DATING

in geology, determining a chronology or calendar of events in the history of the Earth, using to a large degree the evidence of organic evolution in the sedimentary rocks accumulated through geologic time in marine and continental environments. To date past events, processes, formations, and fossil organisms, geologists employ a variety of techniques. These include some that establish a relative chronology in which occurrences can be placed in the correct sequence relative to one another or to some known succession of events. Radiometric dating and certain other approaches are used to provide absolute chronologies in terms of years before the present. The two approaches are often complementary, as when a sequence of occurrences in one context can be correlated with an absolute chronlogy elsewhere. in geology, determining a chronology or calendar of events in the history of the Earth, using to a large degree the evidence of organic evolution in the sedimentary rocks accumulated through geologic time in marine and continental environments. To date past events, processes, formations, and fossil organisms, geologists employ a variety of techniques. These include some that establish a relative chronology in which occurrences can be placed in the correct sequence relative to each other or to some known succession of events. Radiometric dating and certain other approaches are used to provide absolute chronologies in terms of years before the present. The two approaches are often complementary, such as when a sequence of occurrences in one context can be correlated with an absolute chronology elsewhere. In its simplest form, relative dating uses two main conceptschronological succession and synchroneity. If a range of events or organisms, for example, can be placed in chronological succession by observing the stratigraphic order in the rocks in which they occur at a particular locality, this can provide the reference sequence with which less-complete records from elsewhere can be correlated. Where this type of correlation is based on synchronous occurrences, such as volcanic-ash layers from the same explosion or the remains of a distinct temporally restricted fossil organism, the correlation schemes developed become the framework for a relative chronology. Stratigraphic superposition and the identification of regionally or even globally synchronous events are thus crucial. Absolute dating is achieved by recognizing the effects of some time-dependent process in the geologic record. Such processes may result from seasonal cycles or from radioactive decay. Seasonal cycles give rise to annually recurrent deposition sequences such as glacial varves that can be counted and also correlated from site to site by comparing their thickness and character. Dating by radiometric assay is applicable on timescales ranging from days to billions of years, depending on the half-life of the radioisotope being used. The principles involved in radiometric dating and the range of materials used vary markedly. For example, carbon-14 dating (q.v.) is used for timescales of some 500 to 50,000 years and is applicable to the fossil remains of organisms that were in exchange with the atmospheric reservoir of carbon-14 during their life. It rests on the assumption of a roughly constant ratio of radioactive-to-nonradioactive carbon at the time when the organic material to be dated ceased to exchange with the atmospheric reservoir. Potassium-argon dating (q.v.) is applicable to crystalline rocks in which the radioisotope potassium-40 (half-life of 1.3 billion years) disintegrates to argon-40. This dating method can be used on some of the oldest rocks on Earth. Rubidium-strontium dating (q.v.) can reach even further back in time and has been used to estimate the age of the solar system. There are several dating techniques that provide indirect, or proxy, chronologies. That is to say, once a timescale has been calibrated by, for example, a radiometric technique, it can then be used for establishing chronologies of geologic significance. The Earth's magnetic field has changed polarity many times in the geologic past. The record of such polarity changes in basalts on the ocean floor, calibrated by potassium-argon dating, has provided a timescale for seafloor spreading and long-term marine sedimentation. Because any single dating method is subject to poorly quantified errors as well as statistical uncertainty, cross-referencing between methods for mutual consistency is important. Absolute dating Although relative ages can generally be established on a local scale, the events recorded in rocks from different locations can be integrated into a picture of regional or global scale only if their sequence in time is firmly established. The time that has elapsed since certain minerals formed can now be determined because of the presence of a small amount of natural radioactive atoms in their structures. Whereas studies using fossil dating began almost 300 years ago, radioactivity itself was not discovered until roughly a century ago, and it has only been from about 1950 that extensive efforts to date geologic materials have become common. Methods of isotopic measurement continue to be refined today, and absolute dating has become an essential component of virtually all field-oriented