Seismic Waves
P Waves & S Waves · Body & Surface Waves · Velocity Characteristics (28 Micro-Realms)
The Acoustic X-Ray of the Planet
When lithospheric stress snaps at the subsurface Hypocentre (Focus), elastic energy radiates in all directions—splitting into fast interior Body Waves (P & S) and high-amplitude, destructive Surface Waves (Love & Rayleigh) whose velocities depend on rock density and elastic moduli.
I. Seismic Energy Release & Wave Fundamentals
Elastic Rebound Theory
- H.F. Reid (1906)
- Fault friction locks rock
- Sudden slip releases energy
Focus vs Epicentre
- Focus: Subsurface origin
- Also called Hypocentre
- Epicentre: Nearest $90^\circ$ surface
3D Wavefront Radiation
- Omnidirectional elastic spheres
- Travels through lithosphere
- Energy decays with distance
Body vs Surface Waves
- Body: Through deep interior
- Surface: Guided along crust
- Two fundamental classes
Seismograph Trace
- 1st: P-wave micro-tremors
- 2nd: S-wave shear jolt
- Last: High-amplitude Surface
3-Station Triangulation
- P–S arrival time lag
- Gives distance radius
- 3 circles pinpoint Epicentre
Focal Depth Classes
- Shallow: $0\text{–}70\text{ km}$ (85%)
- Intermediate: $70\text{–}300\text{ km}$
- Deep Wadati-Benioff: $700\text{ km}$
II. Body Waves: Primary (P) & Secondary (S) Waves
Primary (P) Waves
- Fastest seismic waves ($6\text{–}13\text{ km/s}$)
- First to reach stations
- Lowest destructive amplitude
P-Wave Push-Pull Motion
- Longitudinal compressional wave
- Vibrates parallel to ray
- Compression & rarefaction
P-Wave Multi-Medium
- Analogous to sound waves
- Penetrates Solid, Liquid, Gas
- Slows down in liquids
Secondary (S) Waves
- Arrives after P-waves
- Speed $\sim 3.5\text{–}7.2\text{ km/s}$
- Stronger shaking than P
S-Wave Transverse Shear
- Vibrates perpendicular ($90^\circ$)
- Creates troughs & crests
- Analogous to light waves
S-Wave Solid Constraint
- Requires shear rigidity
- Travels ONLY in solids
- Blocked by outer core
Pg–Sg & Pn–Sn Phases
- Pg/Sg: Upper granitic crust
- P*/S*: Lower basaltic crust
- Pn/Sn: Uppermost mantle
III. Surface Waves: Love (L) & Rayleigh (R) Waves
Surface Wave Origin
- Body waves hit surface
- Interacts with crustal rocks
- Generates guided L-waves
Maximum Destructiveness
- Slowest velocity ($\sim 2\text{–}4.5\text{ km/s}$)
- Largest wave amplitude
- Longest period (Long waves)
Love (L / Q) Waves
- A.E.H. Love (1911)
- Pure horizontal side-to-side
- No vertical displacement
Foundation Shearing
- Fastest surface wave
- Wrenches building pilings
- Zero propagation in water
Rayleigh (R) Waves
- Lord Rayleigh (1885)
- Retrograde elliptical orbit
- Vertical + horizontal motion
Ground Roll Swell
- Rolls like ocean waves
- Slowest of all waves
- buckles highways & rails
Depth Attenuation
- Amplitude dies with depth
- Deep quakes = weak L-waves
- Shallow quakes = severe L-waves
IV. Velocity Characteristics & Elastic Moduli
Density-Velocity Rule
- Higher density = faster wave
- Rigidity rises faster than $\rho$
- Birch's Law in mantle
Bulk Modulus ($K$)
- Incompressibility resistance
- Present in solids & fluids
- Allows P-waves in core
Shear Modulus ($\mu$)
- Resistance to shape twist
- $\mu = 0$ in liquids/gases
- Kills S-waves in fluids
P-Wave Speed Formula
- Combines $K$ and $\mu$
- Always faster than $V_s$
- Drops when $\mu \to 0$
S-Wave Speed Formula
- Depends purely on $\mu$
- $V_p / V_s \approx \sqrt{3} \approx 1.73$
- Vanishes in molten rock
Curved Ray Refraction
- Density increases with depth
- Snell's Law bends rays
- Concave upward paths
Core Phase Codes
- c = Core reflection (PcP)
- K = Outer core P (PKP)
- I = Inner core P (PKIKP)
Core Distinctions
P-Waves (Primary): Fastest; arrive first; longitudinal (parallel push-pull like sound); create density differences (stretching & squeezing); travel through Solid, Liquid, and Gas. S-Waves (Secondary): Slower; arrive second; transverse (perpendicular $90^\circ$ up-down crests/troughs); travel ONLY through Solids.
2. Body Waves vs. Surface WavesBody Waves (P & S): High frequency, short wavelength, fast speed; travel through Earth's interior. Surface Waves (Love & Rayleigh): Low frequency, long wavelength, slowest speed, highest amplitude; last to arrive on seismograph; cause the maximum structural destruction.
3. Why P-Waves Slow Down in the Outer CoreIn liquids, the shear modulus ($\mu$) drops to zero. Looking at $V_p = \sqrt{(K + \frac{4}{3}\mu)/\rho}$, losing the $\frac{4}{3}\mu$ term causes P-wave velocity to drop abruptly from $\sim 13.7\text{ km/s}$ to $\sim 8.1\text{ km/s}$ at the Core-Mantle Boundary.
Seismic Wave Hierarchy
Velocity vs Destructive Amplitude