How Are S Waves And Vertical Surface Waves Different

Understanding the behavior of seismic energy as it travels through the Earth is fundamental to the fields of seismology, earthquake engineering, and geophysical exploration. On the flip side, their physics, propagation mechanisms, speeds, and impacts on the built environment differ significantly. Day to day, among the various types of seismic waves generated by an earthquake or artificial source, S-waves (shear waves) and vertical surface waves (primarily Rayleigh waves) are two distinct categories that often cause confusion due to their shared characteristic of particle motion perpendicular to the direction of propagation. This article provides a comprehensive breakdown of how these two wave types differ, exploring their particle motion, velocity, depth penetration, dispersion characteristics, and destructive potential.

Fundamental Physics: Body Waves vs. Surface Waves

The most fundamental distinction lies in their classification within the seismic wave hierarchy. Seismic waves are broadly divided into body waves, which travel through the interior of the Earth, and surface waves, which propagate along the boundary between the Earth and the atmosphere (or between two distinct layers) Easy to understand, harder to ignore..

S-waves (Secondary waves or Shear waves) are body waves. They radiate outward from the hypocenter in three dimensions, traveling through the volume of the rock. Their propagation depends entirely on the shear modulus (rigidity) of the material; fluids like water and the Earth’s outer core have zero rigidity, meaning S-waves cannot travel through them. This property creates the famous S-wave shadow zone on the opposite side of the Earth from an earthquake epicenter Worth knowing..

Vertical surface waves, most commonly identified as Rayleigh waves, are surface waves. They are guided waves trapped near the free surface. Their existence relies on the interaction between compressional (P) and shear (SV) body waves reflecting and interfering at the free surface boundary. Because they are confined to a layer near the surface, their amplitude decays exponentially with depth. They do not travel through the deep mantle or core in the same way body waves do; instead, they circle the globe along the crust Turns out it matters..

Particle Motion: Retrograde Ellipses vs. Pure Shear

While both wave types involve vertical particle motion, the geometry of that motion is the primary visual differentiator on a seismogram or in a physical model.

S-Wave Particle Motion

S-waves are transverse waves. The particle motion is perpendicular to the direction of wave propagation. In a homogeneous, isotropic medium, this motion is linearly polarized Practical, not theoretical..

• SV-waves (Vertical component): Particle motion occurs in the vertical plane containing the ray path (up and down).
• SH-waves (Horizontal component): Particle motion is horizontal and perpendicular to the ray path (side to side).
• Key trait: The motion is a straight line. There is no rotation or orbital path; the particle simply oscillates back and forth along a single axis.

Rayleigh Wave Particle Motion

Rayleigh waves exhibit retrograde elliptical particle motion in the vertical plane (radial-vertical plane). As the wave crest passes, a particle at the surface moves in an ellipse:

1. Upward (vertical)
2. Backward (horizontal, opposite to propagation direction)
3. Downward (vertical)
4. Forward (horizontal, in the direction of propagation)

This motion is retrograde (counter-clockwise when viewing the wave moving left-to-right) at the surface. Crucially, the shape of this ellipse changes with depth. Think about it: at a specific depth (approximately one-fifth of the wavelength), the horizontal motion cancels out, leaving purely vertical motion. Deeper still, the ellipse becomes prograde (clockwise). This depth-dependent rotation is a unique fingerprint of Rayleigh waves absent in S-waves Turns out it matters..

Velocity and Arrival Times

Velocity is a practical differentiator used daily by seismologists to identify phases on a seismogram And that's really what it comes down to..

• S-wave Velocity ($V_s$): Determined by the formula $V_s = \sqrt{\mu / \rho}$, where $\mu$ is the shear modulus and $\rho$ is density. In the crust, $V_s$ typically ranges from 3.0 to 4.5 km/s. S-waves are the second major arrival on a seismogram (after P-waves), hence the name "Secondary waves."
• Rayleigh Wave Velocity ($V_r$): Rayleigh waves are dispersive (discussed below), but their phase velocity is always slightly lower than the S-wave velocity of the same near-surface material. Typically, $V_r \approx 0.92 V_s$ (for a Poisson solid). In the crust, this translates to roughly 2.5 to 3.5 km/s.

Because Rayleigh waves are slower, they arrive after the S-waves on a seismogram. On a typical local earthquake record, the sequence is: P-wave -> S-wave -> Surface waves (Love then Rayleigh). The time gap between the S-wave arrival and the Rayleigh wave arrival increases with distance from the epicenter because the velocity difference accumulates over the travel path.

Dispersion: The Defining Characteristic of Surface Waves

Dispersion—the dependence of wave velocity on frequency (or wavelength)—is the most profound physical difference between these two wave types in layered media.

S-Waves: Generally Non-Dispersive (in homogeneous layers)

In a uniform, horizontally layered half-space, body waves (P and S) are non-dispersive. A 1 Hz S-wave and a 10 Hz S-wave travel at the same velocity. They maintain their waveform shape as they propagate (ignoring attenuation and scattering). While S-waves can show apparent dispersion in complex structures (like waveguides or strong lateral heterogeneity), it is not an intrinsic property of the wave mode itself in simple media.

Rayleigh Waves: Intrinsically Dispersive

Rayleigh waves in a layered Earth are strongly dispersive. Different frequencies sample different depths:

• High frequencies (short wavelengths): Travel shallower, slower velocities (sampling low-velocity surface sediments/soil).
• Low frequencies (long wavelengths): Penetrate deeper, faster velocities (sampling higher-velocity bedrock).

