Final Examination Geol 282 Answer 12 Of 14 Questions All

Final Examination Geol 282answer 12 Of The 14 Questions All Quest

Analyze the given questions and instructions for the final examination of Geol 282. The exam requires answering 12 of 14 questions, with all questions having equal value. Calculators and reference materials are permitted. The completed exam should be submitted via email by midnight, Saskatoon time, on April 25th. Answers exceeding 12 questions should have the additional questions clearly marked for grading. Communication with others about the exam or seeking assistance beyond the instructor is prohibited to maintain academic integrity during the pandemic.

Paper For Above instruction

The final examination for Geol 282 encompasses various topics in earth sciences, requiring detailed understanding and analytical skills. This paper addresses chosen questions, emphasizing core concepts such as Earth's magnetic field, plate tectonics, seismic activity, planetary physics, oceanography, and geomorphology, integrating both theoretical and quantitative approaches.

Question 1: Earth's Magnetic Field and IGRF Coefficients

The International Geomagnetic Reference Field (IGRF) coefficients for 2020 include values g01 = -29405 nT, g11 = -1451 nT, and h11 = 4652 nT. The coefficient g01 characterizes the axial dipole component, aligned with Earth's rotation axis, thus representing the primary dipole nature of Earth's magnetic field. The other coefficients, g11 and h11, account for the inclined and declinated components of the non-axial dipole contributions.

The current dipole moment (m) of Earth's magnetic field can be calculated using the formula:

m = 4π R³/μ₀ √(g₁₀² + g₁₁² + h₁₁²).

Given Earth's radius R ≈ 6.37 x 10⁶ m, and μ₀ = 4π x 10⁻⁷ H/m, substituting the known values (g10 = -29405 nT, g11 = -1451 nT, h11 = 4652 nT) yields an estimate of Earth's magnetic dipole moment in A·m², highlighting the magnetic strength and orientation.

The longitude of Earth's geomagnetic pole (φ) can be derived using:

φ = arctan(h11 / g11),

which, when computed, provides the declination in degrees, illustrating the offset of Earth's magnetic field from geographic north.

Question 2: Plate Kinematics at the Triple Junction

The Nubian, Antarctic, and Australian plates converge at a triple junction located at 23° south, 71° east, involving three ridge boundaries. Plate velocities are specified as follows: ANvNU = 16.48 mm/yr at a azimuth of 348.61°, and AUvAN = 50.59 mm/yr at 229.95°. To determine NUvAU, vector subtraction of plate motions is performed, resulting in a relative velocity vector with magnitude and orientation, indicating the relative motion between Nubian and Australian plates.

The heading or strike of each ridge is calculated from the velocity vectors' azimuths, converted into angles clockwise from north. These calculations help visualize the plate motions and the potential stress regimes at the ridges, critical for understanding tectonic processes and seismic hazards.

Question 3: Stability of the Triple Junction

Using the velocity data, the velocity diagram for the Nubia-Antarctica-Australia junction can be plotted, ensuring the vector sum closes within the triangle, a key indicator of junction stability. Stability analyses rely on evaluating whether the relative motion vectors satisfy conditions such as the existence of a non-rotating triple junction or the possibility of junction migration. When the velocity vectors are consistent and mutually compatible, the triple junction remains stable over geological timescales.

Question 4: Solar Power at Mars

The solar constant at Earth is 1370 W/m². Since solar irradiance decreases with the square of the distance from the Sun, the power per unit area at Mars can be calculated as:

P_Mars = Solar constant x (Earth–Sun distance / Mars–Sun distance)².

Using the given distances, this yields approximately:

P_Mars ≈ 1370 W/m² x (1.496 x 10¹¹ m / 2.1822 x 10¹¹ m)² ≈ 1370 x (0.685)² ≈ 1370 x 0.469 ≈ 643 W/m².

This demonstrates that Mars receives roughly 644 W/m², less than Earth due to its greater distance, influencing considerations for solar energy applications and planetary climate modeling.

Question 5: Earthquake Depth Trends and Tectonic Settings

The trend of increasing earthquake depths toward the northwest, with the deepest (>300 km) earthquakes and volcanoes, suggests a subduction zone with a slab dip oriented northwestward. The presence of volcanoes aligns with subduction-related magmatism, and the deep earthquakes indicate slab dehydration and mineral phase transformations at high pressure. If a subduction zone, the slab dips in the same direction as the deepest earthquake trend, typically northwestward or southwest depending on regional tectonics. If interpreted as a transform fault, lateral slip occurs with a sense of dextral (right-lateral) or sinistral (left-lateral) motion, discernible through geological and seismic data, with the reasoning rooted in the observed earthquake distribution and volcanic activity.

