Seismic Wave Velocity Calculator

Body wave speeds in an isotropic elastic solid follow from applying Newton second law to a deforming continuum, and they involve only the elastic moduli and the density. Compressional waves alternately squeeze and stretch the material, mobilising resistance to both volume change and shape change: Vp = sqrt((K + 4G/3) / rho). Shear waves distort without changing volume, so they sample the shear modulus alone: Vs = sqrt(G / rho). The immediate consequence is that fluids, having G = 0, transmit no shear wave at all, which is how the liquid outer core was identified. The ratio Vp/Vs depends only on Poisson ratio nu, through sqrt(2 x (1 - nu) / (1 - 2 x nu)); for the classical Poisson solid with nu = 0.25 the ratio is 1.732. Representative P wave speeds are about 1500 m/s in water, 2000 to 4500 m/s in sandstone, 3500 to 6500 m/s in limestone, 5500 to 6500 m/s in granite and basalt, and just over 8000 m/s in the uppermost mantle below the Mohorovicic discontinuity. Shear velocities are typically 55 to 65 percent of these. Density sits in the denominator, yet denser rocks are generally faster, because stiffness rises with density more steeply than mass does; the empirical Gardner relation of 1974 captures that trend for sedimentary rocks. The formulas assume a homogeneous, isotropic, non-dispersive medium, whereas shales can be 10 to 30 percent anisotropic and moduli measured with megahertz laboratory pulses exceed the low-frequency values that a seismic survey actually samples.

The existence of two body waves was a mathematical prediction long before it was an observation. Simeon Denis Poisson showed in the late 1820s that an elastic solid supports two distinct wave types travelling at different speeds, and George Gabriel Stokes clarified in 1849 that these correspond to dilatational and distortional motion. Lord Rayleigh added the surface wave that bears his name in 1885. Recognising any of them in real records had to wait for sensitive seismographs at the end of the century. Richard Dixon Oldham identified primary, secondary and surface phases on seismograms around 1900, and in 1906 argued from the shadow cast on the secondary arrivals that the Earth has a central core, the first use of velocity structure to see inside the planet. Andrija Mohorovicic found the crust-mantle velocity jump in 1909 while analysing a Croatian earthquake, Beno Gutenberg placed the core boundary near 2900 km depth in 1913, and Inge Lehmann inferred the solid inner core in 1936. Harold Jeffreys and Keith Bullen published global travel time tables in 1940 that stood for decades, and the Preliminary Reference Earth Model of Dziewonski and Anderson in 1981 tied velocity, density and attenuation into a single radial profile. Fritz Gassmann supplied the complementary rock physics link in 1951, relating saturated to dry moduli and explaining how pore fluid alters Vp while leaving Vs almost unchanged.