Seismology — Earthquakes, Seismic Waves, Magnitude & Intensity — Earthquake Engineering Notes

Last reviewed 16 Sept 2026 · 9 min read

Structure of the earth

Layer	Features
Crust	Thin outer rigid layer — continental (thicker, granitic, roughly 30–70 km) and oceanic (thinner, basaltic, roughly 5–10 km)
Mantle	Up to about 2900 km depth; upper mantle includes the rigid lithosphere (with crust) and the weak, plastic asthenosphere
Outer core	Liquid iron–nickel — S-waves cannot pass
Inner core	Solid iron–nickel

The Mohorovičić discontinuity (Moho) separates crust and mantle; the Gutenberg discontinuity separates mantle and core.

Causes of earthquakes

Plate tectonics

The lithosphere is divided into large tectonic plates moving a few cm per year over the asthenosphere. Most earthquakes occur at plate boundaries:

Boundary	Motion	Examples
Convergent	Plates move towards each other — subduction or continental collision	Himalaya (Indian and Eurasian plates), Andaman–Sumatra subduction
Divergent	Plates move apart	Mid-ocean ridges
Transform	Plates slide past each other	San Andreas Fault

Intraplate earthquakes occur within plates on old faults (e.g. Latur 1993, Bhuj 2001 in the stable continental region of India).

Elastic rebound theory

Proposed by H. F. Reid after the 1906 San Francisco earthquake: rocks on either side of a fault accumulate elastic strain due to slow tectonic movement; when strain exceeds the strength, sudden slip occurs and the rocks rebound to an unstrained position, releasing energy as seismic waves.

Other causes

Volcanic earthquakes.
Collapse of underground cavities (mines, caves).
Reservoir-induced seismicity — filling of large reservoirs (e.g. Koyna, 1967).
Explosions (nuclear tests), fluid injection.

Faults

Normal fault — hanging wall moves down relative to the footwall; due to tension.
Reverse (thrust) fault — hanging wall moves up; due to compression (thrust if low dip).
Strike-slip fault — horizontal movement along strike (left-lateral or right-lateral).
Oblique-slip — combination.

(See Geological Structures in Engineering Geology.)

Earthquake terminology

Term	Meaning
Focus (hypocentre)	Point inside the earth where rupture starts
Epicentre	Point on the surface vertically above the focus
Focal depth	Distance from epicentre to focus
Epicentral distance	Distance from epicentre to the observation point
Hypocentral distance	Distance from focus to the observation point
Foreshocks / main shock / aftershocks	Smaller shocks before, the largest shock, smaller shocks after

By focal depth: shallow (0–70 km) — most damaging; intermediate (70–300 km); deep (300–700 km).

Seismic waves

Wave	Type	Particle motion	Speed / features
P-wave (primary)	Body wave	Compression–dilatation along the direction of travel	Fastest; travels through solids, liquids and gases; arrives first
S-wave (secondary)	Body wave	Transverse (shear) — perpendicular to travel	Slower (about 0.6 times P-wave speed in rock); cannot travel through liquids; larger amplitude, more damaging than P
Love wave	Surface wave	Horizontal transverse motion	Faster than Rayleigh waves; damaging to foundations
Rayleigh wave	Surface wave	Elliptical, retrograde motion in the vertical plane (like ocean waves)	Slowest; long duration; felt as rolling

Order of arrival: P → S → Love → Rayleigh.
Surface waves decay more slowly with distance and dominate at large distances.
The absence of S-waves in the shadow zone revealed the liquid outer core.

FormulaLocating an earthquake (S–P time)

d = \frac{t _{S - P} V _{p} V _{s}}{V _{p} - V _{s}}

$t_{S - P}$ = S minus P arrival time. For typical crustal speeds ( $V_{p} \approx 6$ km/s, $V_{s} \approx 3.5$ km/s), $d \approx 8.4 t_{S - P}$ km (a common rule of thumb is about 8 km per second of S–P time).

With distances from three stations, the epicentre is located by triangulation (intersection of circles).

Recording instruments

Seismograph — records ground motion (seismogram); seismometer is the sensor.
Strong-motion accelerograph — records ground acceleration during strong shaking near the source — used by engineers.
Peak ground acceleration (PGA) — maximum absolute acceleration, expressed as a fraction of g; also peak ground velocity and displacement, duration and frequency content matter.

Magnitude

Magnitude is a measure of the size (energy released) of an earthquake at the source — one value for an earthquake.

Scale	Basis
Local (Richter) magnitude $M_{L}$	Maximum trace amplitude on a Wood–Anderson seismograph at 100 km epicentral distance (Richter, 1935): $M_{L} = lo g_{10} A - lo g_{10} A_{0}$
Body wave magnitude $m_{b}$	Amplitude of P-waves (deep/distant events)
Surface wave magnitude $M_{s}$	Amplitude of surface waves (shallow distant events)
Moment magnitude $M_{w}$	Based on seismic moment — does not saturate for very large earthquakes; preferred today

FormulaMoment and energy

Seismic moment $M_{0} = μ A D$ ( $μ$ = rigidity of rock, $A$ = rupture area, $D$ = average slip)

Moment magnitude $M_{w} = \frac{2}{3} lo g_{10} M_{0} - 6.07$ ( $M_{0}$ in N·m)

Energy (Gutenberg–Richter): $lo g_{10} E = 1.5 M + 4.8$ ( $E$ in joules)

One unit increase in magnitude → 10 times the amplitude and about 31.6 (≈ 32) times the energy.
Two units → 100 times amplitude and 1000 times energy.

Magnitude scales are open-ended (logarithmic), not limited to 10; older scales saturate for great earthquakes.

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