Seismic Wave Propagation Simulator

simulator intermediate ~10 min
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P-wave: 15.4s, S-wave: 26.6s — S-P lag: 11.2s at 100 km. Energy: 6.3×10¹³ J (Mw 6.0).

A magnitude 6.0 earthquake at 33 km depth produces P-waves arriving at 100 km distance in approximately 15.4 seconds, with S-waves following 11.2 seconds later.

Formula

V_P = sqrt((K + 4G/3) / ρ), V_S = sqrt(G / ρ)
log₁₀ E = 1.5 M_w + 4.8
p = sin(i) / v = constant (Snell's law for seismic rays)

Body Waves in Earth's Interior

Earthquakes generate two types of body waves that travel through Earth's interior. P-waves (compressional) travel fastest and arrive first, while S-waves (shear) follow. Their velocities depend on the elastic moduli and density of the material they traverse, providing a direct probe of Earth's internal composition and state.

Ray Paths and Snell's Law

Seismic rays bend continuously as they descend into Earth because velocity generally increases with depth due to increasing pressure. Snell's law governs this refraction: the ray parameter p = sin(i)/v remains constant along each ray. At sharp discontinuities (Moho, core-mantle boundary), rays reflect and refract, generating distinct arrivals on seismograms.

The Shadow Zone

Earth's liquid outer core creates one of geophysics' most dramatic observations: a P-wave shadow zone between 103° and 142° angular distance, and a complete S-wave shadow beyond 103°. S-waves cannot traverse liquids (zero shear modulus), while P-waves are strongly refracted at the core-mantle boundary. Weak arrivals in the P shadow revealed the solid inner core in 1936.

Seismic Energy and Magnitude

Earthquake magnitude scales quantify the energy released at the source. The moment magnitude (Mw) is derived from seismic moment M0 = µAD, where µ is rigidity, A is fault area, and D is average displacement. The logarithmic energy-magnitude relation means a magnitude 9 megathrust releases energy comparable to several hundred million tons of TNT, while a magnitude 3 is barely felt.

FAQ

What is the difference between P-waves and S-waves?

P-waves (primary) are compressional waves that oscillate parallel to propagation direction and travel through solids, liquids, and gases. S-waves (secondary) are shear waves that oscillate perpendicular to propagation and travel only through solids. P-waves are faster (Vp/Vs ~ 1.73 in typical rock), arriving first at seismometers.

What causes the seismic shadow zone?

The liquid outer core (2900-5150 km depth) refracts P-waves downward and blocks S-waves entirely. This creates a P-wave shadow zone between 103-142 degrees from the epicenter and a complete S-wave shadow beyond 103 degrees, providing key evidence for Earth's liquid outer core.

How is earthquake magnitude related to energy?

The Gutenberg-Richter energy-magnitude relation gives log(E) = 1.5*M + 4.8 in joules. Each unit increase in magnitude corresponds to about 31.6 times more energy. A magnitude 9.0 earthquake releases roughly 2 billion times more energy than a magnitude 3.0 event.

How do seismic waves reveal Earth's structure?

By analyzing travel times, reflections, and refractions of seismic waves from earthquakes recorded at stations worldwide, seismologists map velocity discontinuities that correspond to compositional and phase boundaries — the Moho (crust-mantle), the 410 and 660 km transitions, the core-mantle boundary, and the inner core boundary.

Sources

Embed

<iframe src="https://homo-deus.com/lab/geophysics/seismic-waves/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub