Earth science

Seismic waves

P, S, and surface waves, travel-time curves, magnitude, and Earth’s interior sketch.

Basics

Body waves

P waves are compressional, fastest, and travel through solid, liquid, and gas. S waves are shear and do not propagate in liquids. That contrast is why we know the outer core is liquid. Speeds change with depth and rock, so waves refract and reflect. The P–S lag estimates epicentral distance.

Surface waves

Love and Rayleigh waves travel near the surface and often drive damage. Amplitude falls more slowly with distance than for body waves. Dispersion (speed by frequency) stretches the seismogram. Overlap with a building’s natural period raises resonance risk. Soft local geology amplifies shaking.

Magnitude and intensity

Magnitude tracks the quake’s energy or moment; intensity is shaking felt at a place. Richter is a historic local scale; moment magnitude M_w is near the modern standard. One magnitude unit is roughly thirty times the energy. Depth and ground still split damage at the same magnitude. Forecasts are probabilities, not certainties.

Earth’s interior

The Moho separates crust and mantle. An S-wave shadow across the outer core is evidence of liquid. The inner core is read as solid again. Tomography maps fast and slow patches to hint at mantle flow. High-pressure labs and meteorite chemistry back the models. This page is a classroom cross-section.

Formulas

P–S lag (rough)

Δt ≈ d (1/v_S − 1/v_P)

Epicentral distance d; speeds are regional averages.

Symbols

v_P P-wave speed
v_S S-wave speed

Moment magnitude

M_w = (2/3) log₁₀ M₀ − 상수

M₀ is seismic moment; the constant follows network convention.

Symbols

M₀ seismic moment

Energy vs magnitude (sketch)

E ∝ 10^{1.5 M}

Magnitude +1 ≈ ×30 energy.

Symbols

M magnitude

Key table

P speed (crust)	roughly 5–7 km/s; S is slower
Shadow zone	P weakens ~104°–140°; S has a wider mute
Moho	mean ~35 km under continents; shallower under oceans