On statistical estimation in fission track dating

Statistical methodology is described for obtaining point and interval estimates of age in fission track dating experiments, particularly for (a) the external detector method, which is reviewed briefly, and (b) the population method, which is considered in more detail. Some mathematical background to models, based on the underlying physical process, is given. This is used to suggest appropriate statistical methods, to assess them and to help understand sources of variation in the data. For the external detector method, a model is required for numbers of tracks given the amount of uranium; the usual Poisson model is derived as a consequence of independent thinning of a bivariate point process. For the population method, uranium heterogeneity does not necessarily invalidate the estimate but does represent a source of variation that must be allowed for in its error; thus an interval estimate of age might be relatively uninformative.     

石英裂变径迹蚀刻条件的对比实验研究

通过 40%的 HF溶液、KOH饱和溶液和 19 mol/L的 NaOH溶液这三种常用方法对大、小颗粒石英进行裂变径迹蚀刻实验的对比发现,用环氧树脂固定的小颗粒石英样品,不宜用 KOH饱和溶液(150 ℃)和 19 mol/L的 NaOH溶液(沸点,约 120 ℃)作为裂变径迹的蚀刻剂,宜用 40%的 HF溶液;三种方法均适宜于大颗粒石英,但不同的蚀刻方法蚀刻效率不同, 40%的 HF溶液(29 ℃)的蚀刻效率最高,且操作简单、安全性高.40%的 HF溶液最佳蚀刻时间为: 温度在 4 ℃左右(冬季)时为 40 min,温度在 29 ℃左右(夏季)时为 30 min,可在全年室内常温条件下操作.     

Statistical treatment of experimental errors in the fission track dating method

The major stochastic elements in the fission track dating method are (i) the number of spontaneous fission tracks (N _s ) in a sample, and (ii) the number of induced tracks (N _i ) observed when the sample is irradiated with neutrons. The foundations for the statistical uncertainty in these measures are of two kinds: (i) there exists a definite probability of uranium fission by means of natural decay and by neutron activation, and (ii) within a crystal the distribution of uranium is not uniform and perhaps follows something like a Poisson law. In any event, the natural logarithm of the ratio (N _s /N _i ) is proportional to age. A plausible statistical fission track dating model should, therefore, start by considering the joint distribution of N _s and N _i . In this paper a joint bivariate normal model is described which allows the rigorous definition of the probability distributions of N_s, N _i , the ratio N _s /N _i , and age itself. A general computer program (FISSION) has been developed to perform all the necessary computations. By accounting for the correlation between N _s and N _i , the statistical model here ascribes smaller standard errors to N _s /N _i (and therefore age) than do previous methods. In addition, the error associated with neutron flux is a significant factor in the age relationships and has been incorporated into the model.     

A determination of the decay constant for spontaneous fission of natural uranium using fission track accumulation

The decay constant for spontaneous fission of natural uranium has been determined by accumulating fission fragment tracks in Lexan plastic held adjacent to uranium metal for one year. The value, 6.8 ± 0.6. 10⁻¹⁷ yr⁻¹, is consistent with values most commonly used in fission track dating.     

秭归盆地中新生代构造-热演化的裂变径迹约束

通过磷灰石裂变径迹年龄的测定以及时间-温度热历史的反演,揭示了秭归盆地中新生代构造-热演化过程。结果表明:秭归盆地自120 Ma左右开始缓慢隆升,主要经历了3个强烈的隆升阶段:(1)晚白垩世100~80 Ma开始强烈隆升,是燕山期造山运动在该地区作用的结果,也可能是黄陵背斜晚白垩世强烈抬升向西延伸的响应;(2)晚始新世40 Ma的强烈隆升,可能是印度板块和亚欧板块碰撞初期作用的远程响应;(3)中新世中期到末期10~5 Ma的强烈隆升,是青藏高原东部边界向东扩展及亚洲季风气候变化的响应。秭归盆地内部自白垩纪以来一直隆升剥蚀,展现出与盆地边缘构造-热演化的差异。通过与黄陵背斜东部的当阳盆地构造-热事件的对比,暗示了黄陵背斜在晚白垩世已隆升剥露至地表,分割了两个盆地。晚侏罗世—早白垩世,秦岭大规模挤压变形逆冲推覆构造作用使得米仓山—汉南隆起和黄陵背斜地区成为中上扬子地区磷灰石裂变径迹年龄相对最大的区域,江南—雪峰陆内造山作用向西北方向的扩展使得湘鄂西地区向川东地区磷灰石裂变径迹年龄具有整体变年轻的趋势。晚白垩世以来太平洋板块俯冲挤压效应使得川东褶皱带周缘及川东北磷灰石裂变径迹年龄自南东向北西方向减小,江汉盆地、当阳盆地及龙泉山以西记录的年轻的磷灰石裂变径迹年龄则与青藏高原隆升及其向南东方向构造逃逸的挤压作用和亚洲季风等气候变化的影响有关。     

