same end temperatures as in Fig. lb. Again, the trajectories of tracks produced at different times are qualitatively similar, showing the same form as that for the heating case in fig. 3 of Duddy et al. (1988). This type of behaviour, again showing initially rapid shortening followed by slower but progressive shortening, is characteristic of heating and is also understandable in terms of equivalent time (Duddy et al., 1933). In contrast to Fig. la, most of the track paths in Fig. 2a converge to almost the same fmal track length. Only those tracks formed in the last 10% of the history do not shorten quite as much as the older tracks. This is a reflection of the dominance of temperature over time in annealing. Since, in this heating case, all tracks formed at different times throughout the history are subject to the

same. maximum temperature, they are all shortened to more or less the same final length. The final distribution of observed confined track lengths is therefore narrow, with the only source of spread being the inherent spread observed in laboratory-annealed apatites (Green et al., 1986). In Fig. 2d, the evolution of fission-track age corresponding to the thermal history of Fig. 2b is illustrated. In the early stages of the history, the fission-track age is close to the elapsed time, since all tracks then formed have been exposed only to low temperatures and have lengths of N 14-15 pm. However, as temperature increases and tracks are progressively shortened, the fission-track age begins to lag behind elapsed time and ultimately begins to decrease as temperature reaches values where track density reduction is severe.

THERMAL

ANNEALING

z” 2

OF FISSION

TRACKS

IN APATITE,

159

4

1.0

40 8

E

2 05 y

T

30 20

I-z

.

a)

6

g 2

. 160

. 120 TIME

. 80 (Ma

. 40 B.P.)

1 0

.

(1

cl

S. D. =

21.83

B B . g 0.0 ’ % 200

=

9.02

8

0.5

l4dL MEAN

10 0 0 5 10 TRACK LENGTH

15 20 (microns)

0=

e

20

g2

40

2 i

60 80

.

?lOO .

120 200

160

. 120 TIME

. 80 (Ma

40 B.P.)

0

200

160120 TIME

80 40 (Ma B.P.)

0

Fig. 2. Evolution of the length of tracks (a) produced at various times through the thermal history shown in (b) (linear heating from 20 to 100 ’ C over 200 Ma). Each individual shortening trajectory is of the same form as fig. 3 of Duddy et al. (1988)) characteristic of linear heating, and the final length is very similar for all tracks except those produced in the last - 10 Ma, as the maximum temperature each track experiences is the same. When added together in the proportions defined by the bias in revelation of tracks of different lengths (Laslett et al., 1932), the final lengths of the individual trajectories lead to the distribution of confined track lengths shown in (c ) . In (d) , the evolution of fission-track age is plotted against elapsed time. The fission-track age increases more or less linearly at first, where annealing is less pronounced, but as temperature increases the age begins first to increase more slowly and then to decrease as annealing becomes increasingly severe.

2.3. Precision and accuracy of prediction In discussing the extrapolation of an empirical fit to laboratory data over geological timescales, we must consider the precision with which values of track length can be estimated. We must also consider the distinction between precision and accuracy. When assessing precision, we adopt the customary, if possibly unrealistic position that the preferred model for annealing is structurally correct - that is, the mathematical form of the annealing kinetics is known apart from a few parameters which must be estimated from laboratory experiments (Green et al., 1986; Laslett et al., 1987). Future evidence may suggest slight adjustments to the model structure, but such inadequacies in the current model, if they

exist, would usually lead to inaccuracy in prediction, as opposed to imprecision. Nevertheless, discussion of precision is important, because there is little point in using wellcontrolled laboratory data or field data from geological regimes of well-understood thermal history in order to systematically investigate the accuracy of an inherently imprecise method. A number of experimental factors also affect the accuracy of the predictions from our approach. The most important of these is the fact that the predictions relate to a single apatite composition - that of the Durango apatite [Cl/ (Cl/F) N 0.1; Sieber, 19861 in which the laboratory data were obtained. A growing body of evidence (Green et al., 1985,1986,1988; Sieber, 1986; I.R. Duddy, unpublished results, 1987; P.R. Tingate, unpublished results, 1989) sug-

160

gests that the dominant influence on annealing sensitivity is the Cl/ (Cl + F) ratio, with fluorapatites being more easily annealed than chlorine-rich apatites. Therefore predictions based on the Durango apatite data only accurately estimate parameters in apatite with the same composition [Cl/ (Cl + F) ratio]. Experiments to extend the laboratory data set to other apatite compositions are in progress (P.F. Green, I.R. Duddy, G.M. Laslett and K.A. Hegarty, in prep.), and will eventually allow these predictive techniques to be applied to apatites of all compositions. A further limitation is introduced by our imperfect understanding of the bias in revelation of confined tracks with lengths of ,< 10 pm. Unpublished experimental data suggest. that additional bias factors to those recognised and discussed by Laslett et al. ( 1982 ) affect the revelation of such short tracks. Therefore the procedure described on pp. 156 and 157, involving only the recognised factors, tends to overestimate the number of these short tracks. Work is also in progress (P.F. Green, I.R. Duddy, G.M. Laslett and K.A. Hegarty, in prep.) to improve our understanding of these biases, and the results of this work will allow improved treatment of situations involving tracks of lengths of 5 10 pm. The theoretical basis of the precision calculations is given in the Appendix. Table I compares the precision of i, the estimated value of the length reduction r, for several thermal histories. In each row of Table I, temperature increases or decreases linearly from To to Tf over a time period t. The two complex histories illustrate the composite effect of several such linear episodes combined together. The entries in the second-to-last column of Table I are one standard error of fi in the last column, these have been converted to standard errors for estimated mean length L, where i=L/L,,, and L,, is a constant. We have taken L,=16.3, as is commonly observed in Durango apatite. Results in the first three blocks of Table I respectively show that the standard error off increases with increasing time when temperature

P.F. GREEN

TABLE

ET AL.

I

Estimated reduction in mean length i, and its standard error s.e. (i) , for temperature varying linearly between To to Tf over a time period t (in Ma unless otherwise indicated) TO

^ r

s.e. (i)

s.e. (i) (pm)

0.1 1 10 100

0.864 0.813 0.745 0.648

0.009 0.014 0.020 0.031

0.15 0.23 0.33 0.51

100 100 100

0.853 0.759 0.598

0.012 0.020 0.037

0.20 0.33 0.60

1 hr. 1a 1 100

0.745 0.747 0.749 0.746

0.005 0.010 0.019 0.021

0.08 0.16 0.31 0.34

Linear heating and cooling: 1 20 80 100 0.747 2 80 20 100 0.751

0.020 0.020

0.33 0.33

(“C)

Tf CT)

t (Ma)

x

16.3

Constant temperature: 1 2 3 4

80 80 80 80

80 80 80 80

Constant time: 1 2 3

45 65 85

45 65 85

Constant r: 1 2 3 4

325 205 93 67

325 205 93 67

Complex histories: 1 +2

20 90

90 20

5 5

0.772

0.017

0.28

1 +2 +3 +4

20 20 90 20

20 90 20 20

45 5 5 45

0.772

0.017

0.28

is constant, and increases with time when temperature is manipulated to produce constant ? (here N 0.75). The fourth block of Table I considers heating and its symmetric cooling: both i and s.e. (i) are virtually identical. The final block considers complex histories: the second complex history being the same as the first, apart from being surrounded before and after by two 45Ma periods at constant temperature (20’ C ). It is seen that the reductions are identical, as are the estimated standard errors. Most of these effects can be understood qualitatively as a combination of two factors: error increasing with increasing distance from the data set

