A geophysicist is analyzing the elastic-wave radiation to infer the body force equivalent of a seismic source. She has plotted the horizontal component of the displacement field, denoted as \( u(m, t) \), for time \( t \) and location \( m \). The measured field at two locations \( m \) and \( n \) is plotted in the figure. Note that \( S \) and \( P \) waves have negligible amplitudes at locations \( m \) and \( n \), respectively. Assuming a homogeneous medium, select the most probable direction (specified by the angle \( \alpha \)) along which the force \( \vec{F} \) is applied.
A geophysicist is analyzing the elastic-wave radiation to infer the body force equivalent of a seismic source. She has plotted the horizontal component of the displacement field, denoted as \( u(m, t) \), for time \( t \) and location \( m \). The measured field at two locations \( m \) and \( n \) is plotted in the figure. Note that \( S \) and \( P \) waves have negligible amplitudes at locations \( m \) and \( n \), respectively. Assuming a homogeneous medium, select the most probable direction (specified by the angle \( \alpha \)) along which the force \( \vec{F} \) is applied.
Show Hint
- \( \alpha = 0^\circ \)
- \( \alpha = 90^\circ \)
- \( \alpha = 135^\circ \)
- \( \alpha = 315^\circ \)
The Correct Option is A
Solution and Explanation
P-waves are strong along ⇒F, weak perpendicular
S-waves are strong perpendicular to ⇒F, weak along it
Given:
At point m: S-waves are negligible ⇒ m is along ⇒F
At point n: P-waves are negligible ⇒ n is perpendicular to ⇒F
This means:
⇒F must point directly toward m
n must be at 90° to ⇒F
From the options:
α = 0° matches this (force along x-axis)
Other angles don't align properly
⊥ A
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