Uplift and cooling pathways derived from fission track analysis and mica dating: a review

Definition of time and temperature pathways for episodes of lithospheric movement provides not simply a chronological framework for crustal dynamism but also permits estimation of rates of crustal cooling and uplift. Important aspects of such pathways are the constraints provided for timing of both plate collision and lithospheric extension. Classically Rb-Sr and K-Ar mica ages have been used to delineate rates of cooling and exhumation in the Central Alps, by comparison of the measured ages with estimates of temperatures for the retention of daughter isotopes. Similar use of fission track apatite and zircon ages has provided data for lower temperature intervals (～ 100 and ～ 200°C respectively). Recent detailed studies of the annealing kinetics of fission tracks in apatite yield more precise estimates of cooling rate and permit predictive modelling of age and length parameters for given T,t pathways. In continental collision zones, fast episodic uplift in the western Alps can be contrasted with contemporaneous monotonic uplift in the Central Alps. Additional examples may be seen in the Tibet-Himalayan orogenic belt, in the southern Alps of New Zealand and in the Bolivian Andes. In divergent teceonic regimes, the record of uplift associated with rifting has been recorded by fission track ages in the southeastern Australian margin and around the Red Sea. In an intra-plate tectonic setting, our current fission track reconnaissance study in the British Isles is revealing a hitherto unrecognised thermal history for crystalline and sediment alike.     

Absolute dating of the youngest sediments of the Swiss Molasse basin by apatite fission track analysis

A set of ash layer samples within the uppermost Upper Freshwater Molasse (OSM) sediments (N and E of Frauenfeld, Switzerland) was dated by apatite fission track (FT) means. The ages indicate an early Tortonian (perhaps latest Serravallian) eruption and sedimentation age of 11.5 ± 0.3 Ma. The age is in agreement with time constraints by Mammalian relicts which point to MN7-8. Due to the position of the ash layers close to the erosional gap and overlying Quaternary cover, the age represents a maximum age for the cessation of OSM sedimentation in the Swiss Molasse Basin. However, the end of Molasse sedimentation in this region had not stopped before the cover of OSM sediments by volcanic ash layers at the Höwenegg volcano (southern Germany), an event further constrained by an apatite FT age of 9.8 (?0.7/+0.8) Ma from a hornblende-bearing ash layer at Höwenegg. An isolated bentonitic ash layer occurring 25 km to the WSW of the main set of dated ashes (near Humlikon) has an age component identical to the OSM ash layers near Frauenfeld. The age suggests a source for this material within the Hegau, but is too young to be related to the volcanic activity at the Kaiserstuhl.The apatites from the ash layer samples show two distinct compositional populations, one very close to a Cl end member and one with apatites of equal proportions of Cl and OH end member. These populations are interpreted to have possibly originated from at least two distinct igneous sources for the ashes, separated by their eruption site or eruption time or both. The distinct compositional data on the volcanic apatites may provide a basis to clarify their origin in future work.     

辽东凸起北段新生代隆升时间的确定:来自裂变径迹的证据

对取自辽东凸起北段凸起带和陡坡带的6个岩芯样品进行了磷灰石裂变径迹(AFT)测试并分析了裂变径迹特征,选定其中2个样品在约束条件下进行热史模拟。结果表明,辽东凸起北段新生代经历了距今50 Ma±孔店组沉积期末及距今24 Ma±的东营组沉积期末的2次构造隆升。通过对辽东湾坳陷东西部的沉积结构和控凹断裂对比可知,辽东湾坳陷一系列NE向隆起具有相似的发育机制。结合渤海湾盆地区域构造背景,推断辽东湾坳陷辽东凸起的形成是古近纪地幔热活动引起的伸展作用在孔店组沉积期末的构造响应,形式为拆离性质的翘倾断块;而辽东凸起的第二次抬升是受东营组沉积期末发生的区域性构造抬升运动影响的结果。     

裂变径迹长度测量的标准化研究

总结了影响裂变径迹长度测量的主要因素——蚀刻程序和测量误差，提出了对应的解决方法：采取统一的蚀刻程序和蚀刻标准，确立长度参照标准。由于锆石铀含量具有差异，蚀刻标准是锆石长度测量标准化的主要研究内容。     