THERMAL

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4

on which the prediction model was built (Laslett et al., 1987), and also increasing with decreasing ?, as the isoannealing contours in the Arrhenius plot become more closely spaced. From the second block, it may be concluded that the annealing model is sufficiently precise that it should be possible to use it to distinguish between substantially different temperature regimes over a typical geological time period. In addition, the two complex histories, line 3 of block 1, line 2 of block 2, lines 3 and 4 of block 3, and the linear heating and cooling all suggest that the standard error is not strongly dependent on time (for geological time periods) if r is constant. 3. Geological behaviour

constraints

on annealing

3.1. Introduction In this section we consider a number of geological situations in which the thermal history is known or can be inferred with some confidence, and in which AFTA data are available. We will show that the predictions of fissiontrack parameters in these situations are consistent with observations, suggesting that extrapolation from laboratory timescales is valid. 3.2. “Undisturbed

volcanic” apatites

In a survey of confined track length distributions in apatites from a wide variety of geological environments, Gleadow et al. (1986) showed that apatites from rocks that could be reasoned, on geological grounds, to have cooled extremely rapidly, and never to have been subsequently subjected to temperatures in excess of N 40-50’ C, showed a characteristic type of confined track length distribution, with a mean in the region of N 14-15 pm, and a standard deviation of N ? 1 pm. This was termed an “undisturbed volcanic” type of distribution by Gleadow et al. (1986). The apatite age standards employed in calibration of the fission-

161

track system (Green, 1985) all show this type of distribution. Fig. 3 shows the evolution of fission-track parameters in an apatite which has spent 30 Ma at 30°C (Fig. 3b). Fig. 3a shows that tracks formed at different times throughout the history are reduced rapidly at first to N 0.9-0.95 of their original length, after which very little further length reduction takes place. The final predicted distribution of confined track lengths shown in Fig. 3c is very similar to that described above as characteristic of such “undisturbed volcanic” samples, with a mean of 15.0 ,um and a standard deviation of N + 0.8 p. The fission-track age of such an apatite, as shown in Fig. 3d, is equal to the formation age of the sample (within rounding errors), since the age standards used in the technique also have mean confined track lengths of around this figure. The behaviour shown in Fig. 3a is very important to understanding the response of the AFTA system. The initial phase of very rapid length reduction results because the ends of a track are highly unstable, and are easily repaired, even at low temperature. This initial rapid decrease in length will be noted in all similar diagrams in this paper. The Arrhenius plot representation of the annealing description of Laslett et al. (1987) shows that at the earliest stages of annealing, the iso-annealing contours are very widely spread, and that conditions in which no annealing is predicted are not met in any realistic time-temperature regime. This emphasises the ease with which the first 5-10% of length reduction occurs. For all reasonable combinations of likely surface temperatures and geological times, the predicted track lengths resulting from thermal histories characteristic of undisturbed volcanic rocks lie in the region of 14-15 pm. Thus the pre@cted behaviour of fission tracks in apatite very closely mimic the observed behaviour (Gleadow et al., 1986)) giving confidence in both the procedures employed and also the assumptions on which they are built.

P.F. GREEN

162

z

30

24

18 TIME

12 (Ma

8 B.P.)

0

0

5 TRACK

10 LENGTH

ET AL,

15 20 (microns)

30 24 18 12 8 0 30

24

18 TIME

12 (Ma

8 B.P.)

0

30

24 18 12 8 TIME (Ma B.P.)

0

Fig. 3. Similar diagram to Figs. 1 and 2, for a thermal history consisting of residence at 30°C for 30 Ma. In this case tracks produced at all times undergo a rapid decrease in length initially, after which practically no further shortening occurs. The resulting length distribution shown in (c) has a mean of - 15 pm and a standard deviation of - f 0.8 pm, and is very similar to the “undisturbed volcanic” type of distribution defined by Gleadow et al. ( 1986).

3.3. Undisturbed

basement

Gleadow et al. (1986) also suggested that the type of length distribution resulting from a progressive monotonic cooling path shows a negatively skewed distribution, with a mean of 1213 pm and a standard deviation in the 2 1-2pm range. Consideration of Fig. 1 in this regard shows once more that the predicted parameters are in good agreement with observation. A similar distribution of confined track lengths is predicted for any thermal history in which temperatures decrease progressively with time, regardless of duration, although the mean length and the position of the distribution on the length scale shows some dependence on timescale. 3.4. Otway Basin reference wells Possibly the most rigorous constraint on the annealing behaviour of fission tracks in geolog-

ical situations comes from direct observations of in situ geological annealing in samples from boreholes at temperatures of up to 2 120’ C. In previous attempts to define the geological annealing behaviour of fission tracks in apatite (e.g., Gleadow and Duddy, 1981; Naeser, 1981; Harrison, 1985), thermal histories causing a given degree of annealing (age reduction) have been reduced to a single combination of effective temperature and time conditions, from geological evidence, and plotted on an Arrhenius plot together with laboratory data. This approach is prone to subjective judgement as to the appropriate temperature-time combination, as shown by attempts at reassessment of earlier work by Harrison ( 1985 ) . Here we take a different approach, made possible because of the existence of a near-ideal natural laboratory for studying fission-track annealing - the Otway Basin, of southeastern Australia. The Early Cretaceous Otway Group occurs

THERMAL

ANNEALING

OF FISSION

TRACKS

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4

throughout the Otway Basin, with correlative units in the Bass Basin and the Gippsland Basin (Strzelecki Group). This unit consists of a very thick ( > 3 km in places) sequence of interbedded sandstones and mudstones, derived from volcanism contemporaneous with sedimentation (Duddy, 1983 ). The sandstone beds contain abundant volcanic apatites, deposited soon after eruption containing no accumulated fission tracks. Therefore all tracks present in these apatites today have been formed after deposition, and the degree of annealing of those tracks reflects the effects of annealing due to the thermal history of the host rocks since deposition in the Early Cretaceous. As discussed in more detail by Green et al. (1989)) the sequences in a number of “reference wells” in the Otway Basin have undergone thermal histories that have involved progressive increase in temperature to present values, with temperatures within a few degrees of present values having prevailed for around the last lo-40 Ma. Further, the Otway Group is encountered at different depths in these wells, which reveals the response of fission tracks at all temperatures between surface ( N 1O’C) and > 125°C. Analysis of the thermal history of the sediments encountered in the four Otway Basin reference wells using a lithospheric stretching model (Hegarty, 1985; Hegarty et al., 1988) suggests that thermal gradients during rifting were N 1520% greater than the present gradients, and that extension was N 40% in the Otway Basin and along Australia’s southern margin. The amount of extension was derived from a comparison of observed and modelled subsidence histories. The highest thermal gradients (35-40°C km-‘) occurred in the Mid- to Late Cretaceous, associated with rifting, and gradually decayed to the present value of N 30” C km-l. Thermal histories for various horizons within the Otway Group in the four reference wells have been calculated using this model, and a representative selection is shown in Fig. 4. Note that in each of the wells, the Otway Group has

163

been progressively buried through time, and now resides at its maximum temperature since deposition. Since fission-track annealing is dominated by highest temperatures, as discussed in preceding sections, the apatite fission-track parameters in these reference wells will be insensitive to the elevated thermal gradients predicted during the early stages of burial, and will be determined largely by annealing within the last few tens of Ma. Exothermic diagenetic reactions may have contributed an additional source of heat, of uncertain magnitude, during early burial, which may have further enhanced the thermal gradients in this early stage (Duddy, 1983). The effect of these higher gradients on AFTA parameters during the Cretaceous would have been significant at the time, but unless gradients reached N 80 o C km- ‘, their effect will have since been masked by the effects of later heating due to simple burial (see Fig. 10 and further discussion in Section 5). This makes these wells ideal for constraining the geological annealing behaviour of fission tracks in apatite. From the modelled thermal histories for the four reference wells the expected mean confined track length and fission-track age have been predicted using the procedure outlined in Section 2, and the results are shown in Fig. 5. Up to temperatures of m 70’ C, agreement between predicted and observed mean confined track length is very good, while above 70 oC, the measured lengths begin to exceed the predicted value. Predicted fission-track age agrees well with measured values up to N 90’ C, while above this temperature, measured values exceed predicted ages. The predicted age and mean length fall to zero at N llO”C, whereas the measured values fall to zero at N 125’ C. These systematic departures of prediction from observation can be understood primarily in&rms of the effect of apatite composition on annealing kinetics. The predictions refer to the composition of the Durango apatite [Cl/ (Cl+ F) 1: 0.11 on which they are based. The Otway Group apatites show a range of compo-

164

P.F. GREEN

(Ma

TIME 120

TIME

(Ma

B.P.)

