Dating methods

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?

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.

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).

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.

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

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.

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.

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.

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.

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 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?