The articles in this Elements issue highlight various aspects of the formation and evolution of the Earth’s earliest crust. This Toolkit includes a glossary of terms, concepts, and analytical approaches important to the study of Archean cratons to provide context for the methodologies discussed in these articles.

Geologic timescales are rarely presented without compressing the Precambrian portion of Earth history. For this reason, it is easy to overlook the fact that the time between Earth formation and the end of the Archean at 2.5 Ga (billion years ago)—the time period covered by the articles in this issue—represents fully 45% of Earth history (Fig. 1).

The geologic timescale for the earliest part of Earth history is divided into two eons: the Hadean (4.6 to 4.0 Ga) and the Archean (4.0 to 2.5 Ga) (Fig. 1). The Hadean is defined as the time from Earth formation to the earliest part of the rock record. We use the 4.568 billion-year-old age of the oldest grains condensed from the solar nebula found in meteorites (Ca-Al-rich grains included in chondritic meteorites) to mark the start of Earth accretion (Bouvier and Wadhwa 2010). The beginning of the Archean has been established at 4.031 Ga based on the 10 oldest U-Pb zircon ages from the Acasta gneiss complex in the Slave craton of northern Canada (Bowring and Williams 1999). Consequently, we refer to all ages older than this as Hadean.

The Archean eon is divided into the Eoarchean (4.03–3.6 Ga), the Paleoarchean (3.6–3.2 Ga), the Mesoarchean (3.2–2.8 Ga), and the Neoarchean (2.8–2.5 Ga). Unlike the Phanerozoic, where the times-cale is related to the evolution of fossil life forms, these time divisions are arbitrary, as is the end of the Archean eon at 2.5 Ga. The geologic timescale is updated periodically by the International Commission on Stratigraphy (

It is not possible to determine the average geochemical composition of the entire Earth directly, so its overall composition—often expressed as the bulk Earth composition—is estimated from the composition of Type-1 carbonaceous chondrite meteorites, a class of meteorites that is thought to have formed during condensation of the solar nebula and formation of the Solar System and has not undergone melting or meta-morphism since that time. This composition is also referred to as the chondritic uniform reservoir (CHUR).

Very early in its history, the metallic core separated from the silicate portion of the Earth (Nimmo and Kleine 2015). Thus, it is useful to define the geochemical composition of the bulk silicate Earth as the composition of the entire Earth minus the core. The composition of the bulk silicate Earth is equivalent to that of the primitive mantle.

Today, the Earth is composed of a number of geochemically distinct components, including the core, mantle, and crust. These are commonly referred to as reservoirs. The portion of the mantle that partially melted to produce magmas that contributed to forming the Earth’s crust is known as the depleted mantle. The time when the depleted mantle reservoir began to form and the evolution of its composition and volume over Earth history are intricately related to the formation and evolution of the complementary crustal reservoir (Fig. 2). These processes are incompletely resolved in time and space, as discussed by O’Neil et al. (2024 this issue) and Rey et al. (2024 this issue).

The Earth’s oceans constitute another reservoir that appears to have formed early, likely by 3.7–3.8 billion years ago when pillow basalts are first preserved in the rock record (Nutman et al. 2013). The concept of crustal growth is intimately linked to the concept of continental free-board, which refers to the mean height of the continental landmasses with respect to sea level at any given time (Fig. 3; Korenaga et al. 2017). This concept is important because freeboard reflects a balance between the volume of the oceans, the shape of ocean basins, and the volume, density, and thickness of the oceanic and continental crust. See Rey et al. (2024 this issue) for a broader discussion of changes in sea level during the Archean.

