Properties of Seismic Waves

Primary Waves (P-waves) are compressional waves where particle motion is parallel to the direction of travel. Their velocity is defined by the formula: $v_p = \sqrt{\frac{K + \frac{4}{3}G}{\rho}}$ where $K$ is bulk modulus, $G$ is shear modulus, and $\rho$ is density.

Secondary Waves (S-waves) are shear waves where particle motion is perpendicular to the direction of travel. Their velocity is defined by: $v_s = \sqrt{\frac{G}{\rho}}$ Because $G$ is always less than $K + \frac{4}{3}G$, S-waves are inherently slower than P-waves.

In Fluids (liquids and gases), the shear modulus $G$ is zero because fluids cannot resist a change in shape. Consequently, $v_s$ becomes zero, meaning S-waves cannot propagate through liquid layers like the Earth's outer core.

Arrival Order: Always remember the sequence of arrival on a seismogram: P-waves first, then S-waves, followed by the high-amplitude Surface waves. The time gap between P and S arrivals is used to calculate the distance to the epicenter.

Shadow Zone Logic: If a question asks why S-waves are missing at a specific station, check if the path crosses the Earth's outer core. The absence of S-waves is the primary evidence for a liquid outer core.

Velocity Trends: In the Earth's mantle, velocity generally increases with depth because the increase in stiffness (elasticity) due to pressure outweighs the increase in density. If a material becomes liquid, $v_p$ drops significantly and $v_s$ vanishes.

Sanity Check: Ensure that $v_p$ is always calculated as greater than $v_s$ for any given solid material. If your calculation shows otherwise, check your use of the shear modulus.