Seismic source functions for explosions in a non‐spherical cavity embedded in a scattering environment: application to the regional discrimination of nuclear explosions and earthquakes

A quantitative theory is advanced to account for the non‐isotropic linear source effects of underground nuclear explosions. Both the cavity's non‐sphericity and the scattering caused by source‐induced inhomogeneities are considered. Starting with the vector elastodynamic equation for inhomogencous media, the Born‐Rayleigh approximation is used for a regime in which the radiation's wavelength is large compared with both the cavity's size and the dimensions of the scatterers but small relative to the source observer distance. Applying the general vector Huygens representation theorem, the total field is expanded in a triple‐infinite multipole sum of vector spherical harmonics with summations representing the source, medium and field. When the dust settles over this intricate and complex analysis, there emerges an equivalent localized force system consisting of a singlet force plus a symmetric moment tensor, the elements of which depend on the scattering matrix of the source as well as on its non‐sphericity. The moment tensor, in turn, is reducible to an arbitrarily oriented compensated linear vector dipole and a double‐couple. Once the equivalent force system is obtained in closed form, the separate contributions of body waves and surface waves are routinely derived and expressed in terms of the source elements. The solution shows that, in addition to the standard explosion‐generated P waves and Rayicigh waves, shear displacements, in the form of SH, Lg and Love waves, are exhibited, the amplitudes of which strongly depend on the scattering coefficients and the source's non‐sphericity. The theory is applied to explain the observed Lg/Pn spectral ratios and it is suggested that these ratios be employed as a diagnostic tool in the discrimination of explosions from natural seismic events. Provided that an adequate inversion procedure is formulated, the spectral ratios can be used to obtain the explosion source parameters. Beyond the applicability of our analysis to the discrimination problem, the theory developed enables a formulation of a new class of problems in which complexities in source geometry and media physics can be treated simultaneously under a uniform mathematical formalism for a variety of boundary, source, and near‐source conditions.