100

80

60

40

20

I

I

I

I

I

B.P.)

100

80

60

40

20

I

I

I

I

I

0

120

I

I

ET AL.

0

I

20 G e

40

2 3 2

60

5e

80

60

~100

E z

80

d L

100

3 ?

120

20 o^ e

40

2 2

60

d E s

80

I!! 100

PORT CAMPBELL-4 I

I

I

I

I

I

I

I

I

I

I

I

I

I

120

100

80

60

40

20

0

120

100

80

60

40

20

0

TIME

Fig. 4. Thermal (SE Australia),

(Ma

B.P.)

TIME

(Ma

B.P.)

histories for the Otway Group in four “reference wells” (as defined by Green et al., 1989) in the Otway Basin predicted from a lithospheric stretching model developed by Hegarty (1985) and Hegarty et al. (1988).

sitions (Duddy, 1983; Green et al., 1985; Sieber, 1986) from pure fluorapatite [Cl/ (Cl+F) ~0.01 to grains rich in chlorapatite [Cl/ (Cl + F) N 0.81. On the basis of studies of the role of composition on annealing as discussed on pp. 159 and 160, if we predict a given degree of annealing for a Durango apatite composition, pure fluorapatite will show a greater degree of annealing, and the more Cl-rich grains will show less annealing. Thus, in Fig. 5, above N 70°C observed lengths begin to exceed the predicted values because of the contribution of tracks in Cl-rich apatites which show less annealing (and there-

fore show longer lengths) than those in grains of Durango apatite composition. Since measurement of track length is biased towards longer lengths (Laslett et al., 1982), the measured track length distribution is dominated by the longer tracks, and the mean length is greater than that predicted for the composition of Durango apatite. This is most easily visualised above N llO”C, where Durango. apatite compositions should be totally annealed and any tracks measured will come only from more Clrich compositions. Whereas measured lengths exceed predicted values between 70” and 9O”C, the measured and

THERMAL

ANNEALING

OF FISSION

TRACKS

IN APATITE,

165

4

r

150

0

Im

I 0

20

40

60 TEMPERATURE

80

100

120

(“Cl

Fig. 5. AFTA data (mean confined track length and fissiontrack age) from the Otway Basin reference wells (from Greenet al., 1989) togetherwithpredictedparameters (solid lines) from the techniques outlined in this paper. The agreement between predictions and observations is good, in general. Some slight but systematic discrepancies appear above u 70 ’ C, which can be explained in terms of the compositional influence on annealing properties, as discussed in the text.

predicted fission-track ages agree much more closely. This arises because the fission-track age is affected more strongly by the more easily annealed compositions than is the mean length. For example, a grain that is totally annealed and gives a zero fission-track age has a strong influence on the final pooled fission-track age of the sample, but has no influence at all on the length measurement. Thus the measured fission-track age more accurately reflects the range of compositions present, while the mean length is dominated by the more Cl-rich compositions. Since Durango apatite composition is close to the modal apatite composition in the Otway Group apatites (Sieber, 1986), the measured fission-track age in the Otway Group is close to the predicted age for Durango apatite composition up to the temperature at which the most

sensitive apatite compositions are totally annealed. As shown by Green et al. ( 1988)) grains with zero age first appear in samples from the reference wells at w 90’ C, which is consistent with the apparent agreement of measured and predicted ages in Fig. 5 up to -90°C. At N 110’ C and above, Durango apatite compositions should be totally annealed, and since the more Cl-rich apatites still contribute a finite age, the measured age exceeds the predicted value in, this temperature range. This discussion emphasises that, when due allowance is made for the influence of composition on annealing kinetics, the parameters predicted from the procedures developed in this paper agree extremely well with observation in this geological setting. This, combined with the laboratory experiments reported by Duddy et al. (1988)) gives us confidence in both the qualitative and the quantitative predictions of the predictive model of the evolution of AFTA parameters through geological thermal histories, and shows that the various assumptions and simplifications on which the approach is based appear to be acceptable.

4. Illustrations of the AFTA

of the geological system

4.1. The relative influences time

response

of temperature

and

Fig. 6 shows the shortening behaviour of tracks produced at various times through three thermal histories involving linear heating to the same maximum temperature, T,, ( = 80 ’ C ) . In Fig. 6A, heating is rapid and T,, is reached after 10 Ma, followed by residence at T,,,,, for a further 90 Ma. In Fig. 6B, heating is less rapid, is reached after 50 Ma, followed by and Lx an&her 50 Ma at T=,. In Fig. 6C, T,,, is reached after 100 Ma. In all three cases the overall duration of the history is the same, at 100 Ma. A point to note in Fig. 6 is the subtle differ-

P.F. GREEN

166

^p

(A)

Tmax

after

10

Ma 40 (A,1 30 20

0 ?

(A,)

s sj 0.0 9 loo

10 0

80

K

0

0

60 TIME

(:a

5

10 LENGTH

TRACK

B.P:p

15

20

(microns)

0 G e

20

g

40

’ 2 E

60 80

$00 120

2(1 100

( B) d

60 TIME

80

Tmax

after

50

(;lnoa

0

100

0

0

B.P.)

80 60 TI ME

40

(Ma

20 B.P.)

0

Ma

1.0

E 0~ 4 y

0.5

P E 9 2 9

0.0 100

60

K

60 TI ME

40

(Ma

20 B.P.)

g

r

. . 100

60

.

. 60 TIME

(:a

B.P.)

5

TRACK

.

I

20

0

15 20 (ml crons)

100

wP

80

Y

60

Y f

40

g D E

10 LENGTH

20 0 TIME

(MB

B.P.)

ET AI

THERMAL

ANNEALING

OF FISSION

(C)

-0

TRACKS

Tmax

IN APATITE,

after

100

167

4

Ma

r

MEAN

=

12.27

t-

(C3) l-l

S. D. =

I-II

t h to.89

Q 0.0 2 100

80

ii

60 TIME

0

0

(:a

B.P?p

5 TRACK

10 LENGTH

15

20

(ml crons)

80 60

120

’

.

.

100

80

60 TIME

. 40 (MB

. 20 B.P.)

