Study of the decay rate with epicentral distance of P-wave amplitudes from nuclear explosions in the distance range 1° to 98° has revealed that instead of the continuous amplitude curve of Gutenberg, the amplitudes are most appropriately represented by six discontinuous curves. Corresponding to these six amplitude decay curves, magnitude relations were worked out. The new magnitude relations yield consistent magnitudes for nuclear explosions as well as earthquakes independent of epicentral distance over the entire distance range of 1° to 98°. The magnitude values are however slightly shifted towards the higher side by 0.22 magnitude unit (at M = 4.5) as compared to those predicted by the Gutenberg-Richter method. Magnitudes are evaluated for Logan, Blanca and Salmon explosions using the new magnitude relations and they agree fairly well with the published magnitudes for these events determined by other workers using the Gutenberg-Richter method.
These amplitude decay curves when compared with the travel-time curves of Carder (1964) do show a reasonable correspondence between the starting points of amplitude curves and the distances where the deeply refracted phases from plausible velocity discontinuities in the mantle start appearing as first arrivals on the surface of the Earth.