磷灰石裂变径迹实验流程的建立及验证——外探测器法和LA-ICP-MS/FT法

磷灰石裂变径迹定年作为揭示岩石低温热年代学的一种重要方法,能够有效重塑地壳浅部约3～5 km内数百万年以来的热演化历史,已经被广泛应用于地球科学的相关研究中。依托于中国地质科学院地质力学研究所建立的裂变径迹实验室,同时采用外探测器法和LA-ICP-MS/FT法对国际上普遍使用的Durango磷灰石进行了测定,得到2个Durango磷灰石外探测器法年龄为：32.9±1.6 Ma、31.9±2.3 Ma; 7个Durango磷灰石LA-ICP-MS/FT法年龄为：31.97±0.82 Ma、30.9±1.5 Ma、32.3±1.4 Ma、30.6±1.1 Ma、30.7±1.4 Ma、29.7±1.9 Ma、31.1±1.3 Ma,两种方法测得的年龄均与国际推荐值在误差范围内一致;此外,我们也应用这两种方法对采集于天山的花岗岩样品18HS-5进行了测试,年龄分别为126.7±3.8 Ma、126.4±3.6 Ma,两种方法得到的年龄在误差范围内一致。实验对比分析表明,实验流程可靠,可推广测试。     

The effects of magma replenishment processes on 238U-230Th disequilibrium

Short lived isotope data are increasingly used to investigate magma chamber residence times. Arc lavas have excellent potential as tracers of magma evolution because their magmas are often out of U-series isotope equilibrium, and some arc magmas have yielded surprisingly old pre-eruption U-series ages from mineral separates. A model is presented to examine the behaviour of U-Th isotopes for a range of conditions between closed system and steady-state magmatic systems. Magmas can be maintained out of secular equilibrium for long periods of time by periodic mixing events with new magma batches. The latter results in oscillations in (²³⁰Th/²³²Th) consistent with the relatively constant values observed in lavas of different ages from some centres. The effects of periodic reinjection of magma and mixing of old and young crystals on U-series mineral isochrons are also considered. Mixtures of crystals produced by either replenished or closed system processes can readily result in linear arrays. In many cases it may be valid to interpret these as minimum average residence times for the crystals, whereas the liquid residence times calculated from U-series data for periodically replenished systems are maximum values.     

赞比亚东北部班韦乌卢地块泛非期以来构造演化的裂变径迹约束

本文利用锆石和磷灰石裂变径迹方法探讨了班韦乌卢地块泛非期以来的主要构造演化时间。为研究班韦乌卢地块的构造活动,本文从班韦乌卢地块中部卡帕图地区的沉积盖层姆波罗科索群的姆巴拉组、萨马组和卡布韦卢马组中采集多件新鲜的岩石样品,并获得5件锆石和2件磷灰石样品裂变径迹分析结果。5件锆石裂变径迹年龄介于575±35～380±22 Ma之间,其峰值年龄组为600～572 Ma和420～390 Ma。2件磷灰石裂变径迹年龄介于59±6～27±4 Ma之间,其峰值年龄组为99～80 Ma和19～11 Ma。它们的峰值年龄组分别对应的主要时代为新元古代的埃迪卡拉纪、早泥盆世、晚白垩世和中新世。对比区域上已有的年龄数据可知,南部非洲地区新元古代的埃迪卡拉纪、早泥盆世和晚白垩世的构造活动是一个区域性的构造事件,仅中新世(19～11 Ma)的构造活动在区域上的表现尚不明确。综合前人成果资料,自泛非构造运动以来,班韦乌卢地块至少经历600～572 Ma、488～441 Ma、420～390 Ma、375～293 Ma、99～80 Ma及19～11 Ma六个构造事件。班韦乌卢地块泛非期以来的构造演化研究程度很低,...     

Fission track annealing characteristics and dating of vermiculite

Fission track annealing experiments for vermiculite mineral have been performed under optimised etching conditions and a correction curve translating track length reduction to track density reduction has been constructed. The blocking/closing temperature of the fission track system in the mineral has been calculated to be 125°±30° C. The corrected fission track age of vermiculite from Kasipatnam (Visakhapatnam), South India, has been calculated as 544±14 Ma. The activation energy and average uranium concentration of the mineral are 1.7 eV and 9.9×10^?8 gg^?1 respectively.     

