Crustal Thickness Calculator (H-k)

When a teleseismic P wave strikes the Moho from below, part of its energy converts to an S wave that travels the remaining crustal path more slowly and therefore arrives at the surface after the direct P. That delay, tPs, is the primary observable. Because the S leg and the P leg traverse the same crustal thickness at different vertical slownesses, the delay equals H multiplied by the difference of the vertical slownesses, giving H = tPs / (sqrt(1/Vs squared - p squared) - sqrt(1/Vp squared - p squared)), where p is the horizontal ray parameter conserved along the ray. Since Vs is obtained as Vp divided by the Vp/Vs ratio kappa, the thickness depends jointly on the assumed average crustal velocity and on kappa, and the two trade off strongly. Representative values are Vp near 6.3 km/s for average continental crust, kappa near 1.73 corresponding to a Poisson ratio of 0.25, and ray parameters of 0.04 to 0.08 s/km for epicentral distances between roughly 30 and 90 degrees. A tPs of about 4.5 s indicates a normal continental crust near 37 km, while the Tibetan Plateau exceeds 70 km and thinned rifted margins fall below 25 km. The crustal reverberations PpPs and PsPs+PpSs provide independent estimates that break part of the depth-velocity trade-off, which is the basis of H-kappa stacking. Limitations are real: a dipping or gradational Moho smears the conversion, sedimentary basins generate strong shallow reverberations that mask the Moho phase, and an error of 0.05 in kappa shifts H by several kilometres.

The boundary being measured was identified by Andrija Mohorovicic, director of the meteorological observatory in Zagreb, who analysed seismograms from the Kupa Valley earthquake of 8 October 1909 and found two distinct P arrivals whose travel-time curves crossed at about 200 km distance. He concluded that a sharp velocity increase existed at depth, and the discontinuity has carried his name since. Refraction shooting during the twentieth century mapped this surface but required controlled sources and dense arrays, which limited coverage on continents and made ocean and remote regions expensive to survey. Using distant earthquakes instead of explosions became possible once the source signature could be removed. Lev Vinnik in the Soviet Union described the isolation of converted phases beneath a station in 1977, and Charles Langston formalized the source-equalization deconvolution in a 1979 Journal of Geophysical Research paper on structure beneath Mount Rainier, dividing the radial component by the vertical to leave the local structural response. The technique spread rapidly with three-component digital broadband instruments and networks such as the Global Seismographic Network. Lupei Zhu and Hiroo Kanamori of Caltech introduced the H-kappa stacking method in 2000, summing receiver function amplitudes at the predicted times of the Ps, PpPs and PsPs+PpSs phases across a grid of thickness and velocity ratio, and portable deployments such as USArray later applied it to produce continent-wide Moho depth maps.