CSIR NET June 2016 Q35: Geophysics
The velocity of seismic S-waves through a rock is given by Vs = √(μ/ρ), where μ is the shear modulus (rigidity) and ρ is the density. A rock's S-wave speed depends on the balance between these two properties — a higher shear modulus increases speed, while higher density decreases it.
Gabbro is a mafic rock and is denser than granodiorite (a more felsic, intermediate rock), which on its own would tend to slow down S-waves in gabbro. However, gabbro also has a much higher shear modulus (rigidity) than granodiorite, owing to its more tightly bonded, mafic mineral framework (pyroxene, plagioclase, etc.).
Because Vs = √(μ/ρ), the large increase in shear modulus (μ) in the numerator outweighs the increase in density (ρ) in the denominator, resulting in gabbro having a higher overall S-wave velocity than granodiorite, despite being the denser rock.
Because Vs = √(μ/ρ), the large increase in shear modulus (μ) in the numerator outweighs the increase in density (ρ) in the denominator, resulting in gabbro having a higher overall S-wave velocity than granodiorite, despite being the denser rock.
Option 1 is correct: it captures both facts — gabbro is denser, but its shear modulus is disproportionately higher, resulting in a net increase in S-wave velocity.
Option 2 reverses the density relationship — granodiorite is not denser than gabbro; gabbro (mafic) is denser than granodiorite (felsic/intermediate).
Option 3 similarly gets the density comparison backwards, describing granodiorite as lighter (true) but wrongly assigning it the higher shear modulus.
Option 4 incorrectly claims the two rocks have similar densities, when in fact gabbro is meaningfully denser than granodiorite.
Option 2 reverses the density relationship — granodiorite is not denser than gabbro; gabbro (mafic) is denser than granodiorite (felsic/intermediate).
Option 3 similarly gets the density comparison backwards, describing granodiorite as lighter (true) but wrongly assigning it the higher shear modulus.
Option 4 incorrectly claims the two rocks have similar densities, when in fact gabbro is meaningfully denser than granodiorite.