Geophysics

Step 1: Understanding geothermal gradient.
The geothermal gradient is the rate of temperature increase with depth. It is calculated by the formula: The temperature difference is . The depth is calculated using the lithostatic pressure, with the pressure increasing at 0.3 kbar/km. The depth is:

Step 2: Calculation.
Now, calculate the geothermal gradient:

Step 3: Conclusion.
The geothermal gradient is 25.0°C/km.

Step 1: Understanding the concept.
Isostasy refers to the equilibrium that exists between the Earth's lithosphere and asthenosphere. It involves the vertical movement of the crust in response to changes in load. In continental mountain belts, this process leads to compensation, where the lithosphere adjusts to balance the weight of the mountains.

Step 2: Analyzing the options.
(A) compensation in: This is the correct answer, as isostatic compensation occurs in continental mountain belts.
(B) creation of: This is incorrect because isostasy does not create mountain belts; it adjusts the Earth's crust.
(C) destruction of: This is incorrect, as isostasy does not destroy mountain belts but helps maintain balance.
(D) thrusting in: Thrusting is a tectonic process, not directly related to isostatic compensation.

Step 3: Conclusion.
The correct answer is (A) compensation in because isostasy involves the adjustment of the Earth's crust in response to mountain formation.

Step 1: Identifying the seismic discontinuities and their occurrences.
- The Conrad discontinuity is located between the lower and upper crust.
- The Mohorovičić (Moho) discontinuity is located between the crust and upper mantle.
- The Gutenberg discontinuity is located between the lower mantle and outer core.
- The Lehmann discontinuity is located between the inner and outer core.

Step 2: Analyzing the options.
(A) P-4, Q-2, R-1, S-3: Correct — This matches the seismic discontinuities with their corresponding locations in the Earth's interior.
(B) P-4, Q-2, R-3, S-1: Incorrect.
(C) P-3, Q-2, R-4, S-1: Incorrect.
(D) P-2, Q-4, R-1, S-3: Incorrect.

Step 3: Conclusion.
The correct answer is (A) P-4, Q-2, R-1, S-3, matching the seismic discontinuities with their corresponding positions in Earth's interior.

Step 1: Given data.
Depth below sea surface = 4 km = 4000 m. Thickness of ocean water = 2 km = 2000 m. Depth in rock = 2 km = 2000 m. Density of water = 1000 kg/m³. Density of rock = 3200 kg/m³. Acceleration due to gravity = 10 m/s².
Step 2: Calculate pressure due to water column.
Step 3: Calculate pressure due to rock column.
Step 4: Total overburden pressure.
Step 5: Conclusion.
Overburden pressure = 84 MPa.

Step 1: Understand the principle of isostasy.
In isostatic equilibrium, the weight of the magma column (density ) must be balanced by the weight of the overlying crust and mantle. The total weight of the magma column equals the sum of the weight of the upper and lower crust and the mantle.
Let the depth of the melting be km. Given data:
- Density of magma,
- Density of upper crust,
- Density of lower crust,
- Density of mantle,
Step 2: Write the isostatic balance equation.
The equation for isostatic equilibrium is: Substitute the values and solve for : Step 3: Simplify the equation.
Expanding: Final Answer:

The density contrast across the transition from the lower mantle to the outer core is the maximum. This is due to the significant differences in density between the two layers: the lower mantle is solid, whereas the outer core is liquid, leading to a significant density change.
The Earth's core, especially at the boundary between the outer core and inner core, exhibits the greatest contrast in material properties, significantly affecting seismic waves and other geophysical measurements.
Thus, the correct answer is option (C). Final Answer: