Seismic wave velocity is the speed at which seismic waves propagate through a medium, such as the Earth's subsurface materials. Seismic waves are elastic waves generated by earthquakes, explosions, or other sources that cause disturbances in the ground. These waves include different types, primarily compressional waves (P-waves) and shear waves (S-waves), each traveling at characteristic velocities determined by the physical properties of the material they pass through.
Primary P-wave Formula |
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| \( V_p \;=\; \sqrt{ \dfrac{ K + \dfrac{4}{3} \cdot \mu }{ \rho } } \) (Primary P-wave) | ||
| Symbol | English | Metric |
| \( V_p \) = P-wave Velocity | \(ft \;/\; sec\) | \(m \;/\; s\) |
| \( K \) = Bulk Modulus | \(lbm \;/\; in^2\) | \(Pa\) |
| \( \mu \) (Greek Symbol mu) = Shear Modulus | \(lbf \;/\; in^2\) | \(Pa\) |
| \( \rho \) (Greek Symbol rho) = Density | \(lbm \;/\; ft^3\) | \(kg \;/\; m^3\) |
For P-waves, which are longitudinal waves that can travel through solids, liquids, and gases, the velocity (Vp) is given by a formula involving both the bulk and shear moduli divided by density. For S-waves, which are transverse waves that travel only through solids, the velocity depends solely on the shear modulus and density. P-waves always travel faster than S-waves in the same material.
Seismic velocities are typically expressed in units of meters per second (m/s). They vary significantly depending on the material, they are lower in unconsolidated sediments or fluids and higher in dense, rigid rocks like granite or ultramafic rocks. Velocity generally increases with depth in the Earth's crust and mantle due to increasing pressure and changes in material properties, but it drops sharply at boundaries like the mantle-outer core transition because S-waves cannot propagate through liquids.
Secondary S-wave Formula |
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| \( V_s \;=\; \sqrt{ \dfrac{ \mu }{ \rho } } \) (Secondary S-wave) | ||
| Symbol | English | Metric |
| \( V_s \) = S-wave Velocity | \(ft \;/\; sec\) | \(m \;/\; s\) |
| \( \mu \) (Greek Symbol mu) = Shear Modulus | \(lbf \;/\; in^2\) | \(Pa\) |
| \( \rho \) (Greek Symbol rho) = Density | \(lbm \;/\; ft^3\) | \(kg \;/\; m^3\) |