6 0

00

80 60 40 TIME (Ma

20 B.P.)

0

Fig. 6. Sequence of three AFTA evolution diagrams reflecting the relative influences of temperature and time. The three cases illustrated consist of linear heating to the same maximum temperature (T,, = 85 ’ C ) followed in two cases by residence at that temperature. In (A), I’,,, is reached after 10 Ma and in (B) after 50 Ma, while in (C), T,, is only reached at the end of the history. The duration of the history is 100 Ma in each case. The behaviour in each case is described in detail in the text. Note that the final lengths in the three cases differ by only - 1 mn, despite the large differences in the amount of time spent at T,,. Such a change in length would be caused by a change of only - 10 ’ C in temperature, showing that AFTA parameters are much more sensitive to temperature than time.

ence in the shortening trajectories of individual tracks in situations of linear heating and isothermal conditions, as best illustrated by Fig. 6B1), which combines both styles. During linear heating, all existing tracks converge onto a common trajectory, due to the reduction of equivalent time as temperature increases, whereas in isothermal conditions, the time of formation of individual tracks now has an effect, with older tracks being shortened more than younger tracks. This results in a slightly narrower distribution of track lengths in situations of linear heating than in isothermal conditions. Despite the pronounced differences in the behaviour of tracks formed at different times in the three cases, the resulting mean track lengths are very similar. The predicted values of mean

length in the two extreme cases differ by only N 1 ,um, although the sample represented by Fig. 6A has spent 90% of the total duration at T,,, whereas that in Fig. 6C has only just arrived at T-. In contrast, a difference of 1 pm in mean length would be produced by a change in T,, of the order of only 10°C (i.e. about a 10% change). Therefore it is clear that the final value of mean length in this type of situation is far more sensitive to temperature than to time. As a rough “rule of thumb”, a 10’ C change in temperature is equivalent to an order of magnitude change in timescale. Z’he final fission-track age in each of the three histories is also very similar, reflecting the small difference in length reduction between the three histories. The pattern of evolution of the fission-track age is different in the three cases, re-

168

P.F. GREEN

fleeting the differences in the evolution of track length, although the final ages are similar. 4.2. Heating distributions

during linear heating for all tracks formed prior to the thermal maximum. After cooling, all tracks formed in the initial phase become “frozen” at the length to which they were shortened at the thermal maximum, while those tracks formed after the cooling phase show typical isothermal behaviour and, since the temperature is lower, remain much longer. This results in the bimodal distribution of track lengths illustrated in Fig. 7B3. The “freezing” of the track length of the much shortened component of tracks can easily be understood in terms of the concept of equivalent time. Since these tracks have undergone considerable shortening, after the temperature has dropped to 20 o C the equivalent time appropriate to the observed degree of annealing be-

and cooling; bimodal track length

Fig. 7 shows AFTA response through three thermal histories involving a phase of linear heating over 100 Ma, from an initial temperature of 20’ C to increasing values of T,, (50 O, 85” and 120°C in Fig. 7A, B and C, respectively), followed by rapid cooling to 20°C over 5 Ma, and a further 95-Ma residence at this temperature in each case. Behaviour through this type of history is best illustrated by Fig. 7B1. Here we see, in the first phase of the history, the typical convergence of trajectories ^b

(A)

fmax

ET AL.

= 50°C

*

! O.Cl200

160

120 TIME

60 (MB

0 6 TRACK

0 B.P!)O

w

160

2 ::

120

2 I-

.-200

160

120 TIME

0 (iB

B.P:)O

LL

10 LENGTH

15

20

(microns)

60

200160120 TIME

60 40 (MB B.P.)

0

Fig. 7. Sequence of three AFTA evolution diagrams illustrating the effect of high temperature followed by cooling. Tracks formed during the heating phase are progressively shortened, to a length determined by the maximum temperature. After cooling, the tracks formed at that time are “frozen” at the length to which they have been shortened, while tracks formed subsequently are much longer. In (A), the maximum temperature is only 50: C, and the two generations of tracks cannot be resolved. In (B ) , the maximum temperature is 85’ C, and the two generations of tracks are clearly resolved in the bimodal distribution of track lengths. In (C ) the maximum temperature of 120 ’ C is sufficient to totally anneal all tracks, and tracks are only retained after cooling. This series reflects, in general terms, the pattern of AFTA parameters found in a vertical sequence which has been heated by burial and then cooled by uplift and erosion.

THERMAL

ANNEALING

OF FISSION

TRACKS

IN APATITE,

169

4

(B) Tmax r: 85°C 3

c

40

MEAN

=

(B31

13.65

s E

30

B 8

20

: z

10

8.D.z 21.93

9

200

160

a

120 TIME

80

(Ma B.P!f

G0 e

20

is 2 2

40

h

00

120

cl

I

.

200

160

(C)

200

2

160

5

120

. 120 TIME

. (iB

. B.p:;

.. I . ?I+ (C,) I

00

y

40

E

0

0

200

2 Y f

160 120 80 TIME (MB

40 B.P.)

0

MEAN

=

14.23 30

t

S.D.r t3.09

20 E I

I

.

ml

160

120 TIME

(ia

B.p:;

120 TIME

a0 (Ma

B.p:p

160

40

g

200

200

4

2

Tmax = 120°C

z

Fig. 7B and C.

s

L

15 20 (microns)

60

3 k100

3

0 L-did 0 6. 10 TRACK LENGTH

0

.

.

10

z

q

0

0

0

0 6 TRACK

cl

200

160120

10 LENGTH

80

TIME (Ma

15 (microns)

40 B.P.)

0

170 comes SOgreat that additions of the order of the duration of the thermal history illustrated are insignificant in comparison, and therefore virtually no further annealing takes place. Another point to note from Fig. 7B is the form of the predicted distribution of confined track lengths. Although each phase of the thermal history is of roughly equal duration, the relative heights of the two peaks in the bimodal distribution are not equal, but the longer peak is higher. This is a consequence of the length bias associated with revelation of confined tracks, which mitigates against the revelation of shorter tracks. An additional factor is the broadening of the distribution as mean length decreases, which alsO reduces the height of the shorter peak. The evolution of fission-track age in Fig. 7B also shows two stages. Over the first 100 Ma, the fission-track age becomes progressively less than the elapsed time due to the increasing degree of annealing. After cooling, the age increases linearly with time because all tracks now have lengths in the 14-15 pm range. The final fission-track age is rather less than the total elapsed time, with the amount of age reduction reflecting the degree of shortening in the “older” annealed component. The histories illustrated in Fig. 7A and C involve lower and higher maximum temperatures than in Fig. 7B. In Fig. 7A, with Tmax = 50’ C, a similar Pattern of behaviour to that in Fig. 7B is evident, although the degree of shortening during the initial heating phase is not sufficient to resolve two peaks in the length distribution, and a unimodal distribution results. In Fig. 7C, where the maximum temperature is 120” C, this temperature is Sufficient to totally anneal (i.e. reduce the etchable length to zero) all tracks formed prior to the thermal maximum. Tracks are retained only after the onset of cooling, and the majority of tracks are formed in the later isothermal phase. Note that the final track length distributions in Fig. 7A and C are very similar, with the only difference being the presence of a small number of very short tracks ac-

P.F. GREEN

ET AL.

cumulated during the cooling phase (causing the rather higher standard deviation in Fig. 7C). In practice, there are severe additional biases against the revelation of such short tracks, as discussed on p. 160, and this small component of short tracks would not be seen. The mean track lengths and standard deviations resulting from the thermal histories in Fig. 7A and C would therefore be practically identical, and could not discriminate between the two histories. However, the fission-track ages in the two situations are very different, and will allow the detection of the prior high-temperature excursion. Note that in Fig. 7C4 the fission-track age decreases to zero after 100 Ma due to total annealing, and only becomes finite again when the temperature has cooled to 20’ C, after which the fission-track age increases linearly. The age therefore dates the time of cooling in this case. The sequence of cases in Fig. 7 schematically illustrates the AFTA response in a section which has been cooled, perhaps by uplift and erosion after an initial heating phase due to burial. We will return to this type of situation in Fig. 12 on p. 177. Note the reduction in mean length followed by an increase, as T,, increases downwards in the schematic depth section, whereas the fission-track age decreases monotonically with increasing T,,. In practice, only a narrow range of thermal histories can result in a bimodal track length distribution. Because of the increasing inherent spread of the track length distribution as annealing progresses, in addition to the length bias factor discussed on p. 160, a bimodal distribution is only obtained when the mean length of the shorter component is around 10 or 11 ,um and the longer component has a mean of N 14-15 pm. Thus good examples of bimodal distributions are extremely rare (see Gleadow et al., 1986)) and are immediately diagnostic of a particular style of thermal history. Combining the behaviour shown in Fig. 7 with the discussion of Fig. 6 leads to the recognition that the length of an individual track is a sen-

