Earth Engineering - The Earth and Its Systems

Relative Time

• Principle of cross-cutting relationships: A geological feature (rock from magma intrusion, fault) that cuts across a pre-existing rock body is younger than the rock it penetrates.

Applying Principles of Relative Dating

1. Superposition: Beds A, B, C, and E were deposited in that order (oldest to youngest).
2. Sill (D):
   • A concordant igneous intrusion.
   • Younger than the rocks it intrudes (cross-cutting relationships).
   • Inclusions of fragments from beds C and E confirm it's younger because the adjacent strata was there first.
3. Dike (F):
   • Intrusion occurred after sill D.
   • Cuts through beds A-E, making it younger than all of them (cross-cutting).
4. Tilting and Erosion:
   • Rocks were tilted and then eroded.
   • Tilting happened first (upturned ends of strata are eroded).
   • Tilting and erosion, followed by deposition, created an angular unconformity.
5. Deposition of Beds G-K:
   • Beds G, H, I, J, and K were deposited in that order (superposition).
   • Lava flow (bed H) is surface-deposited, so superposition applies.
6. Erosion:
   • Irregular surface and stream valley indicate a gap in the rock record due to erosion.

Conformable Rock Record vs. Unconformity

• Conformable: Continuous rock record with no breaks.
• Unconformity: Break/gap in the rock record from erosion and/or non-deposition.

Types of Unconformities

• Angular Unconformity:
  • Tilted sedimentary rocks overlain by younger, flat-lying sedimentary rocks.
  • Indicates deformation and erosion during a pause in deposition.
• Disconformity:
  • Unconformity between parallel layers of sedimentary rocks.
  • Indicates no deformation during the pause, but erosion may have occurred.
• Nonconformity:
  • Between sedimentary rocks and metamorphic or igneous rocks.
  • Sedimentary rocks overlay and were deposited on pre-existing eroded metamorphic/igneous rock.

Formation of Angular Unconformity

• Stages:
  • A: Deposition
  • B: Folding and uplifting
  • C: Erosion
  • D: Subsidence and renewed deposition

Dating with Radioactivity

• Dating: Based on the decay rate of unstable (radioactive) isotopes.
• Isotopes: Variable forms of an element with different numbers of neutrons.
• Radioactive Decay: Unstable nucleus spontaneously transforms into a different element's nucleus (stable or unstable).

Half-Life

• Exponential Decay: Radioactive decay curve shows exponential change. Half of the parent isotope remains after one half-life; one-quarter after two half-lives, and so on.

• Half-life Defined: Time it takes for half of the atoms of an unstable parent element to decay into the daughter element.

• Half-lives: Constant and precisely measured; range from less than a billionth of a second to 47 billion years.

• Radioactive decay formula:

  $N = N_0e^{-kt}$

  • Where:
    • $N$ = number of atoms of an isotope.
    • $N_0$ = original number of atoms prior to decay.
    • $k$ = decay rate (per year).
    • $t$ = time

• Requirements: Know $N_0$ (original amount) and it must be invariant in time.

  Example: Phosphorous-32 ($^{32}P$) has a half-life of 14.7 days. If starting with 10 grams of $^{32}P$, after 14.7 days, 5 grams remain, and 5 grams of Sulfur-32 are formed.

Geologic Time Scale

• Divisions (largest to smallest): Eon, Era, Period, Epoch
• Eons: Precambrian, Phanerozoic
• Eras:
  • Precambrian: Hadean, Archean, Proterozoic
  • Phanerozoic: Paleozoic, Mesozoic, Cenozoic
• Key events in each Era related to plant and animal development (e.g.,