The inversion of seismological observations leads to the construction of models of the physical properties of Earth. The basic models take Earth to be spherically symmetric with properties, such as density, the Lamé coefficients of elasticity, and gravity, listed as functions of radius alone. These models form the numerical basis for the calculation of Earth's dynamics, including its short-period and long-period free oscillations, its response to tidal forcing and the dynamics of its rotation.

The Earth models

We list here the files cal8.dat, 1066a.dat, prem.dat and core11.dat for four wellknown Earth models, Cal8 (Bullen and Bolt, 1985, pp. 471–473), 1066A (Gilbert and Dziewonski, 1975), PREM (Dziewonski and Anderson, 1981) and Core11 (Widmer et al., 1988), respectively. The first line in each case gives the name of the Earth model in the format 10A8. The second line gives the number of Love numbers to be calculated in the format I10. The third line gives the number of model points and the initial number of integration steps for the inner core, outer core, mantle and crust in the format 8I10. Although a variable stepsize Runge– Kutta method is used in calculations, initial stepsizes are specified. The columns tabulate the radius, density, the Lamé coefficients of elasticity, and gravity in the format 1X,F10.1,F10.2,F10.1,F10.1,F10.1. Following tradition, radius is expressed in kilometres, density in grams per cubic centimetre, the Lamé coefficients in kilobars and gravity in centimetres per second per second. After they are read in, these Earth properties are scaled to SI units before proceeding to calculations.