Exercises: Dating methods

Explain the difference between relative dating and absolute dating, and give an example of a geological event that can be dated using each type of method.

State the law of superposition of strata and apply it to the quarry sequence in the diagram (layers A, B, and C). Which is the oldest layer and what environmental change does the sequence suggest?

What is an index fossil (or characteristic fossil)? State the three requirements that a good index fossil must meet and explain why human beings cannot serve as such to date ancient rocks.

Define fossil and name three different types of evidence that can become fossilised (hard remains, tracks or ichnites, moulds, coprolites, inclusions in amber), explaining what information each type provides.

Explain what the fossilisation process consists of (rapid burial, mineralisation of the hard parts) and discuss why soft-bodied organisms (jellyfish, worms) rarely appear as fossils.

Explain the principle of faunal identity and how it allows strata from two quarries hundreds of kilometers apart to be correlated, indicating which type of fossils serve best for that task.

Explain what the half-life of a radioactive isotope is using the example of a pile of $100$ coins from which you remove half in each round, and why this regularity turns radiometric isotopes into geological "clocks".

Discuss why sedimentary rocks are the great archive of the history of life even though they can rarely be dated directly by radiometric methods, and indicate how this problem is solved using intercalated igneous rocks.

Carbon-14 has a half-life of $5\,730$ years. An archaeological wood sample retains a quarter of the $\text{C-14}$ it had when the tree died. Calculate the age of the sample, explaining your reasoning.

In a cross-section, a series of horizontal strata is intersected by an igneous dyke, all of which is in turn cut by a fault. Applying the principles of cross-cutting relationships and superposition, list in order from oldest to newest: strata, dyke, and fault, justifying each step.

Folded, eroded strata can be seen in an outcrop with horizontal strata above them. State the name of this structure, order the events that formed it (sedimentation, folding, erosion, and renewed sedimentation), and explain what the "hiatus" or time gap represents.

Carbon-14 has a half-life of $5\,730$ years. A fossil tissue retains $1/16$ of the $\text{C-14}$ it had when alive. Calculate the age of the fossil, showing the number of half-lives elapsed and the final result.

In a cross-section, a stratum with trilobite fossils appears above another with ammonoids, the reverse of what the geological time scale indicates. Explain which two tectonic processes can invert a series of strata (overturned folds, thrust faults) and what clues in the field reveal the inversion.

Explain what dendrochronology consists of: what each ring of a tree records, how series from trees of different ages are overlapped to extend the chronology back thousands of years, and what climatic information the width of the rings contains.

Varves are pairs of light and dark laminae deposited each year in certain lakes. Explain what causes this seasonal alternation, how they are used for dating, and why lake sediments are climatic "archives" comparable to ice cores.

In an outcrop, from bottom to top, one can see: metamorphic slates, an eroded surface with slate pebbles at the base of a conglomerate, horizontal sandstones and, cutting across everything, an igneous dyke. Order the geological events from oldest to most recent and justify each relationship (superposition, cross-cutting, included clasts).

A research team analyzes the skeletal remains of a mammal found in a karst cave. Laboratory A extracts collagen from inside the bone and detects that it retains $12.5\ \%$ ($1/8$) of the initial $^{14}\text{C}$ activity. Laboratory B analyzes a carbonate crust that externally coated the bone and measures $50\ \%$ of the initial $^{14}\text{C}$.

1. a) Calculate the numerical age yielded by each laboratory (half-life of $^{14}\text{C} = 5\,730$ years).
2. b) Justify which of the two results is reliable for determining when the animal died and explain what geochemical process caused the error in the other sample.
3. c) A team member proposes using radiocarbon to date a $1.2$-million-year-old volcanic tuff located at the cave entrance. Demonstrate mathematically why this is unfeasible and propose which alternative isotopic method they should use.

To date a sandstone layer containing fossil footprints of early tetrapods, a student separates muscovite (potassium mica) crystals from the sediment itself. After measuring that $25\ \%$ of the original $^{40}\text{K}$ remains ($T_{1/2} = 1\,250$ Ma), they conclude that the footprints are $2\,500$ million years old (Precambrian).

1. a) Refute the student's conclusion: what physical event resets the K-Ar clock to zero, and what are you actually dating when analyzing detrital clasts from a sandstone?
2. b) In the same stratigraphic series, a lava flow is observed intercalated below the sandstone layer, and a volcanic dyke cuts across both the lava and the sandstone. Design a procedure to constrain the maximum and minimum age of the fossil-bearing sediment using these igneous bodies.

In a marine basin, three outcrops correlated by the same ammonoid fossil species with a short biostratigraphic range are studied:

• Column A: the ammonoid-bearing bed is intercalated between a lower volcanic ash of $115$ Ma and an upper one of $110$ Ma.

• Column B: the fossil-bearing bed is cross-cut by a basaltic dyke dated at $112$ Ma, but this dyke does not affect the overlying strata.

• Column C: a researcher claims to have obtained a radiometric age of $114$ Ma by directly analyzing the calcareous cement of the fossil-bearing bed.

