The Zoeppritz equations are used to determine the energypartition in seismic waves reflected and refracted at the earth's core. First, the assumption is made that the core is fluid and hence does not transmit any shear waves. Then the four possible cases are treated; an incident longitudinal wave in the mantle against the core, an incident longitudinal wave in the core against the mantle, and an incident shear wave both of the SV type (particlesvibrating in the plane of incidence) and of the SH type(particles vibrating perpendicular to the plane of incidence) in the mantle against the core. The square roots of relative energy partitioned among the waves of the above cases are plotted against angle of incidence.
The horizontal and vertical components of the displacement produced at the surface of the earth by seismic waves reflected and refracted at the earth's core are calculated by means of the formula A = CTf √tanio/sinΔ dio/dΔ, which gives the amplitude of the incident wave. C is a constant whose value depends on the energy at the source, and is different for longitudinal and shear waves, T is the period, io the angle of incidence at a distance Δ from the source, and f is the square root of the relative energy calculated earlier. The values of A for a certaintype of wave are multiplied by the ratios u/A and w/A in order to obtain the horizontal and vertical components of surface displacement. u is the horizontal component and w the vertical. u and w are plotted against Δ.
Lastly the variation of u and w with Δ are determinedfor P, PP, S, and SS. Then, depending on whether the seismicwave reflected or refracted at the earth's core started out from the source as a longitudinal or a shear wave, the ratios of u and w of that wave to the u and w of the corresponding direct wave are calculated. This does away with the necessity of determining the value of C in the amplitude equation. However, for application of these results to seismograms the ratio of the periods must be introduced, as in the calculations the period of all waveswas assumed to be 1.00 second, and the magnification of the ground by the instrument must be considered.