Geologic processes are commonly assumed to be uniformitarian, that is, we can infer how ancient rocks were formed and modified by looking at modern processes, including plate tectonics, that affect the Earth today. This assumption cannot be applied to the first 1.5 to 2 billion years of Earth history. For example, the formation of Earth’s core, silicate magma oceans, and the Moon were early, one-time events. Exponential, secular cooling of the Earth as radioactive heat production decreased produced different temperature regimes at different times in the past (Korenaga 2013). This cooling also likely affected Earth’s geodynamics, a general term that refers to the physical stresses that deform Earth’s surface and interior. Instead of stiff plates of crust moving horizontally above a convecting mantle in a modern so-called mobile lid process, Hadean and Archean tectonics may have been driven by mantle plumes beneath a weaker, stationary crust, in a so-called stagnant-lid scenario (Fig. 4A). Instead of subduction, the early crust may have been disrupted and even relocated in response to mantle upwellings and downwellings that have been linked to processes such as sagduction and drip tectonics (Fig. 4B; Martin and Arndt 2021).

In addition, studies of the lunar surface indicate by analogy that impacts of large, extraterrestrial bodies (e.g., planetesimals and large meteorites) strongly affected the early Earth, but the rate of these impacts tailed off by the end of the Archean (see recent compilation on Fig. 2 in Tai Udovicic et al. 2023). Large impacts on the early Earth, including the Moon-forming impact, may have generated enough heat to wholly or partially melt large parts of the mantle. The resulting “magma oceans” may have persisted for millions of years and greatly influenced the chemical and physical evolution of the mantle.

The time at which modern plate tectonics initiated is a subject of considerable debate (Korenaga 2013). As Rey et al. (2024 this issue) point out, it is possible that there was a period when both stagnant and mobile tectonic processes were operating in parallel, a situation they refer to as dual-mode geodynamics. The transition from stagnant to mobile lid tectonics need not have been synchronous globally, but likely occurred at different times in different parts of the Earth and affected individual cratons differently (Frost and Mueller 2024 this issue).

U-Pb in Zircon

The U-Pb system in zircon has evolved to become the most reliable method for obtaining accurate and precise ages of events in the geologic past, particularly the Precambrian. The two radioactive isotopes of uranium (235U and 238U) decay at vastly different rates, providing two independent age determinations and an opportunity to compare ages from one decay system to the other in a unique cross-check. When the ages agree within analytical errors, the ages are considered concordant, implying that the zircon has behaved as a closed system since it formed. The data are often depicted on concordia diagrams, on which curved lines give the ages of concordant data regardless of the ratios used to define concordia. Two different common concordia plots are shown in Figure 5. Discordant ages (ages from the two decay systems that do not agree) are also valuable because the lack of agreement often can be related to loss of Pb from the system (e.g., a zircon grain). Straight lines through discordant points (discordia; Fig. 5) on the concordia plots may intersect concordia at two times, and can then identify both the time of original crystallization and the time of the event that caused Pb-loss, such as metamorphism. Because ancient zircons likely experienced more than one Pb-loss event, the lower intercept of the discordia line with concordia may have only limited or no geologic meaning.

Common Pb and the Age of the Earth

Common Pb isotopes are those found in “common” rocks and minerals that have not necessarily remained closed systems since they formed. The Pb isotopes produced by decay of 235U (207Pb) and 238U (206Pb) are typically reported as ratios relative to the non-radiogenic isotope 204Pb. Lead produced from decay of 232Th is similarly reported as 208Pb/204Pb from the single decay of 232Th to 208Pb. The Pb isotopic composition of an individual rock or mineral evolves with time to higher ratios of radio-genic Pb (206Pb, 207Pb, 208Pb) to non-radiogenic 204Pb along curved paths called growth curves (Fig. 6). The relatively rapid decay of 235U means that ~80% of all 235U on Earth had decayed by the end the Archean and is the reason why the growth curves shown on Figure 6 flatten out at younger ages. Consequently, rocks and minerals with high 207Pb/204Pb relative to 206Pb/204Pb indicate interaction with high-U/Pb reservoir(s) that must have formed in the Hadean or Archean. These are referred to as high-μ or early enriched reservoirs. These reservoirs likely formed by magmatic differentiation within the crust because U is preferentially partitioned into magmas to a greater extent than Pb in crustal and mantle melts.