1. a) Deduce the most precise and rigorous chronological interval for the existence of this ammonoid by combining the valid data from columns A and B.
2. b) Evaluate the validity of the datum from Column C, justifying whether or not the cement of a sedimentary rock meets the requirements of the radiometric method.
3. c) Predict how the time constraint for the species would change if a detailed analysis proved that the igneous structure in Column B is not a discordant dyke, but an intercalated and concordant submarine lava flow.

A laboratory analyzes zircon crystals from a granitic pluton using the decay of $^{235}\text{U}$ to $^{207}\text{Pb}$ ($T_{1/2} = 704$ Ma).

1. a) In an unaltered sample, the isotopic ratio shows that for every remaining $^{235}\text{U}$ atom, there are $7$ accumulated $^{207}\text{Pb}$ atoms. Calculate the number of half-lives that have elapsed and the crystallization age of the granite.
2. b) In another sample taken from a shear zone with strong hydrothermal alteration, a ratio $^{207}\text{Pb}/^{235}\text{U} = 1$ ($50\ \%$ of original uranium) is measured. A geologist claims that this area of the pluton crystallized $1\,400$ Ma later. Refute their hypothesis by explaining what disruption of the closed system has occurred.
3. c) Demonstrate why this isotopic pair is useless for dating a flint handaxe from a $100\,000$-year-old Paleolithic site: estimate what infinitesimal percentage of $^{235}\text{U}$ would have decayed and explain the resulting analytical problem.

Atmospheric $^{14}\text{C}$ concentration is not constant over time: atmospheric nuclear testing (1955-1963) nearly doubled $^{14}\text{C}$ ("bomb effect"), whereas industrial fossil fuel emissions inject huge volumes of $\text{CO}_2$ completely devoid of $^{14}\text{C}$ ("Suess effect").

1. a) If you date the wood of a tree felled in 1965 using the standard formula without calibration, will its apparent radiocarbon age be from the past or "from the future" (negative)? Justify your deduction based on the measured specific activity.
2. b) Predict what error (artificial aging or rejuvenation) dating a lichen currently growing next to a highway with heavy diesel traffic would yield. Reason through the isotopic exchange involved.
3. c) Justify how dendrochronology allows the construction of a calibration curve that resolves these discrepancies for the last $12\,000$ years.

In a cave in Cantabria containing fossil human remains, the following stratigraphic sequence is recorded from top to bottom:

• Level 1: sediments with normal magnetic polarity. An intercalated stalagmite is dated by uranium series to $0.45$ Ma.

• Level 2: sediments with reversed polarity containing a rich lithic industry and bone remains.

• Level 3: basal sediments with normal magnetic polarity.

Knowing that the Brunhes-Matuyama reversal (from normal to reversed going back in time) occurred $0.78$ Ma ago and the Matuyama-Gauss (from reversed to normal) $2.58$ Ma ago:

1. a) Constrain the time interval in which the hominins of Level 2 could have lived based on the combined data.
2. b) A team member suggests that the remains of Level 2 are $600\,000$ years old. Formally refute their claim based on the observed magnetic polarity.
3. c) If a narrow band of normal polarity barely a few centimeters thick were to appear in the center of Level 2, does it force the entire chronology to change, or what short-duration geomagnetic phenomenon (subchron or event) would it represent within Matuyama?

In a coastal necropolis, two human skeletons found in the same burial level are dated:

• Individual A: $4\,150 \pm 30$ years BP.

• Individual B: $4\,600 \pm 40$ years BP.

Stable isotope analysis reveals that individual A based their diet on terrestrial fruits and herbivores ($\delta^{13}\text{C} = -21\ \text{‰}$), whereas individual B consumed predominantly shellfish and marine fish ($\delta^{13}\text{C} = -13\ \text{‰}$).

1. a) Check whether the two standard deviation intervals ($2\sigma$, $95\ \%$ margin) of both individuals overlap.
2. b) Formulate a hypothesis that explains the nearly $500$-year discrepancy based on the "marine reservoir effect". Which of the two dates is closer to the actual time of burial?
3. c) If instead of extracting collagen, the mineral bone carbonate (hydroxyapatite) fossilized in a wet calcareous soil had been dated, predict and justify the direction of the error (apparent aging or rejuvenation) that diagenesis would cause.

A team presents the following proposal to date various elements of a tectonic basin:

1. Date the pottery from a superficial layer using radiocarbon by analyzing the silicon and aluminum of the fired clay.

2. Date a basaltic volcanic flow using dendrochronology by measuring the concentric alteration bands of its gas vesicles.

3. Date the time of sedimentation of a Precambrian schist using K-Ar applied to micas formed during regional metamorphism.

1. a) Detect and explain the conceptual or methodological flaw that invalidates each of the three proposals.
2. b) Design a valid methodological alternative for each of the three materials, specifying the appropriate analytical method and what physical or chemical event exactly represents the resetting of the clock.
3. c) If in a wooden beam from the site you count $95$ growth rings but do not know the dendrochronological curve of the region, explain why you cannot assign it an absolute calendar date and how it would be complemented with radiocarbon to place it in time.