(II) A longitudinal earthquake wave strikes a boundary...

(II) A longitudinal earthquake wave strikes a boundary between two types of rock at a $38^{\circ}$ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8 . Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.

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Key Concepts

Density and Specific Gravity

Specific gravity is a dimensionless measure that compares the density of a material to a reference density, typically that of water. Changes in specific gravity indicate differences in density between rock types, which, under constant elastic modulus conditions, lead to changes in seismic wave velocity. This is a key factor in analyzing how seismic waves refract as they encounter different geological materials.

Seismic Wave Velocity

The velocity of seismic waves in an elastic medium is determined by the square root of the ratio of the elastic modulus to the density of the material. When the elastic modulus is constant across a boundary, variations in density directly affect the wave speed. This relationship is critical for understanding how waves propagate through different types of rock and how their speeds change at boundaries.

Snell's Law

Snell's Law governs the refraction of waves when they pass through an interface between two different media. In seismology, it relates the incident angle and the refracted angle of a seismic wave to the ratio of the velocities in the two media. This fundamental principle explains how a change in the medium properties, such as density or elastic modulus, alters the wave's trajectory.

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