THERMAL

ANNEALING

OF FISSION

TRACKS

IN APATITE,

171

4

sitive indication of the maximum temperature to which that track has been exposed. In this sense, individual tracks can be thought of as self-contained maximum-reading thermometers, continually generated throughout the thermal history, and allowing the deciphering of the variation of temperature with time. In Fig. 8, two more thermal histories are shown which illustrate further important facets of the response of the AFTA system. In Fig. 8A, temperature increases linearly over 100 Ma from 20’ to 85 ’ C followed by rapid cooling~over 5 Ma to 2O”C, as in Fig. 7B. However, the temperature then increases again to a temperature of 95 ’ C over the final 95 Ma of the history. The tracks formed in the later 95 Ma of the history are now progressively shortened as the temperature increases, and in the last 20 Ma or so, as the temperature exceeds the maximum value in the earlier phase, the younger tracks are shortened to a length which is shorter than the value attained by the older tracks at the previous thermal maximum. In addition, the older tracks are also shortened as the temperature exceeds the previous T,,, and all tracks begin to converge towards a similar value of length. The resulting distribution of track lengths therefore retains little or no “memory” of the previous phase of high temperatures. This imposes an important constraint on the type of geological situation in which AFTA can provide paleotemperature estimates, in that reheating to temperatures that are equal to or are higher than a previous peak will erase all evidence of the previous high temperature phase. In Fig. 8B, temperature is constant over 200 Ma, except for a lo-Ma excursion, beginning after 95 Ma, in which temperature climbs to 85°C over 1 Ma, holds constant at this maximum for 8 Ma, and drops over the next 1 Ma to 20°C. The final 95 Ma are spent at 20” C. Shortening trajectories of individual tracks formed throughout the history show the typical isothermal response over the initial 95 Ma, with only a small amount of shortening due to the low prevailing temperature. When temperature

is suddenly increased, however, all tracks formed at this point are rapidly shortened, as are tracks formed during the high-temperature excursion. After cooling, these tracks become “frozen” at their shorter length, while all tracks formed subsequently are only shortened a little due to the low prevailing temperature. Again we obtain a bimodal distribution of track lengths, as in Fig. 7B3. Closer comparison of Figs. 7B3 and 8B3, where the maximum temperatures are identical at 85 oC, shows that the resulting track length distributions in the two cases are practically identical, at 13.65 and 13.54 ,um, respectively, as also are the fission-track ages. This emphasises that when the earlier formed component of tracks has been shortened, it retains no record of the nature of the thermal history responsible for that shortening (a necessary consequence of the concept of equivalent time ) . Thus, in a single sample, annealing due to a short-term thermal event cannot be distinguished from that produced from slow and progressive heating to the same maximum temperature, due to burial for example. Evidence must be sought from sequences of samples, taking advantage of all available geological constraints, to interpret the cause of heating in such situations. 4.3. Short timescale heating As a final illustration of the response of the AFTA system, Fig. 9A shows a thermal history in which temperature gradually increases over 95 Ma to 7O”C, and then in the last 5Ma, increases rapidly to 95 o C. Over the initial 95 Ma, the track trajectories show the behaviour expected under heating or isothermal conditions from previous examples. In the last 5 Ma, when temperature has increased, all tracks formed previously and also those formed within this period are rapidly shortened in response to the hi&& temperatures. Fig. 9B shows the same history projected 20 Ma further in time, leaving the temperature at the maximum value of 95 ‘C. In the final 20 Ma of this history, tracks are shortened towards a

172

P.F. GREEN

-c 2

(A)

Reheating

to

higher

ET AL.

temperature

1.0

(A,)

E B J 5 d

0.5

. .

= . .

l-

B

160

. 120 TIME

. 80 (Ma

. . 40 B.P.)

40

0

200

160

120 TIME

80 (Ma

40 B.P.)

0

200

(B)

Short-lived

2 0.0 200 I.8

E

120

3 2

thermal

0.5

40

$

.

9 2 %

. 0.0 200

1

LENGTH

160120 TIME

(microns)

80 40 (Ma B.P.)

0

event s

y&\\\ . . . -

5

TRACK

1.0

ii s A ::

(A,)

2

u-(r

F

30

MEAN = 13.54 S. D. I

(B,)

(El)

. 160

. 120 TIME

. 80 (Ma

. 40 B.P.)

I 0

0 5 10 TRACK LENGTH

W s

15

20

(microns)

160 120

120

I 200

. 160

. 120 TIME

. 80 (Ma

. 40 B.P.)

:: 2

80

5

40

2 ii

I

0

0

Fig.8. Two A~TA evolution diagrams illustrating important facets of the system response. In (A), the temperature increases linearly to 85 oC, as in Fig. 7B, and then CIJ& rapidly, before increasing once more to a temperature greater than that attained in the earlier heating cycle. The evolution of parameters in the first half of the history is as in Fig. 7B. However, as temperature increases again in the later stages, the lengths of all tracks are shortened to greater degrees than those reached in the first heating phase. All tracks have very similar lengths at the end of the history, and all trace of the earlier heating phase is lost. In (B ) , the thermal history consists of a short-lived heating event, with a maximum temperature of 85 “C. All tracks formed prior to and during the event are shortened to a length characteristic of the maximum temperature, while those tracks formed after subsequent cooling are longer, resulting in the bimodal distribution of track lengths. The final AFTA parameters are very similar to those in Fig. 7B, where the maximum temperature was also 85 “C. This emphasises the dominant role of maximum temperature in determining AFTA parameters, as discussed in the text.

FISSION

TRACK

AGE

(Ma)

REDUCED

NUMBER

TRACK

OF TRACKS

LENGTH

(ULJ

FISSION

Oh

Fo PN. -0

TRACK

TEMPERATURE

AGE

( Ma)

(“C)

NUMBER

OF TRACKS

ifi K

b:

174

mean length of 9.6 pm at which the tracks can be thought of as responding to the prevailing temperature. The much longer mean length of 11.67 pm in Fig. 9A can be thought of as a “snapshot” of the length distribution in its reduction towards the value in Fig. 9B, and the fact that this length is much longer than would be expected at the prevailing temperature can be used to detect those situations where temperature has only recently increased.

5. Integration of AFTA with thermal modelling in sedimentary basins 5.1. Introduction The quantitative understanding of AFTA response lends itself to integration with thermal histories predicted from geophysical modelling procedures, and can provide rigorous constraints on the validity of modelled thermal histories, as well as the theory and values of parameters used to produce them. In the following sections, we illustrate the development of fission-track parameters in sedimentary sections, using four notional thermal histories to illustrate various aspects of AFTA response. Assuming a simple form for geothermal gradient through time, mean confined track length and fission-track age have been calculated for selected horizons. In each case a surface temperature of 20°C has been assumed. We also assume that all rocks contain apatites produced at the time of deposition, for example by contemporaneous volcanism, so that the apatites contain no inherited tracks at deposition. While this is unreasonable in general, this serves to emphasise the response of tracks during the burial cycle. 5.2. Passive margin subsidence Fig. 10a shows a pattern of burial histories intended to resemble those found in a passive continental margin, where a rapid initial phase

P.F. GREEN

ET AL.

