To solve this problem, we need to use Snell's Law for seismic waves, which relates the angle of incidence and refraction to the velocities of the two layers. Snell's Law for seismic waves is given by:
\(\frac{\sin \theta_1}{V_1} = \frac{\sin \theta_2}{V_2}\)
where:
- \(\theta_1\) is the angle of incidence in the first layer.
- \(\theta_2\) is the angle of refraction in the second layer.
- V_1 is the seismic velocity in the first layer.
- V_2 is the seismic velocity in the second layer.
According to the question:
- Angle of incidence, \(\theta_1 = 30^\circ\)
- Angle of refraction, \(\theta_2 = 45^\circ\)
Substitute the given angles into the Snell's Law equation:
\(\frac{\sin 30^\circ}{V_1} = \frac{\sin 45^\circ}{V_2}\)
\(\sin 30^\circ = \frac{1}{2}\) and \(\sin 45^\circ = \frac{\sqrt{2}}{2}\). Thus, the equation becomes:
\(\frac{\frac{1}{2}}{V_1} = \frac{\frac{\sqrt{2}}{2}}{V_2}\)
Simplify and rearrange to find the ratio of seismic velocities:
\(\frac{1}{V_1} = \frac{\sqrt{2}}{V_2}\)
V_2 = \sqrt{2} \cdot V_1
Thus, the ratio of seismic velocities \(\frac{V_2}{V_1}\) is \(\sqrt{2}\).
Therefore, the correct answer is:
- \(\sqrt{2}\) (as per the given options)
Important Questions from Seismic Waves
- The ratio of S-wave to P-wave velocities for zero Poisson's ratio value is
- Which one of the following seismic phases results from a P-wave turning within the crust?
- Which one of the following correctly describes the attenuation property of the Earth expressed in terms of quality factor ($Q$)?
- A weak P-wave diffraction is observed in the epicentral distance range of
- What is the reflection coefficient for a seismic wave incident at normal to the interface between the first and second layers characterized by densities 3 g/cc and 2.5 g/cc, and velocities 5 km/s and 4 km/s, respectively?