geologic investigations. In the process of refining isotopic measurements, methods for low-contamination chemistry had to be developed, and it is significant that many such methods now in worldwide use resulted directly from work in geochronology. It has already been explained how different Earth processes create different rocks as part of what can be considered a giant rock-forming and -reforming cycle. Attention has been called wherever possible to those rocks that contain minerals suitable for precise isotopic dating. It is important to remember that precise ages cannot be obtained for just any rock unit but that any unit can be dated relative to a datable unit. The following discussion will show why this is so, treating in some detail the analytic and geologic problems that have to be overcome if precise ages are to be determined. It will become apparent, for example, that isotopic ages can be reset by high temperatures; however, this seeming disadvantage can be turned to one's favour in determining the cooling history of a rock. As various dating methods are discussed, the great interdependence of the geologic and analytic components essential to geochronology should become evident. The field of isotope geology complements geochronology. Workers in isotope geology follow the migration of isotopes produced by radioactive decay through large- and small-scale geologic processes. Isotopic tracers of this kind can be thought of as an invisible dye injected by nature into Earth systems that can be observed only with sophisticated instruments. Studying the movement or distribution of these isotopes can provide insights into the nature of geologic processes. Principles of isotopic dating All absolute isotopic ages are based on radioactive decay, a process whereby a specific atom or isotope is converted into another specific atom or isotope at a constant and known rate. Most elements exist in different atomic forms that are identical in their chemical properties but differ in the number of neutral particlesi.e., neutronsin the nucleus. For a single element, these atoms are called isotopes. Because isotopes differ in mass, their relative abundance can be determined if the masses are separated in a mass spectrometer (see below Use of mass spectrometers). Radioactive decay can be observed in the laboratory by either of two means: (1) a radiation counter (e.g., a Geiger counter), which detects the number of high-energy particles emitted by the disintegration of radioactive atoms in a sample of geologic material, or (2) a mass spectrometer, which permits the identification of daughter atoms formed by the decay process in a sample containing radioactive parent atoms. The particles given off during the decay process are part of a profound fundamental change in the nucleus. To compensate for the loss of mass (and energy), the radioactive atom undergoes internal transformation and in most cases simply becomes an atom of a different chemical element. In terms of the numbers of atoms present, it is as if apples changed spontaneously into oranges at a fixed and known rate. In this analogy, the apples would represent radioactive, or parent, atoms, while the oranges would represent the atoms formed, the so-called daughters. Pursuing this analogy further, one would expect that a new basket of apples would have no oranges but that an older one would have many. In fact, one would expect that the ratio of oranges to apples would change in a very specific way over the time elapsed, since the process continues until all the apples are converted. In geochronology the situation is identical. A particular rock or mineral that contains a radioactive isotope (or radio-isotope) is analyzed to determine the number of parent and daughter isotopes present, whereby the time since that mineral or rock formed is calculated. Of course, one must select geologic materials that contain elements with long half-livesi.e., those for which some parent atoms would remain. Given below is the simple mathematical relationship that allows the time elapsed to be calculated from the measured parent/daughter ratio. The age calculated is only as good as the existing knowledge of the decay rate and is valid only if this rate is constant over the time that elapsed. Fortunately for geochronology the study of radioactivity has been the subject of extensive theoretical and laboratory investigation by physicists for almost a century. The results show that there is no known process that can alter the rate of radioactive decay. By way of explanation it can be noted that since the cause of the process lies deep within the atomic nucleus, external forces such as extreme heat and pressure have no effect. The same is true regarding gravitational, magnetic, and electric fields, as well as the chemical state in which the atom resides. In short, the process of radioactive decay is immutable under all known conditions. Although it is impossible to predict when a particular atom will change, given a sufficient number of atoms, the rate of their decay is found to be constant. The situation is analogous to the death rate among human populations insured by an insurance company. Even though it is impossible to predict when a given policyholder will die, the company can count on paying off a certain number of beneficiaries