of subsidence due to rifting is followed by a slower thermal sag phase. In this case the thermal gradient is kept constant over the entire 200-Ma history, at 25°C km-‘. Fig. lob shows the predicted pattern of fission-track parameters in apatites at various horizons in this sequence. At shallow levels, at temperatures of 54O”C, track lengths are in the 14-15-pm range, and fission-track ages are close to the stratigraphic age of each sample. At increasing present temperatures, both mean length and fission-track age decrease as annealing becomes more pronounced, until at temperatures of N 90-100’ C, all tracks are annealed, and both mean length and fission-track age fall to zero. In Fig. lla, an identical pattern of burial histories is illustrated, but in this case the geothermal gradient is held at a higher value of 60” C km-l during the first 80 Ma of the history. The pattern of predicted AFTA parameters for this case (Fig. lib) now shows a distinct difference to that in Fig. lob. For example, while fission-track ages in the shallower part of the section are identical to those in Fig. lob, in the deeper parts of the section the fission-track ages become much reduced compared to the values in Fig. lob. This is due to the effect of high temperatures in these samples in the early part of their history, during the phase of high geothermal gradient. In the deepest four samples, these temperatures exceed 100°C and are sufficient to totally anneal all tracks formed in the first 80 Ma. Fission-track ages in these samples therefore relate to the time of cooling due to the reduction in gradient, at 120 Ma B.P. The pattern of length decrease is also rather different to that in Fig. lob, although perhaps subtly so. This is most noticeable in samples 4 and 5 in depth sequence which are rather less in Fig. lib compared to Fig. lob. This is due to the presence in these samples of tracks which have only been partially annealed during the initial high-temperature phase. In the deeper samples, all tracks produced during this phase are totally annealed, and the tracks preserved have a very similar thermal history to those in

THERMAL

ANNEALING

OF FISSION

TRACKS

a) Burial

and

IN APATITE,

4

thermal

history

175 b) Predicted

Time (Ma B.P.) 200

100

n 0

0

I

AFTA

parameters

Mean track length 5 10 15

Ill

Ill

100

0

-e-

(pm)

ll( 200

Fission track age (Ma)

Fig. 10. From the sequence of burial histories in (a), we have calculated the pattern of AFTA parameters to be expected in an exploration well in this sequence, as shown in (b). A number of simplifying assumptions employed in these calculations, and those used in constructing Figs. 11-13, are discussed in the text. The most important of these factors is to assume apatites were deposited with no “inherited” track record. Note in (b) that the fission-track age is close to the stratigraphic age in the upper 1.5 km, where mean track lengths are around 14-15 pm. As the mean track length is reduced with increasing depth (i.e. temperature), the fission-track age is also reduced, with both parameters decreasing progressively to zero at - 110°C.

Fig. 10, explaining the similarity in mean lengths (although the fission-track ages are reduced). These examples illustrate how AFTA could be used, in principle, to detect thermal effects associated with the early stages of continental rifting. But we must add an important caveat to this discussion. Note that the initial phase of high thermal gradient in Fig. 11 is extended to what may be an unreasonably long time, and that the initial thermal gradient is perhaps also unreasonably high at 60°C km-‘. These steps were necessary in order to construct an example which would produce an observable signal in the AFTA parameters. Observations of heat flow in Cenozoic continental rifts show that thermal gradients in rifting environments are highly variable, but generally fall within the range 545°C km-’ (Morgan, 1982). The du-

ration of the rifting event can also be highly variable, generally between 5 and 60 Ma. In the example illustrated in Fig. 11, both the thermal gradient and duration of elevated gradient are outside these ranges, and are probably unrealistic. Using more realistic values of these parameters, no signal is obtained in the AFTA parameters, and similar results to those in Fig. lob are predicted. This results from the behaviour of fission tracks illustrated in Fig. 8A, in that tracks respond dominantly to the maximum temperature to which they are subjected. Thus, for any value of geothermal gradient in the early phase of Fig. 11C below -60°C km-‘, and if this dase extends for less than the 80 Ma illustrated, any sample deposited in this earlier high-. heat-flow period attains a peak temperature during this early phase that is exceeded by later

176

P.F. GREEN

a) Burial

and thermal

hlstory

b) Predicted

W Mean

Time (Ma B.P.) 200

100

APTA

0

0

5

parameters

trBCk

length (pm)

10

100

+

ET AL.

15

200

Fission track age (Ma)

Fig. 11. As in Fig. 10, except that the thermal gradient is higher during the first 80 Ma. Note that high temperatures experienced during this phase introduce a perturbation to the pattern of decrease in mean length, while the age decrease shows a more profound change. These factors are discussed in more detail in the text.

heating due to burial at lower gradient. Therefore, following the discussion of Fig. 8, the fission-track response in such samples is dominated by the thermal regime at present, and the AFTA parameters contain no information on the earlier phase of high heat flow. This imposes an important restriction on the type of situation in which AFTA can provide useful information. As a general rule, AFTA cannot provide information on an earlier phase of high temperatures if subsequent heating has taken the samples to a higher temperature. This is true whether heating and cooling are due either to changes in thermal gradients or to burial followed by uplift and erosion (see below). The effects of changes in thermal gradient may still be observed, for example, in situations where gradients were anomalously high. or where part of the section has been uplifted while the gradient was high, and not re-buried to such high temperatures subsequently, although such situations appear to be rare.

5.3. Uplift and erosion In Fig. 12, we illustrate a section which is progressively buried over 100 Ma, reaches maximum temperatures at this time, and is then uplifted with > 3 km of section lost by erosion. The geothermal gradient is kept constant at 20°C km-l. Subsequent burial is only minor, involving a temperature increase of < 20” C. Prior to uplift, a set of AFTA parameters rather similar to those in Fig. 10 is established, with fission-track age reduced progressively to zero at a temperature of - 110°C ( -4.5 km depth). Uplift and erosion results in cooling by 70°C and samples that were at temperatures of - 90110°C now begin to retain tracks at much lower temperatures, while samples that were above 110’ C, in which tracks were not retained, can now retain tracks once more. This results in the two-phase reduction in fission-track age shown in Fig. 12b, in which the fission-track age is first reduced from - 180 to - 80 Ma as a result of

THERMAL

ANNEALING

OF FISSION

TRACKS

a) Burlal

and

IN APATITE,

thermal

177

4

hlstory

Time (Ma B.P.)

b) Pmdlcted n

AFTA

parameters

Mean track length (pm)

Fig. 12. a. Sequence of burial histories for a section which undergoes uplift and erosion of more than 3 km, followed by a minor amount of subsidence. b. Predicted pattern of AFTA parameters in this section. The unconformity is expressed as a large change in fission-track age, because of the assumption that all tracks are produced after burial, although this will not be true in general. The fission-track ages then undergo a two-stage decrease with increasing depth (temperature). The upper stage can be thought of as an uplifted or “fossil lower annealing zone”, representing samples that were at temperatures prior to uplift where severe annealing was occurring. The break in slope represents a paleotemperature at which total annealing occurred (i.e. prior to uplift the fission-track age had been reduced to zero), so that in all samples below this point, tracks have only been retained after cooling produced by uplift and erosion. The parameters in these deepest samples therefore allow direct estimates of the timing of uplift. The mean track length decreases at fiit due to an increasing degree of shortening in the annealed component in the “fossil” lower annealing xone, and then increases once more as the older component becomes totally annealed, before falling to zero under the influence of prevailing temperatures.

annealing in the earlier thermal regime, and then from 80 Ma to zero under the action of the present-day temperatures. The reduction from 180 to 80 Ma can be thought of as a “fossil annealing zone”, representing part of the section that has previously been subjected to temperatures sufficient to produce near-total to total annealing of tracks. This figure should be compared to those given by Naeser (1979) and Gleadow et al. (1983 ), which show similar pattern of age reduction. The variation of mean track length through this section shows a notable pattern of decrease followed by a slight increase, as noted in Fig. 7, before decreasing once more to zero. The final

decrease to zero is due to annealing under the present thermal regime, in a similar fashion to those shown in Figs. 10 and 11. The initial decrease, at shallower levels, is due to the shortening of tracks produced in the “fossil lower annealing zone”, although the presence of tracks produced at lower temperatures since cooling, associated with uplift and erosion, ensures that the mean length does not reduce to zero. Passing down the fossil lower annealing zone, with iFeasing peak paleotemperature the length of tracks in the older annealed component becomes increasingly shorter and the measured mean length increases again, under the influence of the longer tracks produced since cool-

178

P.F. GREEN

a) Burial

and thermal

history

b) Predicted

Time (Ma B.P.) 100

50

AFTA

ET AL.

parameters

w Mean track length (Km) 0

0

5

10

15

Fig. 13. a. Sequence of burial histories for a section which undergoes an initial burst of rapid deposition followed by much slower sedimentation until the last 10 Ma, when a new burst of sedimentation takes place. b. Predicted pattern of AFTA parameters in this section. Following the discussion of Fig. 9, tracks in apatites from this sequence do not have sufficient time to react to the increase in temperature, and tracks are preserved down to depths where temperatures are -over 130°C. This facet of AFTA system response can be usefully employed to detect situations in which temperatures have recently increased, as discussed in more detail in the text,

ing. Track length distributions in this fossil lower annealing zone may be bimodal, but only in restricted circumstances as discussed on p. 170. Similar comments as those made above concerning Fig. 11 are appropriate to the type of thermal history presented in Fig. 12. If later burial is sufficiently great to produce maximum temperatures greater than those attained prior to uplift and erosion, then annealing under the later thermal regime will dominate the observed AFTA parameters, and no information will be obtained on the pre-uplift history. Again, this is one of the most important limitations of the AFTA technique for providing paleotemperature estimates. On the other hand, when later burial is minor, as in the case illustrated in Fig. 12, then AFTA can provide rigorous estimates of paleotemperatures in the samples in

the upper part of the section, which allow not only the estimation of the amount of cooling due to uplift and erosion but also some estimate of the geothermal gradient prior to uplift and the amount of section lost by uplift and erosion. This is a major strong point of AFTA, and the sort of situation in which it is best applied. Furthermore, the well-characterised kinetic response of the AFTA system renders AFTAbased estimates of such parameters more reliable than those based on other techniques, e.g. vitrinite reflectance, where there is great uncertainty as to appropriate kinetic models of system response. 5.4. Recent .!z.eating Fig. 13a shows a section which is buried rapidly initially, and then undergoes only minor

THERMAL

ANNEALING

OF FISSION

TRACKS

IN APATITE,

4

subsequent burial, until the final 10 Ma, in which 2.5 km of sediment are deposited. The thermal gradient is constant at 25” C km-’ throughout. The resulting pattern of fissiontrack parameters shown in Fig. 13b shows tracks persisting to temperatures of N 130’ C, whereas in Figs. 10-12, all tracks were totally annealed and fission-track ages reset to zero at N lOO110°C. This persistence of tracks to higher temperatures than would normally be expected is due to the short timescale of heating in the case illustrated in Fig. 13. Consideration of Fig. 9 emphasises that the tracks are being rapidly annealed at the present time, and if allowed to reside at currently prevailing temperatures for another N 10 Ma, then the AFTA parameters would once more settle into the expected pattern, decreasing to zero at N 100-110°C. In the case illustrated, heating is due to burial under a constant geothermal gradient. A similar pattern of AFTA parameters would be produced if no further burial had taken place but the thermal gradient had increased in the last 10 Ma. This type of situation is one in which AFTA can provide useful information on the timescale of heating. 6. Concluding

remarks

Since the techniques outlined in this and previous papers are able to account for both laboratory and geological constraints on the annealing behaviour of fission tracks in apatite, we can use the predictions of these techniques with confidence to simulate the response of the AFTA system through any geological thermal history, for apatites similar in composition to Durango apatite [Cl/ (Cl + F ) N 0.11. Compilation of the composition of apatites from a variety of sedimentary and crystalline rocks (Sieber, 1986) has shown that the Durango apatite composition is close to the modal composition in both data sets, so predictions based on this composition should be fairly generally applicable.

179

However, to realistically predict the AFTA parameters expected in geological situations, the incorporation of other apatite compositions into the treatment is essential. Detailed kinetic studies of apatites of a variety of different compositions are in progress to extend the understanding of the kinetics of annealing that we currently have for Durango apatite to all values of Cl/ (Cl + F ). Until this work has been completed, the comparison between predictions and observed data shown in’Fig. 7 affords an empirical means of extending the predictions for Durango apatite to other compositions. The developing understanding of the response of the AFTA system offers considerable insight into those areas in which AFTA can provide useful information, and the most important of these have been outlined above. It also highlights the major limitations of the technique, some of which have also been discussed. Perhaps most importantly, it affords the basis of a method of rigorous paleotemperature estimation in sedimentary basins. The predictive model developed in this paper, based on kinetic parameters determined in the laboratory, gives predictions which are in good agreement with geological observations. This suggests that fission-track annealing proceeds by the same pathway over timescales which differ by many orders of magnitude. No ad hoc assumptions have been made on the details of the kinetic response of the system, which has, instead, been determined directly. Furthermore, the process is independent of the chemical environment since it takes place on the atomic scale within the integral crystal lattice of apatite grains. These represent significant advantages over other paleotemperature indicators in common use and, when combined with the ability of AFTA to provide direct estimates of the timing as well as the magnitude ofti’imum paleotemperatures in the region of N 100’ C, should see AFTA find wide application in the oil and mineral exploration industries.

180

P.F. GREEN

Acknowledgements

ET AL.

(3) Then:

The financial support of the Australian Research Grants Scheme, the National Energy Research, Development and Demonstration Council, Esso Australia Ltd., the CSIRO/University of Melbourne Collaborative Research Fund, and the University of Melbourne Fellowship, Scheme are all gratefully acknowledged. The support of the Australian Institute of Nuclear Science and Engineering for neutron irradiations is also gratefully acknowledged. We are also grateful to the members of the Melbourne Fission Track Research Group and other colleagues for helpful discussions, particularly to Rex Galbraith for invaluable comments on the precision calculations. Appendix The theory of prediction error outlined here is a generalisation of that for regression (see Snedecor and Co&ran, 1967, pp. 153-155). Consider an apatite grain subject to temperature T for time t. The fission tracks, initially of mean length &, will reduce in length to a mean length L. Let r=L/L, be. the observed mean length reduction. Then Laslett et al. ( 1987) suggested that an adequate model for the relationship between r, T and t is:

r,=(l-b[{c,B(r

n )+co}“+l]““)“b

(A-2)

The function B(r) is the slope of the contour line corresponding to length-reduction r on the straight-line fanning Arrhenius model [B(r) is related to g(r) by g(r) = c0+ c,B (r) 1. Note that the iterative procedure predicta B (rJ , and that B (r”) depends only on one parameter, A. The other parameters c,,, cl, a and b are used in the functional form relating B (r ) to ( 1 - r ) (see fig. 3 of Laslett et al., 1987). In this sense, it is the precision with which A is estimated which governs the precision of predicting B (r ) - the other parameters are not really involved in the time and temperature part of the extrapolation. The procedure outlined below for calculating the standard error of a prediction refers t.c variation of r,, as given by eq. A-2, under hypothetical replicates of the following procedure: the 72 annealing experiments (Green et al., 1986) are repeated on Durango apatite, the length reduction r is measured on each sample as before, and the model (A-l ) is refitted by maximum likelihood. This would produce slightly different parameter estimates for each replicate, and hence also a slightly different value of r,, in eq. A-2. Let: 8’ = (a,b,c,,,q, A,#) be the vector of true parameter i? = (ri,b,S&,

values. Similarly,

A,2)

is the vector of estimates, or estimators algorithm above may be written as: r=h(fl;

