Crustal Density Calculator

Crustal density is mass per unit volume of rock, and it can be obtained three ways with very different error characteristics. Direct measurement on a hand sample or core gives density to better than one percent but samples only a few cubic centimetres. Seismic velocity offers a proxy at crustal scale: Francis Birch showed that compressional velocity rises approximately linearly with density for rocks of similar mean atomic weight, and the linear fit used here, rho = 0.32 x Vp + 0.77 with Vp in km/s and rho in g/cm3, reproduces the trend for common crustal lithologies. The Nafe-Drake curve is the more accurate nonlinear alternative, particularly for porous sediments below about 4 km/s. Reference values by rock type provide the third route. Typical values anchor the interpretation: sandstone near 2.35 g/cm3, granite about 2.65, average continental crust 2.67 to 2.7, basalt near 2.95, gabbro about 3.0, and mantle peridotite near 3.3. Derived quantities follow from density plus velocity. Lithostatic pressure is rho x g x depth, giving roughly 27 MPa per kilometre in average crust, so about 1 GPa near the base of a 35 km continental section. Shear modulus is rho x Vs squared and bulk modulus is rho x (Vp squared minus four thirds Vs squared). Poisson ratio derived from the Vp/Vs ratio typically falls between 0.24 and 0.27 for felsic rock and 0.28 to 0.30 for mafic rock, with values above 0.30 suggesting partial melt, high pore pressure or serpentinization. The Airy isostatic thickness shown is a first-order scaling only.

Determining the density of Earth materials began as an attempt to weigh the planet itself. Nevil Maskelyne's 1774 Schiehallion experiment, analysed by Charles Hutton, used plumb line deflection beside a Scottish mountain to derive a mean Earth density around 4.5 g/cm3, and Henry Cavendish's torsion balance experiment of 1797 to 1798 refined it to about 5.45 g/cm3. Because surface rocks measured only 2.5 to 3.0 g/cm3, the discrepancy was immediate evidence that the interior must be far denser than the crust, which pointed toward a metallic core long before seismology could confirm it. The seismic route to density opened once the crust could be probed by wave velocities. Andrija Mohorovicic identified the crust-mantle boundary in 1909, and refraction profiling through the mid-twentieth century mapped crustal velocity structure across continents and oceans. John Nafe and Charles Drake of Lamont Geological Observatory compiled velocity-density pairs for marine sediments and rocks in the late 1950s, producing the empirical curve still cited under their names. Francis Birch of Harvard, working with high-pressure apparatus, published the velocity-density relations in 1960 and 1961 that became Birch's law and underpin the interpretation of seismic models in terms of composition. Nikolas Christensen and Walter Mooney synthesized several decades of laboratory and field results in their 1995 review of continental crustal velocity structure, which remains a standard reference for regional density models.