Questions: Seismic Surface Waves: Rayleigh and Love Waves

Question 1

A seismograph records waves with purely horizontal, side-to-side particle motion perpendicular to the wave propagation direction. What type of seismic wave is this?

• A. Rayleigh waves — retrograde elliptical motion in the vertical plane
• B. P-waves — compressional motion along the propagation direction
• C. Love waves — horizontally polarized SH motion perpendicular to propagation
• D. S-waves — shear motion that can be either horizontal or vertical

Answer: (C)

The purely horizontal, transverse (perpendicular to propagation direction) motion with no vertical component is the diagnostic signature of Love waves. Rayleigh waves produce retrograde elliptical motion in the vertical plane (both vertical and horizontal components in the direction of travel). S-waves can be either SH or SV, but as body waves they radiate through the interior, not as guided surface waves. The distinction between Love and Rayleigh is fundamentally about polarization: Love = horizontal SH, Rayleigh = retrograde ellipse in the vertical plane.

Question 2

Rayleigh waves are observed traveling at different speeds for different periods: longer-period waves arrive earlier than shorter-period waves. What does this indicate about the medium?

• A. The medium is homogeneous — all periods travel at the same speed in a uniform half-space
• B. The medium is layered with seismic velocity increasing with depth, causing longer-period waves (which sample deeper) to travel faster
• C. The source was more energetic at long periods, causing those waves to outrun shorter-period waves
• D. Love waves are contaminating the Rayleigh wave record and arriving at a different speed

Answer: (B)

This is the definition of dispersion and its physical interpretation. Longer-period surface waves penetrate deeper into the Earth, sampling material at greater depth. In the real Earth, seismic velocity generally increases with depth, so longer-period waves travel through faster material on average and arrive sooner. This dispersion is not a complication — it is the key property that makes surface waves useful for imaging Earth structure. By measuring how velocity varies with period, seismologists can invert for how shear velocity varies with depth.

Question 3

Rayleigh waves require a low-velocity layer overlying a higher-velocity substrate in order to exist.

• T. True
• F. False

Answer: False

This describes the requirement for Love waves, not Rayleigh waves. Rayleigh waves exist wherever there is a free surface — they require no layering at all and occur even in a perfectly homogeneous half-space. Love waves, by contrast, require a low-velocity layer over a higher-velocity substrate because they are sustained by total internal reflection within the low-velocity layer. Getting these requirements reversed is a common misconception; remembering that Rayleigh waves involve the free surface directly (retrograde ellipse at the surface) while Love waves are trapped in a layer helps keep the distinction straight.

Question 4

Surface waves travel more slowly than body waves but carry more energy at large distances from the earthquake source.

• T. True
• F. False

Answer: True

Surface waves are slower than both P and S body waves — Rayleigh wave velocity in a uniform half-space is about 0.92 times the shear wave velocity. Despite arriving later, they dominate seismograms of distant earthquakes because their energy is confined to the shallow subsurface rather than spreading through the full volume. Body waves spread in three dimensions (amplitude decays as 1/r), while surface waves spread in two dimensions along the surface (amplitude decays as 1/√r). This geometric spreading difference means surface waves retain much higher amplitude at large distances, which is also why they cause the majority of earthquake damage far from the epicenter.

Question 5

Why are surface wave dispersion curves useful for imaging Earth's interior, and what physical property do they constrain?

Model answer: Surface wave dispersion is useful because different periods sample different depths: short-period waves are sensitive to shallow structure, long-period waves penetrate deeper. By measuring how phase velocity and group velocity vary with period, seismologists construct dispersion curves that are then inverted mathematically to recover shear-wave velocity as a function of depth. Short periods (5–20 s) constrain crustal thickness and velocity; intermediate periods (20–100 s) resolve the lithosphere and asthenosphere; long periods (100–300 s) sense the upper mantle. The physical property constrained is primarily shear velocity (Vs) structure, because both Rayleigh and Love waves are shear-dominated.

Surface wave tomography has produced some of the highest-resolution images of the upper mantle, revealing cratonic roots, subducting slabs, and plumes. The power of the method comes from the depth sensitivity being tunable simply by measuring different periods — you do not need different types of seismic sources or receivers, just a broad-band seismograph and a distant earthquake.