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Q11. The d18O value of modern seawater is 0 per mil while the average value of that of the polar ice cap is -45 per mil. The ice cap holds 2 wt% of the total water on the Earth. What is the d18O value of an ice-free ocean? (Other water reservoirs can be ignored)
Use a mass balance equation for the bulk Earth: (0.98 * 0) + (0.02 * -45) = -0.9 per mil. If the ice melts completely, all water mixes into the ocean, shifting the ocean's isotopic signature to the bulk Earth value of -0.9 per mil.
Q12. A Mesozoic stratigraphic sequence from bottom to top is: Poorly-sorted sandstone with unimodal paleocurrent -> Sand-mud alteration with bipolar paleocurrent -> Well-sorted sandstone with bimodal paleocurrent. The probable depositional environment is:
Unimodal poorly-sorted sands indicate River (Fluvial) flow. Bipolar sand-mud indicates Tidal influence (ebb and flood). Well-sorted bimodal sands indicate Beach/Shoreface wave action.
Q13. The total observed runoff volume during a storm of 5-hr duration with a uniform intensity of 16 mm/hr is 20 Mm^3. If the area of the basin is 400 km^2, then the infiltration (mm) is:
Total Rainfall = 16 mm/hr * 5 hr = 80 mm. Runoff volume = 20 Mm^3 over 400 km^2 area = (20x10^6 m^3) / (400x10^6 m^2) = 0.05 m = 50 mm. Infiltration = Total Rainfall - Runoff = 80 mm - 50 mm = 30 mm.
Q14. Water entering the Mediterranean Sea from the Atlantic Ocean is 1.75 Sv whereas, water leaving the Mediterranean Sea to the Atlantic Ocean is 1.68 Sv. This means that:
To maintain a steady state, Water In = Water Out + Net Evaporation (E-P). 1.75 = 1.68 + (E-P). E-P = 0.07 Sverdrups. 1 Sv = 10^6 m3/s, so 0.07 Sv = 70,000 m3/s.
Q15. The primary (P) and secondary (S) waves from a shallow focus earthquake reached a seismological observatory at 8:30:04 Hrs and 8:31:16 Hrs respectively. If the velocities of the P and S waves are in the ratio 1.6:1, then the time of occurrence of the earthquake would be:
Time diff = 72s. Using Ts = D/Vs and Tp = D/Vp. Since Vp = 1.6 Vs, then Tp = Ts/1.6. We know Ts - Tp = 72s. Thus, Ts - (Ts/1.6) = 72s. Solving yields Ts = 192s, meaning Tp = 120s (2 minutes). 8:30:04 minus 2 minutes = 8:28:04.
Q16. The simplest sequence of mineral zones that typically develops, in the order of increasing grades, during metamorphism of siliceous limestone in a contact aureole is?
This represents Bowen's classic decarbonation sequence for siliceous dolomites/limestones undergoing contact metamorphism. Talc forms first at lower T, followed by Tremolite, then Diopside.
Q17. Identify the INCORRECT statement:
This is FALSE. Clay has a much higher surface area and porosity than sand, allowing it to hold significantly more water, though it has lower permeability (it doesn't drain well).
Q18. Which one of the following statements is NOT correct regarding oceanic mixed layer?
This is false because oceanic rainfall adds fresh, less-dense water to the surface. This buoyant layer sits on top of the saltier water below, which actually STABILIZES the mixed layer, preventing deep vertical mixing.
Q19. What is the optimum solution of the following set of linear equations? 2x+3y=8 ; 3x+2y=9 ; 2x-6y=0
This is an overdetermined system. Setting up matrices A and B and solving the normal equation (A^T A x = A^T B) yields the least-squares optimum solution where x = 43/17 and y = 42/49.
Q20. The following reaction was inferred on study of a metamorphic rock that was subjected to 0.6 GPa pressure: CaCO3 (Calcite) + SiO2 (Quartz) -> CaSiO3 (Wollastonite) + CO2 (vapour). The temperature at which this reaction took place depends on:
This is a classic decarbonation reaction. The equilibrium temperature is highly dependent on the partial pressure (or mole fraction) of the volatile phase released, which in this case is the mole fraction of CO2 (X_CO2) in the fluid.