T(u),O
of 8’. Then the (A-3)

where

where h ( * ) is a function whose explicit form is unknown, and r= r,.,.We abbreviate eq. A-3 as r = h (6). The estimate iofris:

g(r)= [{U-rb)lb}“-11/a

i=h(8)=h(B)+@-8)‘d

and e is random error, normally distributed with mean of zero and variance 0’. The parameters a, b, c,,, ci, A and u2 were estimated from 72 armealing experiments to be ci= 0.35, b^=2.7, &x-4.87, &=1.68*10-*, A=-28.1 and ih0.00246. Now consider an apatite grain subject to a thermal history {T(t)=Ti, (i-l)dt
where d’ = (ah/da,...,ah/&Y) is a vector of first derivatives with respect to each of the 6 parameters. In eq. A-4 we have performed a fit-order Taylor expansion of h (. ) around the true parameter values. Hence:

g(r)=c,,+c,T(lnt-A)+e

B(r,)=T,

(A-1)

(2) Repeat steps (a) and (b) below for i=1,2,...,n-1: (a)

ln(tP)=B(ri)/Ti+, B(ri+l)=Ti+l

Var(&d

(A-5)

where Var(& is the 6x6 variance-covariance matrix of the parameter estimators. In order to estimate Var (9) , we need first to estimate d. Now ahlaa, ahlab, ah/&, and ah/&z1 can be obtained explicitly by differentiating eq. A2, and ah/W=O. We obtain ahlaA by approximation: ah,aA-h(“,5,%,~~~+sA.b’)

In tl -AT,

(b)

Var(P) zd’

(A-4)

+A In(tP+dt)-AT,+1

- h(6,6,&,,E,,/i-6A,62) 26A we chose 6A =0.05&

but ah/aA

changes little with smaller

THERMAL

ANNEALING

OF FISSION

TRACKS

IN APATITE.

choices for 6A. In other words, the algorithm is rerun at two slightly different values of A near A, so that ah/aA may be calculated. These expressions, all evaluated effectively at 0, yield d. In addition, Var (6) was estimated from the observed information matrix I obtained when fitting the model (A-l), as in Laslett et al. (1987). Let 1 be the loglikelihood of the 72 data values (Green et al., 1986, table I): l= -?n(o’)

-$+

181

4

i ln[ -g’ (r,)] r=l

where n = 72, and:

try of the Otway Formation volcanogenic sediments. Ph.D: Thesis, University of Melbourne, Melbourne, Vie. (unpublished). Duddy, I.R., 1986. Determination of diagenetic and very low-grade mineral reaction temperatures in sediments using apatite fission track analysis. 12th Int. Sedimentel. Congr. Canberra, A.C.T., Aug. 24-30, 1986, sponsored by Geol. Sot. Aust.-Geol. Sot. N.Z.-Int. Assoc. Sedimental.-Bur. Miner. Resour., Aust. Duddy, I.R., Green, P.F. and Laslett, G.M., 1988. Thermal annealing of fission tracks in apatite 3. Variable temperature annealing. Chem. Geol. (Isot. Geosci. Sect.), 73: 25-38.

is the residual sum-of-squares. Var(a)

Then:

nl-’

where ei (i=1,...,6) are the 6 parameters in 8, and I= { - a 21/d&30j} is a 6 x 6 symmetric matrix, the elements of which are evaluated at 6 (Efron and Hinkley, 1978). It is advisable to calculate expression (A-5) as & x, where x is the solution of Ix=& obtained using an t!fficient and stable numerical algorithm for solving sets of linear equations. Note that eq. A-3 is the median value (not the mean) of the distribution of possible values of r for the given thermal history (see Carroll and Ruppert, 1981) , and that our estimate of Var (i’) is a first-order approximation to the variance of this estimated median. This is therefore slightly different from the usual regression situation, in which the mean and median are exactly equivalent (Snedecor and Cochran, 1967). The standard error of the predicted median quoted in Table I should be distinguished from prediction error (p.e.), used to compare a measured value r against a prediction i. Since the new value is statistically independent of the prediction, the difference (r-i) has a variance ( =p.e.‘) of: Var(r)+Var(i)=ua2/g’(rji+s.e.(i)’ (compare with Snedecor and Cochran, 1967, p. 155). For example, the prediction errors for each of the lOO-Ma entries in Table I are - 70% larger than the standard errors, because of this extra term, which is estimated by @/g‘ (i)‘. In practice, however, a suite of samples from boreholes or outcrop is available to assess the thermal history of an area, and it is the variance-covariance matrix of all of the differences (r-i), which is relevant to judge the compatibility of a given thermal history with the fission-track data.

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Efron, B. and Hinkley, D.V., 1978. Assessing the accuracy of the maximum likelihood estimator: observed versus expected Fisher information. Biometrika, 68: 456-487. Gleadow, A.J.W. and Duddy, I.R., 1981. A natural longterm annealing experiment for apatite. Nucl. Tracks, 5: 169-174. Gleadow, A.J.W., Duddy, I.R. and Lovering, J.F., 1983. Fission track analysis: a new tool for the evaluation of thermal histories and hydrocarbon potential. APEA ( Aust. Pet. Explor. Aust.) J., 23: 93-102. Gleadow, A.J.W., Duddy, I.R., Green, P.F. and Lovering, J.F., 1986. Confined fission track lengths in apatite - a diagnostic tool for thermal history analysis. Contrib. Mineral. Petrol., 94: 405-415. Green, P.F., 1985. A comparison of zeta calibration baselines in zircon, sphene and apatite. Chem. Geol. (Isot. Geosci. Sect.), 58: l-22. Green, P.F., 1988. The relationship between track shortening and fission track age reduction in apatite: Combined influences of inherent instability, annealing anisotropy, length bias and system calibration. Earth Planet. Sci. Lett., 89: 335-352. Green, P.F. and Durrani, S.A., 1977. Annealing studies of tracks in crystals. Nucl. Tracks, 1: 33-39. Green, P.F., Duddy, I.R., Gleadow, A.J.W., Tingate, P.R. and Laslett, G.M., 1985. Fission track annealing in apatite: track length measurements and the form of the Arrhenius plot. Nucl. Tracks, 10: 323-328. Green, P.F., Duddy, I.R., Gleadow, A.J.W., Tingate, P.R. and Laslett, G.M., 1986. Thermal annealing of fission tracks in apatite, 1. A qualitative description. Chem. Geol. (Isot. Geosci. Sect.), 59: 237-253. Green, P.F., Duddy, I.R., Gleadow, A.J.W. and Lovering, J.F., 1989. Apatite fission track analysis as a paleotemperature indicator for hydrocarbon exploration. In: N.D. Naeser and T. McCulloh (Editors), Thermal History Analysis in Sedimentary Basins. Springer, Berlin, pp. M-195. Hammerschmidt, K., Wagner, G.A. and Wagner, M., 1984. Radiometric dating on research drill core Urach III: a contribution to its geothermal history. J. Geophys., 54: 97-105. Harrison, T.M., 1985. A reassessment of fission-track an-

182 nealing behaviour in apatite. Nucl. Tracks, 10: 329-333. Hegarty, K.A., 1985. Origin and evolution of selected plate boundaries. Ph.D. Thesis, Columbia University, New York, N.Y., 255 pp. Hegarty, K.A., Weissel, J.K. and Mutter, J.C., 1988. Subsidence history of Australia’s southern margin: constraints on basin models. Am. Assoc. Pet. Geol. Bull., 12: 615-633. Hurford, A.J. and Green, P.F., 1982. A user’s guide to fission track dating calibration. Earth Planet. Sci Lett., 59: 343-354. Hurford, A.J. and Green, P.F., 1983. The zeta age calibration of fission track dating. Isot. Geosci., 1: 285-317. Laslett, G.M., Kendall, W.S., Gleadow, A.J.W. and Duddy, I.R., 1982. Bias in measurement of fission track length distributions. Nucl. Tracks, 6: 79-85. Laslett, G.M., Green, P.F., Duddy, I.R. and Gleadow, A.J.W., 1987. Thermal annealing of fission tracks in

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