Common Pb isotopes have played an important role in our evolving understanding of Earth and Solar System history. For example, Pb isotopic data from galenas, oceanic sediments, and meteorites were combined to provide the first viable determination of the age of the Earth (Fig. 6B; Patterson 1956).


In addition to the U-Pb system, many other radiogenic parent-daughter isotope pairs are used to determine both the timing and nature of events on Earth. Most of these involve parent isotopes with slow decay rates, such as 147Sm-143Nd (half-life (T½) of 147Sm = 107.0 billion years), 176Lu-176Hf (T½ of 76Lu = 37.2 billion years), and 187Re-187Os (T½ of 87Re = 41.6 billion years). As with Pb isotopes, the daughter isotope is reported relative to a stable isotope of the same element. Examples include 143Nd/144Nd (shown on Fig. 7A), 176Hf/177Hf, and 187Os/188Os. The variation in these ratios for Earth materials is very small, so it has become customary to report measured values relative to a standard such as CHUR (the chondritic uniform reservoir, which approximates the bulk silicate Earth composition). This is called the epsilon notation, and is given by the formula:


where (t) is the time of interest. Multiplying by 104 results in values for εNd(t) commonly between +15 (depleted mantle) and −50, (old felsic crust), where positive values denote samples with higher 143Nd/144Nd than the bulk Earth, and negative values identify samples with lower 143Nd/144Nd than the bulk Earth (Fig. 7B). This is the case because mantle melts have lower Sm/Nd than the residual (depleted) mantle. Analogous expressions give εHf(t). In the 187Re-188Os system, the γOs(t) notation refers to percent deviation from CHUR of 187Os/188Os (multiplying by 100 instead of 10,000).

When evaluating diagrams and/or text that use the epsilon notation, it is important to remember that the relative rate of change of a sample compared to a model reservoir or another sample is related to the half-life of the parent isotope, the time since mineral/rock formation, the parent/daughter ratio, and the assumptions used to calculate the ε of model reservoirs. For example, the depleted mantle formed at 4.6 Ga with an epsilon of zero and has evolved to a range of values centered about +13 εNd. Evolution diagrams may be plotted with measured isotope ratios (Fig. 7A) or derivative ratios such as epsilons (Fig. 7B). Although Hf and Nd isotopic compositions of rocks and minerals can be measured very precisely today, extrapolating these values back over 3–4 billion years involves uncertainties beyond analytical errors.

Model Ages

As shown in Figure 7B, a model age is simply an estimate of the time that a sample was extracted from a model reservoir. For example, a given sample’s measured 143Nd/144Nd is extrapolated back in time using the sample’s measured 147Sm/144Nd until its Nd isotopic composition matches that of the evolving reservoir, commonly the depleted mantle. That time is referred to as the depleted mantle model age: TDM. A graphic representation of this concept is shown as point TDM on Figure 7B, where the model mantle evolution curve is intersected by the evolution curve of an individual sample at time T2.

Extinct Radionuclides

Some radioactive isotopes produced during stellar processes have such short half-lives that they have completely decayed and are no longer present in our Solar System. These are known as extinct radionuclides. Extinct radionuclides are especially well suited for understanding events that took place on the early Earth while these short-lived radioactive isotopes were still “alive.” For example, consider the decay of lithophile (crust-loving) 182Hf (T1/2 = 8.9 million years) to siderophile (iron-loving) 182W. In this system, W is fractionated into the core and Hf into the mantle during core formation. The fact that 182W/184W is not completely homogenized in the modern mantle after 4.5 Ga of convection and is more heterogeneous in Archean rocks than modern mantle-derived rocks help us understand the timing of core formation and the extent of mantle mixing over time (Fig. 8). Another extinct radionuclide, 146Sm, has also been applied to the chronology of early Archean rocks. Note that instead of the ε notation, the μ142Nd(t) notation is used with m referring to parts per million (1 × 10−6). See O’Neil et al. (2024 this issue) for more discussion.