every month. The recognition that the rate of decay of any radioactive parent atom is proportional to the number of atoms (N) of the parent remaining at any time gives rise to the following expression: Converting this proportion to an equation incorporates the additional observation that different radioisotopes have different disintegration rates even when the same number of atoms are observed undergoing decay. In other words, each radioisotope has its own decay constant, abbreviated l, which provides a measure of its intrinsic rapidity of decay. Proportion 1 becomes: Stated in words, this equation says that the rate at which a certain radioisotope disintegrates depends not only on how many atoms of that isotope are present but also on an intrinsic property of that isotope represented by l, the so-called decay constant. Values of l vary widelyfrom 1020 reciprocal seconds (i.e., the unit of 1 second) for a rapidly disintegrating isotope such as helium-5 to less than 10-25 reciprocal seconds for slowly decaying cerium-142. In the calculus, the rate of decay R in equation 2 is written as the derivative dN/dt, in which dN represents the small number of atoms that decay in an infinitesimally short time interval dt. Replacing R by its equivalent dN/dt results in the differential equation Solution of this equation by techniques of the calculus yields one form of the fundamental equation for radiometric age determination, in which N0 is the number of radioactive atoms present in a sample at time zero, N is the number of radioactive atoms present in the sample today, e is the base of natural logarithms (equal to about 2.72), l is the decay constant of the radioisotope being considered, and t is the time elapsed since time zero. Two alterations are generally made to equation 4 in order to obtain the form most useful for radiometric dating. In the first place, since the unknown term in radiometric dating is obviously t, it is desirable to rearrange equation 4 so that it is explicitly solved for t. Second, the more common way to express the intrinsic decay rate of a radioisotope is through its half-life (abbreviated t1/2) rather than through the decay constant l. Half-life is defined as the time period that must elapse in order to halve the initial number of radioactive atoms. The half-life and the decay constant are inversely proportional because rapidly decaying radioisotopes have a high decay constant but a short half-life. With t made explicit and half-life introduced, equation 4 is converted to the following form, in which the symbols have the same meaning: Alternatively, because the number of daughter atoms is directly observed rather than N, which is the initial number of parent atoms present, another formulation may be more convenient. Since the initial number of parent atoms present at time zero N0 must be the sum of the parent atoms remaining N and the daughter atoms present D, one can write: From equation 4 above, it follows that N0 = N(elt). Substituting this in equation 6 gives If one chooses to use P to designate the parent atom, the expression assumes its familiar form: and This pair of equations states rigorously what might be assumed from intuition, that minerals formed at successively longer times in the past would have progressively higher daughter-to-parent ratios. This follows because, as each parent atom loses its identity with time, it reappears as a daughter atom. The increase in D/P with time is evident in equation (7) because larger values of time will increase the value of elt, where l is constant. Equation (8) documents the simplicity of direct isotopic dating. The time of decay is proportional to the natural logarithm (represented by ln) of the ratio of D to P. In short, one need only measure the ratio of the number of radioactive parent and daughter atoms present, and the time elapsed since the mineral or rock formed can be calculated, provided of course that the decay rate is known. Likewise, the conditions that must be met to make the calculated age precise and meaningful are in themselves simple: 1. The rock or mineral must have remained closed to the addition or escape of parent and daughter atoms since the time that the rock or mineral (system) formed. 2. It must be possible to correct for other atoms identical to daughter atoms already present when the rock or mineral formed. 3. The decay constant must be known. 4. The measurement of the daughter-to-parent ratio must be accurate because uncertainty in this ratio contributes directly to uncertainty in the age. Different schemes have been developed to deal with the critical assumptions stated above. In uraniumlead dating, minerals virtually free of initial lead can be isolated and corrections made for the trivial amounts present. In whole rock isochron methods that make use of the rubidiumstrontium or samariumneodymium decay schemes (see below), a series of rocks or minerals are chosen that can be assumed to have the same age and identical abundances of their initial isotopic ratios. The results are then tested for the internal consistency that can validate the assumptions. In all cases, it is the obligation of the investigator making the determinations to include enough tests to indicate that the absolute age quoted is valid within the limits stated. In other words, it