Determine relative age with original horizontality, superposition and cross-cutting relationships, determine absolute age by radiometric dating, and combine the two to date a rock sequence

Learning goal: Distinguish relative age from absolute age; apply the principles of original horizontality, superposition and cross-cutting relationships (with inclusions, unconformities and faunal succession) to put events in a geologic cross-section in order; explain how radioactive decay of isotopes gives absolute age; choose the correct isotope for a given rock and age, and explain why different isotopes can give different ages for the same rock; and combine relative and absolute data to bracket the age of rocks that cannot be dated directly.

Where this lesson sits. Ohio's PG.EH.1 (The geologic rock record) is taught on this site in two lessons meant to be studied together. This lesson is part 1 of 2: relative and absolute age, the principles used to determine relative age, radiometric dating and its correct uses (including which isotope to choose and why isotopes can disagree), and combining relative and absolute age data. Part 2, the lesson on the geologic time scale, teaches the divisions of geologic time, comprehending geologic time, climate changes evident in the rock record, the fossil record, and Ohio's bedrock and glacial history, with the local field study and 3-D model. Neither part alone covers PG.EH.1.

Two kinds of age. Relative age places events in order, older and younger, without a number: "the sandstone is older than the dike that cuts it." Absolute age gives a number of years with an uncertainty: "the dike crystallized 310 ± 2 million years ago." Geologists established the order of most of Earth's rock record by relative methods long before radioactivity was discovered; radiometric dating then attached numbers to that order. The two are complementary, and neither alone is enough.

Principles of relative age. In 1669 Nicolaus Steno set out ideas that still anchor the method. Original horizontality: sediment settles under gravity in layers that are horizontal or nearly so; layers found tilted or folded were disturbed after they formed, unless they were deposited on a slope, such as cross-beds or the front of a delta, which are inclined from the start and are recognized by their shape and by flat layers above and below them. Superposition: in an undisturbed sequence of sedimentary layers, each layer is younger than the one below it and older than the one above. The condition matters: superposition applies to layers deposited one on another and not overturned by folding or faulting; indicators such as mud cracks, graded bedding and cross-beds show which way was originally up. Cross-cutting relationships: a feature that cuts across rock, a dike, a fault or an erosion surface, is younger than the rock it cuts. Two further principles help. Inclusions: fragments of one rock enclosed in another are older than the rock that holds them, so pebbles of granite in a sandstone mean the granite was there and eroding first. Faunal succession: fossil species appear, persist and disappear in a definite order, recognized by William Smith in England in the early 1800s, so a layer's fossil assemblage places it in that order even far from other outcrops.

Unconformities. An unconformity is a buried erosion surface, a gap in the record where rock was removed or never deposited. In an angular unconformity, tilted or folded layers are cut off by an erosion surface and overlain by flat layers; it records deposition, tilting, uplift, erosion and renewed deposition, and James Hutton's recognition of one in Scotland in the late 1700s helped convince geologists that Earth is very old. A nonconformity is sedimentary rock resting on eroded igneous or metamorphic rock. A disconformity is an erosion surface between parallel sedimentary layers, often detectable only because fossils show that time is missing. The misconception to avoid is that a stack of rock records all of time: every sequence has gaps, and some gaps represent more time than the rock that remains.

Here is a model worked through, using the diagram. At the bottom are tilted beds A. Flat layers B, C, D and E lie above them, separated from A by an erosion surface. Dike F cuts A and B but not C; its top is cut off flat along the base of C, and C contains pebbles of F's granite. Step 1: A was deposited horizontally (original horizontality), then tilted, then eroded flat, producing the angular unconformity. Step 2: B, C, D and E were deposited in that order (superposition). Step 3: F cuts B, so F is younger than B (cross-cutting); F does not cut C. That alone does not prove C is younger, because a dike can stop before reaching the surface. Here C does contain pebbles of F's granite (inclusions) and rests on an erosion surface that truncates F, so F was intruded and eroded before C was laid down; without that evidence C could only be called younger than B. The full order is A, tilting, erosion, B, F, erosion, C, D, E.

Absolute age: isotopes and radioactive decay. Atoms of one element with different numbers of neutrons are isotopes. Some isotopes are unstable and decay, emitting particles and changing into a different element: the parent isotope becomes a daughter isotope. Decay of an individual atom is random, but a large number of atoms decays at a constant rate, measured by the half-life, the time for half of the remaining parent atoms to decay. Half-lives are not changed by ordinary temperature, pressure or chemistry, which is why they work as clocks. After one half-life 50% of the parent remains, after two 25%, after three 12.5%. If a mineral contained no daughter when it formed and has neither gained nor lost parent or daughter since, measuring the parent-to-daughter ratio gives the time since it formed: age = half-life × log₂(original parent ÷ remaining parent), and original parent = remaining parent + daughter. That last step is a simplified model for a system in which every decayed parent atom becomes the daughter that is counted. Potassium-40 is the important exception: only about 11 percent of its decays produce argon-40 (the rest produce calcium-40, which cannot be told apart from ordinary calcium), so a real potassium-argon age is calculated with that fraction built in, not by simply adding the potassium and the argon.