Oxygen Isotopes

The most abundant element in the silicate Earth is oxygen. The isotopes of oxygen are all stable, yet their abundance varies in Earth materials because the mass difference between isotopes results in different equilibrium and kinetic behavior. A delta notation (δ) is used for oxygen isotope ratios, which most commonly compare the 18O/16O of a sample to a standard material, typically “standard mean ocean water” (SMOW), and is expressed as per mil deviations (103) from the standard’s ratio. Samples with positive δ18O have higher 18O/16O than the standard, and samples with negative δ18O have lower 18O/16O than the standard. In zircon, δ18O higher than values for the depleted mantle (5.3‰ ± 0.6‰) can indicate incorporation of a sedimentary component and/or interaction of their parent magmas with meteoric water. Figure 9 shows a compilation of oxygen isotope data for zircons of different ages depicting a distinct change across the Archean-Proterozoic boundary.

Presentation of Trace Element Geochemical Data

A common approach to constraining the origin of (meta)igneous and (meta)sedimentary rocks is through the use of trace elements, i.e., elements present below 0.1% by weight. These abundances are often reported in parts per million (ppm) and shown graphically as ratios relative to chondritic meteorites and major Earth reservoirs, such as estimates of the primitive mantle, average crust, average shale, etc. (Fig. 10). The regular behavior of the rare earth elements (REE) is particularly useful because the contraction of ionic size with increasing atomic number leads to predictable behavior in many systems, from igneous to sedimentary. Be aware that the normalizing composition grossly affects the shape of the patterns and that the y-axis is always logarithmic. Moreover, the REE are often discussed under the broader term “incompatible elements,” which refers to elements that do not readily substitute for the major cations in rock-forming minerals. Depending on a rock’s mineralogy, an element may be incompatible in one rock, but not in another.

Seismic tomography is not only a method to image the Earth’s interior, but also a term that refers to a collection of different modeling methodologies centered around an inverse problem. Solutions to inverse problems involve using observations to create a model of the conditions that created the observations. For imaging crustal- or lithospheric-scale structures, tomographic methods are dependent on the number and distribution of seismometers or seismic stations that record the observations. The data recorded on these instruments, such as earthquake waveforms, or even “noise” generated by the oceans, can be used to illuminate the changes in seismic velocities of materials in the subsurface. Body wave tomography, which uses the arrival times of P or S waves, and surface wave tomography, which uses the dispersive nature of Rayleigh or Love waves, have quite different resolutions and sensitivities. The resolution of the models generated is primarily controlled by the wavelength of the seismic waves used in the tomographic inversion, regardless of the specific technique or seismic wave type analyzed. Seismic waves are only sensitive to, or able to detect, heterogeneities that have length scales that are similar to the seismic waves themselves. For example, a 1-second (1-Hz) P-wave with a velocity of 5 km/s has a wavelength of 5 km, which roughly corresponds to the size of the smallest detectable heterogeneity. Surface wave tomography can produce cross sections similar to those shown in Figure 3 of Cooper and Miller (2024 this issue). These cross sections are based on much longer wavelength Rayleigh waves, providing lateral resolution on the scale of 10s of kilometers. Because of the way these waves propagate through the Earth, they are most sensitive to lateral variations in the lithosphere and less sensitive to sub-horizontal structures, such as the crust-mantle boundary (Moho). Other types of seismic imaging techniques that use body waves (P and S waves), which travel along more vertical paths, are more sensitive to boundary layers. These methods, typically referred to as receiver functions, are more often used for determining the depth to the Moho or the lithosphere-asthenosphere boundary. Regardless of methodology, these seismic images can then be tested against the temperature and pressure estimates provided by crustal and mantle xenoliths.

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