 Solution

ID: past-exam-of-the-year-2-of-the-earth-sciences-geology-course-of-the-university-of-oxford/2022/paper-1/6/a/solution

For an approximately isotropic elastic solid,

V_{P} = \frac{K + 4 μ /3}{ρ}, V_{S} = \frac{μ}{ρ},

where

K

μ

ρ

is mass density. Five relevant controls are:

Mineral composition and texture: different elastic moduli and densities give different seismic velocities; compliant clay-rich material generally differs from crystalline igneous framework rock.
Porosity, cracks and fractures: compliant voids reduce the effective moduli and usually reduce both speeds; aligned fractures produce seismic anisotropy.
Effective confinement: increasing effective stress closes compliant cracks and tends to raise speeds. Higher pore fluid pressure at fixed total confinement can reopen or preserve cracks and lower the effective stiffness.
Fluid saturation and phase: replacing gas by liquid commonly increases the saturated bulk modulus and $V_{P}$ ; fluids have no static shear rigidity, so $V_{S}$ changes through the frame, density and frequency-dependent interactions rather than a direct fluid shear modulus.
Temperature and alteration: heating commonly reduces elastic moduli and may create thermal cracks; hydrothermal alteration can replace strong minerals by clay or other weaker phases. The sign depends on alteration products and crack sealing, so reservoir-specific measurements are needed.

These controls interact: a dense rock is not automatically faster if its moduli are also different.

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