Apatite fission track dating of fluorite ore veins from Santa Catarina state,Brazil: a complex hydrothermal evolution

The fluorite of Santa Catarina that occurs in veins cutting Precambrian granitic rocks of coastal Brazil has been difficult to date by Rb/Sr, K/Ar and Sm/Nd methods. New fission track dating of apatite in granites next to the veins yields ages of 144–76 Ma, which are related to the opening of the South Atlantic Ocean. Four groups of fission track ages were identified: the ca 145 Ma group is a hydrothermal event that preceded fluorite mineralization; the second group of ages, 131–107 Ma, records the first hydrothermal mineralizing event; the third group, 98–93 Ma, represents the second hydrothermal mineralizing event; and the fourth group, 89–76 Ma, dates the last hydrothermal mineralizing event. As shown by previous studies, the temperatures of these events varied from 170° to 70°C, but the last hydrothermal event occurred during a gradual cooling. The smaller lengths of the confined fission tracks from the fourth event support this interpretation. These results are based on sixteen carefully selected samples from four veins ranging from 1 to 4 m in thickness. The ages of these samples were established using the standard methods of fission track dating. Our study clearly demonstrates the value of apatite fission track dating for deposits whose mineralization occurred over a long time span at a wide range of temperatures.     

Closing temperatures of different fission track clocks

The fission track closing temperatures of the minerals which are found to be suitable for fission track geochronology have been calculated for various cooling rates using the stepwise cooling. Biotite is found to have the lowest closing temperature whereas the sphene is having the highest. The closing temperature falls with decrease in cooling rate.     

The fission track records of the Estherville,Nakhla and Odessa meteorites

Investigation of fossil charged-particle track densities in various mineral phases of three meteorites—Estherville, Nakhla and Odessa—coupled with U content determination, has led to the evaluation of various contributions to the total fossil track density, including those due to the spontaneous fission of ²³⁸U and ²⁴⁴Pu. A fission-track age for Estherville of around 4 × 10⁹ yr is found, which is thought to reflect slow cooling of the parent body. A Pu track excess of (106 ± 9): 1 over the spontaneous fission of ²³⁸U is found in Odessa diopside, which is larger than may be allówed on a simple ‘continuous synthesis’ model for the production of heavy elements prior to solar system formation. Possible explanations for this value are discussed, including fractionation of Pu relative to U. No detectable U was found in Nakhla diopside, and a measurable contribution of track densities from the fission of superheavy elements is ruled out on the basis of track-length measurements and laboratory calibration with Fe ions.     

Precision,accuracy and meaning of fission track ages

The precision, meaning, and accuracy of the fission track (ft) dating method are reviewed from an examination of the recent literature as well as previously unpublished data from the author's laboratory. It is concluded that forapparent ft ages (i.e. ages derived from the canonical age equation) a precision (2σ level) of the order of ±4% to ±5% can be reached provided that (i) uranium is sufficiently homogeneously distributed in the dated samples, at least locally; and (ii) a large enough number of tracks can be counted. Model ft ages,i.e. ages for which partial geological track annealing is taken into account, have variable degrees of precision. While model ages obtained with the track-size method seem, as evaluated from the literature, to have usually a limited precision of the order of ±30% (2σ), plateau ages usually have a precision better than ±5% at a 2σ confidence level. Because it provides an objective test on the accuracy of track identification, as well as some insight of the variability of closing temperatures between various samples of a given mineral phase, the Isochronal Plateau (icp) method, when applicable, will be preferred (Poupeauet al 1980a). However, for phases which could be damaged by heating at relatively high temperatures, as for example hydrated glass shards from tephra, an Isothermal Plateau (itp) approach is to be preferred. Due to uncertainties about the value of the²³⁸U spontaneous fission decay constant λ _f as well as difficulties inherent in the dosimetry of thermal neutrons in nuclear reactors, theft method of dating is not an independent one. Presently, it relies on the existence of geological standards (volcanic rocks) of known age, allowing to determine anoperational ‘λ _f ’ value (Naeseret al 1980). Accordingly, the accuracy of anft age is limited by the accuracy on the age of the standard. It should be better than ～5%. For volcanic, hypovolcanic rocks, and shallow intrusives, theft method dates the time of formation, provided they were not further reheated. More generally, the track method providescooling ages. Closing temperatures calculated from laboratory experiments vary from ?300°C to 100°C, according to minerals, for slow cooling rates (～1°C/m.y.). For apatites, recent geological calibrations (Naeseret al 1980; Gleadow and Duddy 1980) confirmed laboratory extrapolations. The association of theft method with other geochronometers is therefore critical to the study of the cooling history of old cratons as well as to the evaluation of uplift/erosion rates in recent belts.