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Geologic Age

Introduction

There are few problems more fascinating than those that are bound up with the bold question: How old is the Earth?

--Arthur Holmes

Overview

• Learn about geologic dating methods.
• Determine the relative age of some surface features of Europa.
• Determine the absolute age of several rock samples.
• Determine the age of the Earth.

Introduction

To fully understand the geology of  body with a solid surface, such as a terrestrial planet or moon, planetary scientists need to know about the history of the surface.  Generally, the easiest thing to study is the relative geologic age. Planetary scientists determine the chronology of features, such as whether a crater or streambed is younger. They can also determine if activity was recent, or if the surface of one planet is younger or older than the surface of another. However, there is a limit to how much information this really gives scientists.  The numerical or absolute geologic age is usually of much more interest, and provides much more specific information. However, we have to have actual samples of the surface material to figure out the absolute geologic age, which make it much harder to determine for extraterrestrial objects.

Relative Dating

There are several principals geologists use to determine relative age.  One of the most useful when studying other solar system bodies is the principal of cross-cutting relationships.  It states that any geological feature is younger than any features it cuts across.  For example, a river channel must be younger than the plain it crosses.  If a crater alters the course of the river channel, the crater must be younger than the channel.   Cross-cutting relationships can usually be determined from spacecraft images, allowing planetary scientists to determine the relative age of a surface and, in some cases, compare it to other solar system bodies.  Once they have a relative chronology from the cross cutting relationships, they can make estimates about the ages of other surface features based on the amount of wear or erosion they display.  For example, older craters on the moon are worn down by gravitational slumping and erosion by micrometeorites.  Planetary scientists can estimate the relative age of the craters by comparing their appearance to craters of known age.  However, the best they can do with these techniques is an estimate.

Numerical or Absolute Geologic Dating

The numerical or absolute geologic age gives a narrow age range for the formation of a structure, such as a lava flow.  Determination of the numerical age usually depends on obtaining rock samples and separating out some particular mineral (the individual element or compound, such as salt, or lead), then performing spectroscopy to obtain the data needed to calculate the age. The method for extracting the mineral depends on the mineral. For example, to extract Argon, the sample is baked in a special oven to force the gas out that allows scientists to capture the gas as the rock is heated.  Getting samples from other bodies requires sending a lander, which is generally a very expensive and difficult thing to do.

It should be noted that the age obtained by radiometric dating is the age at which the rock attained its present form.  For example, when lava flows out onto the surface and solidifies, an igneous rock is formed (e.g. basalt or granite).  That rock could subsequently be buried under more rock, or under sediments.  If the pressure and temperature are great enough, it can be changed into a metamorphic rock, such as gneiss or marble.  Radiometric dating will give the date of metamorphosis, not the time when the lava solidified.  If the metamorphosis is incomplete or contamination, such as from sediments occurs, some of the techniques will not work.  Contamination can also occur in igneous rock if fragments of older rock get trapped in the lava flow, causing xenoliths. On active planets like Earth, rocks can undergo multiple transformations. For example, basalt from an ancient volcano could be buried under a latter lava flow and compressed into gneiss. That chunk of gneiss is then subducted and melted, expelled as a new lava flow (basalt), then crushed into granite and thrust up as a mountain by a continental plate. The age measured for the rock will be the age it was turned into granite, and all previous age will be erased.

Absolute age measurements are determined by examining the relative numbers of various isotopes in a rock.  Recall that the number of protons determines what element an atom is, and the number of neutrons determines the isotope.  If an atom has a large nucleus with a lot of protons, the repulsive electromagnetic force between the protons may overcome the strong nuclear force.  The nucleus undergoes radioactive decay, in which a parent isotope (P) decays into a daughter isotope (D).  The parent and daughter may be the same or different elements.  The time it takes for the decay to occur varies for different isotopes.  The half-life is the time it takes for half of the parent isotope to turn into daughter isotope. As the number of parent isotopes deceases, the number of daughter isotopes increases by the same amount, so the SUM remains constant.

The ratio of daughter to parent atoms indicates how many half-lives have elapsed, and the age can be determined by multiplying the half-life by the number of half-lives elapsed. This is called radiometric dating.

half life

The first step in radiometric dating is determining the half-life of a particular isotope. The half-life is the time it takes for half of the parent isotope to turn into the daughter isotope. The half life is given by the equation:

where λ is the decay constant for a particular decay process. Each isotope will have a different half-life dependant on the decay constant. Nuclear physics provides a theoretical prediction for the value of λ, and experimental evidence confirms that the theoretical time is accurate.  Mass spectrometers are used to create a very pure sample with a known number of atoms.  The sample is placed in a controlled environment for years or even decades, and the number of decay events is recorded.  Some detectors are sensitive enough to record nearly every decay event, so it only takes a few thousand decay events to get a very highly accurate measurement of the half life (if a few thousand events sounds like a lot, consider this: there are around 10^21 atoms in one gram of U238, which has a half-life of 4.5 billion years, so we'd see 10^12 events in a decade) In this way, the half-lives of many isotopes is known to a high degree of accuracy, and the models are confirmed.  Additionally, theory is also confirmed using spectroscopy of supernovae, especially for the short lived isotopes.  Many of the heaviest radioactive elements, including such well-known ones as uranium and plutonium, are only generated naturally in supernovae.

If the number of half lives elapsed is known, it is simple to calculate the age of the rock: simply multiply the number of half-lives elapsed by the half-life

However, this technique only works if there was NO daughter isotope in the original.  That is usually the case for the laboratory, but seldom true in the real world.

