9. The age of rocks
9.1. Absolute vs. relative ages
The issue of time is central to earth science. Geologists want to know how old rocks are and how
long it takes for geological processes to occur. Until the 20th century and the discovery ofradioactivity, geologists could only tell whether a rock was younger or older than another rock. In
other words, they could only determine the relative age of rocks. Knowing the number of years
elapsed since a rock has formed, in other words knowing the absolute age of the rock, could onlybe achieved after the development of radiometric dating in the 20th century.

9.2. The relative age of rocks
9.2.1. Stratigraphic principles
Stratigraphy is the study of sedimentary layers (or strata). The founder of stratigraphy is a Danish
scientist named Nicolas Steno (1638-1686). He is also known for his study of the fossil
Glossopetrae which he correctly identified as fossilized shark teeth, a notable achievement at atime when the true nature of fossils was poorly understood. His interest for geology led him tostudy the sedimentary rocks of northern Italy (where he lived) and to enounce two fundamental
rules of stratigraphy:

1. Principle of original horizontality
Sediments are deposited horizontally (or nearly so) by gravity. This implies that sedimentary layers
which are folded or faulted have been subjected to deformations after their deposition.

2. Principle of superposition
New sedimentary layers form on top of older layers. Therefore in an undeformed succession of
sedimentary layers, layers at the bottom are older than layers at the top.
The principle of superposition is of course very useful to determine the relative age of sedimentarylayers. When studying a section of sedimentary rocks, this principle can be used to reconstruct thechronological order of the layers providing that we understand the deformation history of the rocks
in question.
What if we have two sections that are very distant from each other? How can we know that therocks of one section are younger or older than the rocks of another section located far away? To
solve this problem, one way is to study the fossil content of sedimentary layers.
9.2.2. Biostratigraphy
Due to folding, a succession of sedimentary layers can become up-side down and the chronological order inverted. If thedeformation is not noticed, the chronological reconstruction will be completely wrong!

44Biostratigraphy is the branch of stratigraphy which uses fossils to correlate sedimentary rocks
and find out their relative ages. The technique relies on the fact that life evolves. Some species go
extinct while new species appear. As a consequence, fossil assemblages of different geologicalintervals are not the same. The geological record is characterized by fossil assemblages whosespecies composition is changing through time. This is the principle of faunal succession. For
example, a fossil of Australopithecus (one ancient genus of hominids －the family of primate towhich we belong－ who appeared around 4 million years ago and went extinct 2 million yearslater) cannot be found in the same layer as a fossil of dinosaur because dinosaurs went extinct 65
million years ago (61 million years before the first Australopithecus appeared!).
Some species are more useful than others when it comes to determine the relative ages ofsedimentary rocks. Widespread species which have existed for a limited time and arecharacteristic of specific geological periods are excellent biostratigraphic markers. These species
are called index species.
NB: the concept of the evolution of life was accepted before Charles Darwin (1809-1882) proposed
his theory of evolution by natural selection. The roots of biostratigraphy are to be found in the 18thcentury when scientists noticed that sedimentary rocks of different ages were characterized bydifferent fossils. What Darwin discovered is a mechanism explaining how new species arise andtherefore how evolution can take place.

9.2.3. Unconformities: gaps in the stratigraphic record
The stratigraphic record is not continuous. There are gaps which can result from prolonged lack ofdeposition or from the erosion of preexisting sedimentary layers. The surfaces corresponding tothese gaps are called unconformities.
In many cases unconformities result from an episode of erosion. Sedimentary layers formed in alake or in the sea can be eroded during a long period of emergence. How do sedimentary layers
initially formed under water become emerged? There are two important mechanisms that cancause long period of emergence: sea level fall (1) and upward ground movement or uplift (2).
(1) During ice ages (glacial periods), more ice accumulates on landmasses and sea level falls
dramatically. During the maximum of the last ice age about 20,000 years ago (Last GlacialMaximum = LGM), the sea level was 125 m lower than today! The continental shelves stood above
sea level and sediments were exposed to the erosional action of the wind and the rain. New
sedimentary layers formed only when the sea re-flooded the continental shelves during the current
warm period. The surface which separates these new layers from the layers deposited before theLGM is an unconformity and represents a time gap of thousands of years.
(2) Regions of the crust near convergent plate boundaries experience tremendous compressional
forces which can cause folding and bring portions of the crust at higher elevations, a process45

called tectonic uplift. Uplifted sedimentary layers can be raised above sea level where they are
exposed to erosional processes. Once compression stops, an episode of subsidence (downward
movement of the crust, see section 7.5) may create a depression in which new sediments canaccumulate. The surface between the older folded sedimentary layers and the new sediments is
an unconformity which may encompass a time lapse of millions of years.
There are three types of unconformities:
Disconformity: the sedimentary layers below and above the unconformity are both undeformedand horizontal. An example of disconformity is the unconformity corresponding to the episode ofsea level fall presented above [see (1)].
Angular unconformity: the sedimentary layers below the unconformity are folded whereas thesedimentary layers above the unconformity are undeformed and horizontal. An example of angular
unconformity is the unconformity related to the episode of compressional deformation followed byerosion, subsidence, and deposition of new sediments presented above [see (2)].
Nonconformity: unconformity between sedimentary rocks and metamorphic or igneous rocks.
This type of unconformity may represent a very extensive time gap of tens of millions of years ormore.
9.2.4. Cross-cutting relationships
The geometrical relationships between sedimentary rock formations, igneous intrusions (e.g.
dykes －sheet-like intrusion intersecting rock layers－), faults, and unconformities can be used toreconstruct the chronological order in which these geological features formed. The rule is simple:
younger geological structures cut older ones. For example, a dyke intersecting sedimentary layers
must be younger than these layers or a fault cutting a dyke must be younger than the dyke.
9.2.5. The geological time scale
Geologists of the 19th century used the principle of superposition and biostratigraphy to divide thegeological record into successive intervals characterized by distinct fossil assemblages. Thisapproach led to the construction of the geologic time scale. The basic subdivisions of thegeologic time scale (from longer to shorter time units) are eras (e.g. Cenozoic), periods (e.g.
Quaternary), and epochs (e.g. the current epoch called Holocene).
The boundary between geologic periods is characterized by abrupt changes in fossil assemblages.
Several of these boundaries correspond to mass extinctions. A mass extinction event represents a
relatively short geologic time span (a few million years or less) during which a large proportion of
the total number of species living on the Earth (e.g. 75% or more) disappears (see chapter on theevolution of life).
.