This causes a single impulsive source to stretch out into a long "wave train" or "dispersive tail" on a seismogram. In practice, the low-frequency energy arrives first, followed progressively by higher frequencies. Day to day, this property is exploited in Surface Wave Analysis (MASW/ReMi) to derive 1D shear-wave velocity profiles ($V_s$ vs. On the flip side, depth) of the subsurface. S-waves do not provide this depth-sampling capability inherently; they require borehole receivers or complex inversion of reflection data to achieve similar resolution.

Amplitude Decay and Geometric Spreading

Energy conservation dictates how amplitude decreases with distance, and the geometry of the wavefront differs radically It's one of those things that adds up..

• S-Waves (Spherical Spreading): Energy radiates in 3D (spherical wavefront). Amplitude decays proportionally to $1/r$ (where $r$ is distance). Energy flux decays as $1/r^2$.
• Rayleigh Waves (Cylindrical Spreading): Energy is trapped near the surface, radiating in 2D (cylindrical wavefront). Amplitude decays proportionally to $1/\sqrt{r}$. Energy flux decays as $1/r$.

Consequence: Surface waves lose amplitude much more slowly with distance than body waves. At large epicentral distances (teleseismic), the surface waves are often the largest signals on the record, completely dominating the seismogram. This is why "long-period" surface waves are used to determine the magnitude of great earthquakes (Mw) — they carry the bulk of the radiated seismic energy at the surface Took long enough..

Depth Penetration and Sampling Volume

• S-Waves: Sample the entire volume along their ray path. A deep S-wave turning point in the mantle samples the deep Earth structure. They

Depth Penetration and Sampling Volume (continued)

• S‑Waves: Sample the entire volume along their ray path. A deep S‑wave turning point in the mantle samples the deep Earth structure, while a shallow S‑wave that only traverses the crust is sensitive primarily to near‑surface properties. In practice, the sensitivity of an S‑wave to a given layer is proportional to the length of the ray segment that lies within that layer. So naturally, a single S‑wave from a distant earthquake provides a relatively broad, path‑averaged constraint on shear‑wave velocity, but it does not isolate the velocity of any specific depth without the aid of many rays at different take‑off angles (as in global tomography).

• Rayleigh Waves: Because the particle motion is confined to the near‑surface half‑space, the energy of a Rayleigh wave decays exponentially with depth. The e‑folding depth is roughly one wavelength. Higher‑frequency components (short wavelengths) are therefore limited to the top few meters to tens of meters, whereas the lowest frequencies (periods of 20–100 s) can “feel” several kilometers of crust and even the upper mantle. This depth‑selective behavior makes Rayleigh waves an exceptionally efficient probe of the shallow subsurface, which is why they dominate the signal in most engineering‑seismic surveys and why they are the primary tool for ambient‑noise surface‑wave tomography.

Summary of Key Differences

Practical Implications for Field Work

1. Survey Design

   • When the goal is to obtain a high‑resolution shear‑wave profile of the upper 20–30 m, a MASMAS (Multi‑channel Analysis of Surface‑Wave) or ReMi acquisition is optimal. The dispersive nature of Rayleigh waves provides the necessary depth‑frequency trade‑off.
   • If the aim is to image deeper structures (tens to hundreds of meters), one must either lower the source frequency (e.g., use a large weight drop or vibroseis) to generate longer‑wavelength Rayleigh waves, or complement the surface‑wave data with S‑wave reflection or borehole S‑wave logs.

2. Data Processing

   • For Rayleigh waves, the first step is usually phase‑velocity extraction via frequency‑‑time analysis (FTAN) or multi‑taper methods, followed by inversion for a 1‑D (V_s(z)) model.
   • For S‑waves, processing focuses on arrival‑time picking and velocity‑analysis (e.g., semblance) to build a velocity model that can later be used for migration of reflection data.

3. Interpretation Caveats

   • Mode conversion (e.g., P→S, S→R) can introduce mixed‑mode arrivals that masquerade as either body‑ or surface‑wave energy. Careful polarization analysis or component rotation is required to isolate the pure Rayleigh component.
   • Attenuation (intrinsic Q) affects amplitude decay and, for Rayleigh waves, also modifies the apparent dispersion. In high‑attenuation soils the low‑frequency tail may be suppressed, biasing the inversion toward shallower velocities if not accounted for.

Concluding Remarks

Although both S‑waves and Rayleigh waves are shear‑dominated, they belong to fundamentally different families of seismic motion. Now, S‑waves are body waves that travel through the Earth’s interior with a constant phase velocity in a simple, horizontally layered half‑space. Their lack of intrinsic dispersion, spherical spreading, and deep‑penetrating ray paths make them indispensable for probing the bulk elastic structure of the planet, but they provide only coarse, path‑averaged information about any specific depth interval.

Rayleigh waves, by contrast, are surface‑guided modes whose phase velocity is a function of frequency because each frequency samples a different effective depth. Their cylindrical spreading ensures that they retain appreciable amplitude even at great distances, and their strong, predictable dispersion makes them the workhorse of near‑surface geophysical investigations. By measuring how the phase velocity varies with frequency, we can invert for a detailed shear‑wave velocity profile of the shallow subsurface—a capability that no single S‑wave can match without dense arrays of borehole receivers But it adds up..

In practice, the two wave types are complementary. A well‑designed seismic survey will exploit the high‑resolution depth sensitivity of Rayleigh waves to constrain the shallow velocity structure, while using S‑wave (and P‑wave) body‑wave data to anchor deeper sections of the model and to provide a global context for the surface‑wave inversion. Understanding the intrinsic dispersion of Rayleigh waves versus the non‑dispersive nature of S‑waves, together with their distinct geometric spreading laws, equips the geophysicist to interpret seismic records correctly, design efficient acquisition geometries, and ultimately build more accurate subsurface models.