K-Ar

A few methods have a built in re-set for the daughter isotope: if the daughter isotope is a gas, any event that changes the rock should also force the gas out of the rock. For example, in the potassium-40 Argon-40 technique (K-Ar technique), Potassium-40 decays into Argon-40 and calcium-40.  Argon is a gas, so any argon trapped in the rock probably came from the decay of the potassium since any event with enough heat or pressure to make or alter the rock should also have enough heat or pressure to force out any gas.  Additionally, 11.2% of the potassium always becomes argon, while 88.8% becomes calcium, so the total amount of the daughter isotopes can be calculated just from the argon alone. A comparison of the argon and calcium will show if the rock underwent any alteration that would invalidate this method.  So, under most circumstance the potassium-argon method should be very accurate.

However, there are a few cases where the K-Ar technique can’t be used, and they are common to all the methods that use the half-life calculation: potassium is not uniformly distributed through the Earth’s crust so rocks may be K-poor; Argon-40 occurs in tiny amounts in our atmosphere so there could be an excess or Ar, especially if the rock solidified in air; there are events that can cause contamination especially if xenoliths are trapped in igneous rock; and metamorphism could force some but not all the 40Ar out of the rock. For an age measurement to be considered reliable, we need to confirm it with other methods.

Generic age determination

If there was some of the daughter isotope present at the beginning, and we have a way of determining how much, we can find the age of the rock from:

where Dt is the amount of daughter isotope now, D0 is the amount present at the beginning, and Pt is the amount of parent isotope now.

Usually, it is very difficult to determine D0.  However, a technique called isocrons (“age graphs”) can be used to measure the age.

Simple Isocrons (Rb-Sr)

In simple isocrons, this is done by normalizing the parent and daughter to a stable isotope of the daughter. For example, in the Rb-Sr technique, rubidium-87 (Rb-87) naturally decays into strontium-87 (St-87).  Strontium-86 is another isotope of St.  It is highly stable and is only created if you bombard St-87 with high energy radiation, so the amount of St-86 should remain relatively constant.   As the rock ages, the amount of Rb decreases and the amount of St-87 increases, so the ratio of Rb/St-86 decreases but the ratio of St-87/St-86 increases.  Since different minerals solidify at different rates, the minerals that solidify late will have a lower Rb/St-86 ratio than the minerals that solidified early.  A graph of Sr-87/Sr-86 vs Rb/Sr-86 has a slope of
Which is equivalent to  if Sr-86 is constant. The age of the rock can be calculated using

where m is the slope of the graph.   As with the other techniques,  contamination from xenoliths, sediment, or partial metamorphosis can cause problems.  However, the isocrons usually show problems right away: a good sample will have a clear line with very little scatter, though one or two data points that fall off the best fit line is common.

Age Spectrum (Ar-Ar)

In some cases, the Age Spectrum is more useful than the simple isocron. For example, the argon-40 argon-39 (Ar-Ar), which is an alternative to the K-Ar technique. In this technique, the sample is bombarded with fast neutrons, which forces the potassium-39 to decay in argon-39. Ar-39 has a half-life of only 256 years, so it should not be found in nature in significant quantities. Then the sample is heated to force the release of all the argon gas trapped inside. The amount of Ar39 and Ar40 can be measured as it is heated, and the ratio of Ar-40 to Ar-39 can be used in place of the ratio of K-40 to Ar-40. If the heating is done gradually, the ratio can be captured at many stages, which will show if the sample has been disturbed: at low temperatures only a little gas is forced out, but at high temperature the rock will soften and all the gas will be released. If the sample has never been disturbed, the ration will remain constant. However if the rock underwent metamorphosis, some of the Ar-40 could have ben forced out.In the analysis of the rock, at low temperatures the Ar-40 to Ar-39 ratio will be lower, but should reach a plateau when the rock is heated enough. A graph of the Ar-40/Ar-39 ratio to the percent of Ar-39 released is called the age spectrum. The plateau shows the rock's age, and fluctuations show where Ar-40 was released. The precise theory for why this works is not well understood, but repeated cross checks with other techniques show it is actually more precise than other methods, and it will quickly show if a sample is contaminated or underwent a partial metamorphosis.

Some final notes

Overall, there are more than 40 methods useful for dating the oldest rocks. Almost all the other methods use isocrons, similar to the Rb-Sr method. The others, and many of the shorter half-life methods, use the same basic technique as the K-Ar method. However, only the isocron and Ar-Ar methods are considered useful as a stand-alone test (contamination and other problems are generally readily apparent in the graph, though it is still better to do tests on multiple rocks taken from the same area). In fact, tests involving uranium (U) and lead (Pb) need at least two techniques (e.g. the U-Pb and Pb-Pb) to be considered valid. In particular, However, all of the methods rely on the rock being old enough for a significant amount of the isotopes to decay. These rocks have been sitting out in nature, not in a lab, and they are not purified samples. The error in all of these methods for "natural" rocks is on the order of thousands of years, which is significant for rocks that are less than a million or so years old.

An important final note: Carbon-14 dating is NOT useful for measuring the ages of rocks.  Carbon-14 is formed when cosmic rays strike carbon in the atmosphere.  Living organisms respire the 14C along with the normal 12C, which doesn't decay.  When the organism dies, it ceases to collect 14C, so the ratio of 14C to 12C tells us when the organism died.  However, the 14C will drop to undetectable levels in only a few hundred thousand years (“yesterday” in geologic terms), and the amount of cosmic rays hitting our atmosphere has fluctuated throughout history, making 14C dating accurate only for organisms that died within about the last 50,000 years or so.  In other words, it’s great for human civilization, but lousy for geology and paleontology.

The Age of the Earth by G. Brent Dalrymple is an excellent reference for many of the dating methods used by geologists. An overview of geologic time and dating methods is at http://pubs.usgs.gov/gip/geotime/contents.html.

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