If a seismic wave is travelling along the radial direction, then which of the following statements is/are CORRECT for Rayleigh (R) and Love (L) waves?
Show Hint
- Radial component shows the largest amplitude for both R and L waves
- Transverse component shows the largest and smallest amplitudes for L and R waves, respectively
- Vertical component shows the largest and smallest amplitudes for L and R waves, respectively
- Vertical component shows largest amplitude for R wave only
The Correct Option is B, D
Solution and Explanation
Set up local ground-motion axes at a receiver for a wave arriving along the radial (great-circle) direction: radial (R-component, horizontal, along the source-receiver azimuth), transverse (T-component, horizontal, perpendicular to that azimuth) and vertical (Z-component).
Love waves are formed by constructive interference of horizontally-polarised shear (SH) waves trapped in a low-velocity surface layer. Their particle motion is PURELY horizontal and PURELY perpendicular to the propagation direction -- i.e. entirely on the transverse component. A Love wave therefore has essentially ZERO radial and ZERO vertical motion, and its transverse-component amplitude is the largest (in fact the only) component present.
Rayleigh waves arise from coupled P-SV motion at the free surface. Particle motion is retrograde-elliptical and confined entirely to the vertical plane containing the propagation direction -- i.e. it has radial and vertical components only, and ZERO transverse component (SH motion plays no part in Rayleigh waves). Of its two non-zero components, the vertical component is typically the larger/dominant one (this is why vertical-component seismometers are used to pick Rayleigh-wave dispersion), with the radial component present but generally smaller.
Now check each option:
- (A) False -- radial component is zero for the Love wave, so it cannot be the largest for both wave types.
- (B) Transverse component: the Love wave's motion is entirely transverse, so it is the LARGEST (in fact the only) component for L; the Rayleigh wave has zero transverse motion, so it is the SMALLEST (zero) for R. This is exactly what option (B) states -- CORRECT.
- (C) False -- this reverses the truth. Vertical motion is zero for the Love wave and dominant for the Rayleigh wave, i.e. smallest for L and largest for R -- the opposite of what option (C) claims.
- (D) Vertical component shows the largest amplitude for the R wave only -- correct, since Rayleigh has substantial (dominant) vertical motion while Love has none at all, so R wave only is an accurate qualifier -- CORRECT.
So the correct statements are (B) and (D).
\(\boxed{\text{(B) and (D)}}\)
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