is the obligation of geochronologists to try to prove themselves wrong by including a series of cross-checks in their measurements before they publish a result. Such checks include dating a series of ancient units with closely spaced but known relative ages and replicate analysis of different parts of the same rock body with samples collected at widely spaced localities. The importance of internal checks as well as interlaboratory comparisons becomes all the more apparent when one realizes that geochronology laboratories are limited in number. Because of the expensive equipment necessary and the combination of geologic, chemical, and laboratory skills required, geochronology is usually carried out by teams of experts. Most geologists must rely on geochronologists for their results. In turn, the geochronologist relies on the geologist for relative ages. Edwin A. Olson Thomas Edvard Krogh Absolute dating Major methods of isotopic dating Isotopic dating relative to fossil dating requires a great deal of effort and depends on the integrated specialized skills of geologists, chemists, and physicists. It is, nevertheless, a valuable resource that allows correlations to be made over virtually all of Earth history with a precision once only possible with fossiliferous units that are restricted to the most recent 12 percent or so of geologic time. Although any method may be attempted on any unit, the best use of this resource requires that every effort be made to tackle each problem with the most efficient technique. Because of the long half-life of some isotopic systems or the high background or restricted range of parent abundances, some methods are inherently more precise. The skill of a geochronologist is demonstrated by the ability to attain the knowledge required and the precision necessary with the least number of analyses. The factors considered in selecting a particular approach are explored here. Uraniumlead method As each dating method was developed, tested, and improved, mainly since 1950, a vast body of knowledge about the behaviour of different isotopic systems under different geologic conditions has evolved. It is now clear that with recent advances the uraniumlead method is superior in providing precise age information with the least number of assumptions. The method has evolved mainly around the mineral zircon (ZrSiO4). Because of the limited occurrence of this mineral, it was once true that only certain felsic igneous rocks (those consisting largely of the light-coloured, silicon and aluminum-rich minerals feldspar and quartz) could be dated. Today, however, baddeleyite (ZrO2) has been found to be widespread in the silica-poor mafic igneous rocks. In addition, perovskite (CaTiO3), a common constituent of some ultramafic igneous rocks, has been shown to be amenable to precise uraniumlead dating. As a result of these developments, virtually all igneous rocks can now be dated. This capability, moreover, has been enhanced because the most advanced geochronological laboratories are able to analyze samples that weigh only a few millionths of a gram. This amount can be found in a comparatively large number of rocks, whereas the amount previously required (about 0.1 gram) cannot. Age determinations also can now be made of low-uranium trace minerals such as rutile (TiO2), a common constituent found in mineral deposits, adding still further to the number of entities that are datable by the uraniumlead method. Other minerals commonly employed to date igneous and metamorphic rocks include titanite, monazite, and even garnet in certain favourable cases. Additional minerals listed in Table 2 have been tried with varying success. Additional reading Surveys of methodologies of ascertaining geologic time include Frederick E. Zeuner, Dating the Past: An Introduction to Geochronology, 4th rev. ed. (1958, reissued 1972); Patrick M. Hurley, How Old Is the Earth? (1959, reprinted 1979); E.I. Hamilton, Applied Geochronology (1965); G. Brent Dalrymple and Marvin A. Lanphere, Potassium-Argon Dating: Principles, Techniques, and Applications to Geochronology (1969); and Henry N. Michael and Elizabeth K. Ralph (eds.), Dating Techniques for the Archaeologist (1971). Stratigraphic geology as the basis of relative age measurement is discussed in W.B. Harland, A. Gilbert Smith, and B. Wilcock (eds.), The Phanerozoic Time-Scale (1964); John W. Harbaugh, Stratigraphy and the Geologic Time Scale, 2nd ed. (1974); Arthur Holmes, Holmes Principles of Physical Geology, 3rd ed. rev. by Doris L. Holmes (1978); N.J. Snelling (ed.), The Chronology of the Geological Record (1985); Derek V. Ager, The Nature of the Stratigraphical Record, 2nd ed. (1981); and Gilles S. Odin (ed.), Numerical Dating in Stratigraphy, 2 vol. (1982). The development of methods of absolute age measurement is examined in Henry Faul (ed.), Nuclear Geology (1954); Henry Faul, Ages of Rocks, Planets, and Stars (1966); the collected symposium papers published as Radioactive Dating (1963); Robert L. Fleischer, P. Buford Price, and Robert M. Walker, Nuclear Tracks in Solids: Principles and Applications (1975); E. Jger and J.C. Hunziker (eds.), Lectures in Isotope Geology (1979); Gunter Faure, Principles of Isotope Geology, 2nd ed. (1986); and Robert Bowen, Isotopes in Earth Sciences (1988). Thomas Edvard Krogh