Question 6: Human Activities Inducing Earthquakes

Activities like hydraulic fracturing (fracking) and reservoir-induced seismicity from large dams can cause earthquakes. Fracking involves injecting high-pressure fluid into subsurface rocks, decreasing stress barriers and inducing fault slip, leading to seismic events of varying magnitude. Reservoir-induced seismicity occurs when the filling of large reservoirs alters the stress on nearby faults due to the massive weight of impounded water, potentially triggering earthquakes. Both mechanisms demonstrate human impact on Earth's seismic activity through stress perturbation and fluid pressure changes in fault zones.

Question 7: Seamounts as Hot-Spot Trails

In the context of active seafloor spreading at the mid-Atlantic ridge, the oldest rocks are expected to be located to the northwest of the current spreading center, consistent with the direction of plate motion. The age range of rocks attached to seamounts on the hot-spot trail can be estimated using the half-spreading rate of 1 cm/yr and the length of the seamount chain. For example, if the seamounts are 100 km from the ridge, their ages are approximately 1 million years, providing a chronological record of volcanic activity and plate movement over geological time.

Question 8: Continental Crust Support and Thickness

Assuming isostatic support, the relation between the crust thickness H and the shelf height h involves balancing the buoyant forces:

H = (Ïm / Ïw) h + (Ïc - Ïw) / Ïw * h.

Using the provided values h = 3 km, Ïw = 1000 kg/m³, Ïm = 3300 kg/m³, and Ïc = 2700 kg/m³, the calculation yields a crust thickness H ≈ 35 km, indicating the significant role of density contrasts in maintaining crustal elevation and structure.

Question 9: Planetary Moment of Inertia

Modeling a planet with core radius r_c and density Ïc, and total radius r_e and density Ïm, and assuming a spherically symmetric distribution, the moment of inertia I can be expressed as:

I = (8π/15) [Ïc r_c^5 + Ïm (r_e^5 - r_c^5)],

which accounts for the contributions of the core and mantle layers, derivable from integrating the density distribution over the spherical volume and using the moments of inertia for each spherical shell.

Question 10: Ocean Ridge Profiles and Spreading Rates

The profile showing broader and more gentle elevation gradients corresponds to a ridge with faster spreading, as rapid divergence of plates leads to less pronounced topography. The East Pacific Rise (lower profile) is characterized by fast spreading rates (~10-15 cm/yr), while the mid-Atlantic ridge (upper profile) spreads more slowly (~2-5 cm/yr). These differences influence ridge morphology, seafloor roughness, and volcanic activity patterns, aligning with observed elevation profiles.

Question 11: Rayleigh Number and Convective Patterns

- When Ra

- When Ra > Racrit but convection is steady, convection cells develop with well-defined, stable thermal patterns, manifested as organized temperature contours.

- Large Ra values induce unsteady, chaotic convection, with time-dependent and irregular thermal patterns, reflecting vigorous and possibly turbulent flow regimes.

Question 12: Planet Rotation and Day Lengths

If a planet's rotation period matches its orbital period, then its sidereal day—the time to complete one rotation relative to distant stars—equals its orbital period, i.e., one year. The solar day, measured from successive appearances of the Sun at the same position in the sky, would be twice the orbital period if the rotation is synchronized with the orbit. The star would appear to rise and set at the same position but with potential phase differences, affecting daily weather and climate cycles.

Question 13: Geoid Low and Sea Level

Sailing through a geoid low indicates approaching a region of decreased gravitational potential, corresponding to a slight bulge of Earth’s surface. In this area, the ship would be closer to Earth's center, requiring less effort for buoyancy. Conversely, engines work harder moving out of the low, and the sky's visibility might differ owing to the change in local gravity affecting horizon perceptions and atmospheric conditions.

Question 14: Magnetic Navigation and Declination

Magnetic compasses are ineffective near the magnetic poles because the horizontal component of Earth's magnetic field diminishes, causing the compass needle to tilt or fluctuate uncontrollably. Magnetic declination is the angle between geographic north and magnetic north at a specific location, essential for accurate navigation. In forested areas, knowing declination ensures correct orientation, preventing disorientation during navigation, especially when landmark visibility is limited.

References

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