 Solution

ID: past-exam-of-the-year-2-of-the-earth-sciences-geology-course-of-the-university-of-oxford/2024/paper-3/1/a/solution

For an approximately isotropic rock, the P wave and S wave speeds are

V_{p} = \frac{K + 4 μ /3}{ρ}, V_{s} = \frac{μ}{ρ},

where

K

μ

ρ

is density. Five important controls are:

Mineralogy and cementation. Stiff, well-cemented mineral frameworks usually have higher elastic modulus values and faster seismic velocities than poorly consolidated sediments. Density alone is insufficient: both stiffness and density enter the equations.
Porosity and cracks. Larger porosity, especially compliant cracks, usually lowers effective elastic modulus values and seismic velocities. Crack orientation can make the seismic velocities direction-dependent through seismic anisotropy.
Pore-fluid composition and saturation. Replacing liquid water by gas generally lowers the effective bulk modulus sharply and reduces $V_{p}$ . Pore fluids have negligible static shear modulus; $V_{s}$ responds chiefly through the solid framework and the changed bulk density, rather than through a shear restoring force in the fluid.
Effective confining pressure. Increasing effective stress closes cracks and improves grain contacts, usually increasing both seismic velocities. Increasing pore fluid pressure at fixed total stress reduces effective stress and can reverse this trend.
Temperature. At otherwise comparable conditions, increasing temperature generally softens minerals and lowers seismic velocities; thermal cracking or partial melting can lower them further. Increasing burial commonly increases both temperature and pressure, so their separate effects need not have the same sign.

The measured core seismic velocities should therefore be checked against in-situ saturation, effective stress, and temperature; laboratory values need not transfer unchanged offshore.

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