Earthquake Seismic Wave Propagation - 2D Map and Seismograms

Presets

Earthquake source

Magnitude M

Focal depth

Crust

P-wave speed Vp

Vp / Vs ratio

Playback speed

show S-P distance circles

Click the map to move the epicentre.

Live readouts

Graphs

Seismograms at the three stations (time from origin, s)

Travel-time curves: P and S arrival vs distance

Radiated energy vs magnitude (log scale, joules)

Numerical checks

running...

How to use

Press Replay: the quake at the epicentre sends out a fast P wave (orange ring, compressional) followed by a slower S wave (blue ring, shear). Each station records the arrivals on its seismogram. The gap between the S and P arrivals gives that station's distance; the three distance circles intersect at the epicentre. Click the map to move the epicentre, change the magnitude, depth and rock stiffness, and watch the arrival times, amplitudes and the circle fix respond.

The science

Body waves. In an elastic solid with shear modulus mu, bulk modulus K and density rho,

Vp = sqrt((K + 4 mu / 3) / rho), Vs = sqrt(mu / rho)

so P waves are always faster than S waves (Vp / Vs near 1.73 for a Poisson solid). A station at epicentral distance r from a source at depth h is at hypocentral distance R = sqrt(r^2 + h^2) and sees arrivals at

tP = R / Vp, tS = R / Vs, tS - tP = R (1/Vs - 1/Vp)

Inverting the S-P lag gives the distance, R = (tS - tP) Vp Vs / (Vp - Vs). Three or more distances fix the epicentre by trilateration.

Magnitude and energy. Local magnitude is logarithmic in peak amplitude, and the radiated energy follows the Gutenberg-Richter relation

log10 E = 1.5 M + 4.8 (E in joules)

so each unit of magnitude releases about 10^1.5 = 31.6 times more energy and the amplitude grows tenfold. Here the pulse amplitude is scaled as 10^(M - 5) / R, a geometric-spreading toy that is not calibrated to a real attenuation law.

Honest simplifications. The crust is uniform with straight rays: real Earth has layering that refracts and reflects waves, surface waves (Love and Rayleigh) that arrive after S and do most damage, and attenuation. The seismogram pulses are idealised wavelets, not a full elastic-wave solution. This is the 2D map-and-seismogram companion to the 3D seismic wave simulator and uses simple scalar speeds, so it has no structural damage content.