Note that uplift does not necessarily imply folding. Rocks can be uplifted without undergoing much folding.

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9.3. The absolute age of rocks
When the geologic time scale was established in the 19th century, geologists did not know theduration of each period. Nobody knew precisely how old the Earth was. This issue was important
not only for science but also for religion because of the strongly held religious belief that the Earthcould not be older than a few thousand years based on the rigorous interpretation of religious texts.
The solution came only after the discovery of radioactivity in 1896 by a French physicist named
Henri Becquerel. At the beginning of the 20th century, the physicist Ernest Rutherford proposed atechnique to date rocks based on radioactive decay. The method of radiometric dating was born.
Based on this method, an American geochemist named Clair C. Patterson calculated in the 1950s
an age for the Earth of 4.56 billion years!
The basic principle of radiometric dating is simple. Elements consist of different isotopes with
nuclei composed of the same number of protons but with different numbers of neutrons.
Radioactive isotopes are isotopes which spontaneously disintegrate (decay) into a different
element. In a rock containing a certain amount of a given radioactive isotope, the concentration of
the element produced by radioactive decay increases with time and can be used as a natural clock
to determine the age of the rock. This can work only if the rate of radioactive decay is known anddoes not vary in time.
The rate at which a radioactive isotope (parent atom) disintegrates into another element (daughteratom) is expressed by its half-life. The half-life of a radioactive isotope is the time its takes for halfof the initial amount to decay into daughter atoms (Figs. 1 & 2).

Figure 147

Figure 2

Different isotopes have different half-lives. For example, 14C (carbon-14) disintegrates into 14N andhas a half life of 5730 years. Another example is 87Rb which disintegrates into 87Sr and has a
half-life of 49 billion years. Therefore if you want to measure the age of rocks that are hundreds ofmillions of years old or more, you can use the rubidium-strontium system but not the radioactive
isotope of carbon. The 14C method is used to measure the age of much younger materials. For
example, you can use 14C to measure the age of corals which were growing thousands of years
ago.
The half-life of a particular radioactive isotope is constant. It is not affected by changes inphysic-chemical conditions, such as variations in temperature and pressure. This is of fundamental
importance because if the half-life of radioactive isotopes varied in time, radiometric dating would
not be possible.
In order to understand how the age of a rock can be measured, let’s take the example of therubidium-strontium system. In this case, the parent atom is 87Rb and the daughter atom is 87Sr.
Let’s say we collected a sample of igneous rock and we want to know its age. The age of thesample in this case is the time elapsed since it crystallized from a cooling magma. The crystals
forming in the cooling magma have trapped a certain amount of parent atoms [87Rb]t=0. First let’s
suppose that there is no daughter atoms 87Sr incorporated in the crystals when they formed(unrealistic!). We can express the amount of 87Rb and 87Sr present in our sample as a function oftime using the following relationship:48

Equation (A) represents a straight line with a slope equal to (2t-1) (Fig. 3). Therefore measuring theamount of 87Sr and 87Rb in our sample would enable us to calculate the age of the rock.

Figure 3

In reality, there is always a certain amount of daughter atoms 87Sr which is incorporated in thecrystals when the rock forms. In such case, equation (A) becomes (Fig. 4):

Figure 4

In this case, measuring the amount of parent atoms and daughter atoms in our sample is notenough to calculate the age of the rock because we don’t know how much daughter atoms has
been trapped initially in the rock (Fig. 5). Each minerals of our rock sample can incorporate any
amount of 87Rb and 87Sr at the time of crystallization.

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Figure 5

The solution to solve this problem is to consider the ratio of 87Sr to a stable isotope of the sameelement which has the same properties. Here the stable isotope in question is 86Sr. Since 87Sr and86

Sr have the same behavior during physico-chemical reactions, they will incorporate different

minerals always in the same proportion*. Let’s say we have 1000 atoms of 87Sr and 1200 atoms of86

Sr initially present in the magma. The table below shows their distribution in three differentminerals. The initial ratio 87Sr/86Sr is independent of the amount of 87Sr trapped in the minerals
when they crystallized.

If we divide equation (B) by [86Sr]t, we obtain the following relationship:

We can thus determine the age of our sample by measuring the ratio of 87Sr and 87Rb to 86Sr inseveral minerals in order to obtain a straight line from which we can derive the age t (Fig. 6). In* Note that the isotopic composition of the magma should be uniform when crystallization occurs.

50addition to the age, we can also find out the initial ratio of 87Sr to 86Sr.

Figure 6

The slope of the line defined by the three minerals in the graph above is a function of the time
elapsed since crystallization. This method is valid only if the minerals have not exchanged
elements with the surrounding environment after they crystallized. Each mineral must haveremained a closed system. For metamorphic rocks, the age obtained corresponds to the timesince the last phase of crystallization. We can also measure the age of biominerals like coralskeletons or algal crusts made of CaCO3. In this case, we measure the time elapsed since theorganism secreted the mineral assuming that the system remained closed afterward.

Note that there are techniques dealing with open systems.

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