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.

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.

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.