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
The first motion polarity of P and S waves in a radiation pattern is crucial for determining the source mechanism. Remember the approximate angular dependence for a single force.
We need to find the direction of force ⇒F based on seismic wave observations:
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
