Part I:
A matrix formulation is used to derive the pressure variation for acoustic gravity waves from an explosive source in an atmosphere modelled by a large number of isothermal layers. Comparison of theoretical and experimental barograms from large thermonuclear explosions leads to the following conclusions: (1) The major features on the barogram can be explained by the super-position of four modes, (2) Different portions of the vertical temperature structure of the atmosphere control the relative excitation of these modes, (3) A normalized point source is sufficient to model thermonuclear explosions, (4) The observed shift in dominance of certain frequencies with yield and altitude can be explained using the empirical scaling laws derived from the direct wave near the explosion.
Part II:
A matrix formulation is used to derive integral expressions for the time transformed displacement fields produced by simple sources at depth in a multilayered elastic isotropic halfspace. The integrals are evaluated for their residue contribution to obtain surface wave displacements in the frequency domain. The theory includes the effect of layering and source depth for the following: (1) Rayleigh waves from an explosive source, (2) Rayleigh waves from a vertical point source, (3) Rayleigh and Love waves from a vertical strike slip fault model. The latter source also includes the effect of fault dimensions and rupture velocity. The theory presented here is the ground work for the numerical computation of theoretical seismograms for use in a later paper in which a comparison will be made between observations and theory in both the time and frequency domain. A discussion is included on how these comparisons might be used in the frequency domain to estimate source depth.