Correct uses of radiometric dating. The clock starts when a mineral crystallizes and begins trapping its daughter, so radiometric dating dates the crystallization of igneous rocks, such as lava flows, volcanic ash beds and intrusions, or the recrystallization of metamorphic minerals. It does not directly date most sedimentary rock, because the grains in a sandstone crystallized in older rocks before they were eroded; dating them gives the age of the source, which is only an upper limit on the sandstone's age. Choose an isotope whose half-life suits the age. Carbon-14 (half-life 5,730 years) dates once-living material up to about 50,000 to 60,000 years old; beyond that too little remains to measure, so it cannot date dinosaur bones or rocks. Potassium-40 (half-life about 1.25 billion years), measured as argon-40, dates volcanic rocks from about a hundred thousand years to billions of years old. Uranium-238 (half-life about 4.5 billion years) and uranium-235 (about 704 million years), decaying to lead, date zircon crystals, which are extremely durable and reject lead when they form, from about a million years to the age of the Earth.

Why isotopes can disagree. Different methods applied to one rock can give different ages, and the differences are informative, not a failure. Each mineral and isotope system stops losing its daughter at its own closure temperature: argon escapes from minerals if the rock is reheated to a few hundred degrees, while lead stays locked in zircon to much higher temperatures. A granite reheated by later metamorphism may therefore give a young potassium-argon age (when it last cooled) and an old uranium-lead age (when it crystallized). Other causes are weathering that removes parent or daughter, older crystals picked up by a magma, and measurement uncertainty, which is larger when too little daughter has formed.

Combining relative and absolute data. Most sedimentary rocks, and the fossils in them, are dated by bracketing: find datable igneous rocks above and below them and use superposition and cross-cutting to place the sediment between. In the diagram, if dike F gives 310 ± 2 million years and ash bed D gives 298 ± 1 million years, then B is older than about 310 million years, C is between about 310 and 298 million years, and E is younger than about 298 million years.

Worked example, half-lives: A hypothetical zircon crystal contains uranium-235 and lead-207 in the ratio 1 : 3, and no lead was present when it formed. Original parent = 1 + 3 = 4 parts; remaining = 1 part, so one quarter remains, which is two half-lives. Age = 2 × 704 million years = 1.408 billion years, about 1.41 billion years. A ratio of 1 : 7 would mean one eighth remains, three half-lives, 2.11 billion years.

Worked example, a non-whole number of half-lives: A piece of wood from a hypothetical Ohio bog retains 60% of its original carbon-14. Number of half-lives = log₂(1 ÷ 0.60) = log₂(1.667) ≈ 0.737. Age ≈ 0.737 × 5,730 ≈ 4,220 years. A mastodon tusk with 25% remaining would be 2 × 5,730 = 11,460 years old, within the range carbon-14 can date.

Worked example, choosing an isotope: (1) Metamorphic rock at the bottom of the Grand Canyon, believed to be well over a billion years old: use uranium-lead in zircon, whose half-lives suit billion-year ages and whose zircons survive metamorphism; carbon-14 is useless because it applies only to once-living material younger than about 50,000 to 60,000 years. (2) A dinosaur bone bed in a sequence of sandstone and mudstone: the bones and sandstone cannot be dated directly; find volcanic ash beds above and below and date them by argon-argon (a refined potassium-argon method) or uranium-lead in zircon. If a hypothetical ash below gives 76.4 million years and one above gives 75.8 million years, the bones are between those ages.

Worked example, ordering events with an unconformity: A hypothetical cross-section shows folded shale at the bottom, cut by a granite pluton; both are truncated by a flat erosion surface; horizontal limestone lies on top; a fault cuts everything including the limestone. Order: shale deposited; folded; granite intruded (cuts the folds); uplift and erosion (the surface cuts both, a nonconformity over the granite and an angular unconformity over the shale); limestone deposited; faulting last, because it cuts all.

Investigation, modeling half-life: Materials: 100 pennies (or two-colored counters) in a shoebox with a lid, a data table and graph paper. Each penny is a parent atom. Shake the box, open it and remove every penny showing tails; these have "decayed" into daughter atoms (set them in a daughter pile). Record the number of parents left. Repeat for 8 shakes. Plot parents remaining against the number of shakes; draw the ideal curve 100, 50, 25, 12.5 on the same axes. Pool class data and compare. Result that supports the claim: each shake removes about half of the remaining parents, so the curve falls by half each step, and pooling more pennies makes it smoother. What the model cannot show: real half-lives are fixed properties of each isotope spanning thousands to billions of years; and the model does not show how parent or daughter can be lost from a real mineral.

Representation task: Draw your own cross-section with at least five sedimentary layers, one angular unconformity, one dike and one fault. Give it to a partner, who must write the sequence of events and name the principle used at each step. Check each other's answers.

Independent performance: Use a published geologic cross-section of a place (your county, a road cut, or a national park such as the Grand Canyon) to interpret its history. Success criteria: the sequence of events names the principle used at each step; at least one unconformity is identified by type; the report states which units could be dated radiometrically, which isotope system suits each and why; it brackets at least one sedimentary unit between two absolute ages; and it states one source of uncertainty in the result.