We analyze the influence of cavity shape on far-field seismic-wave radiation from small explosion sources in isotropic and transversely isotropic media using the indirect boundary-element method (BEM). The analysis utilizes two possible mathematical models for the pressure fields generated by the explosion in the acoustic medium inside the cavity. One simple model for the source is a volume injection (explosion) point source inside the cavity, which generates a pressure field that arrives approximately instantaneously at each point on the cavity wall. The amplitude of the field decays at a rate inversely proportional to propagation distance. We use this model to compare results with finite-difference solutions, and the test confirms the accuracy of the BEM implementation. Strong compressional and shear signals propagate into the far-field from the source cavity, and the compressional-wave amplitude depends strongly on direction of propagation. The behavior is similar at frequencies up to 200 Hz, including those typical of regional seismic-wave propagation (1 to 10 Hz).
A second model of the source, one that has been applied in previous analytical and numerical work, is to assume that the explosion will instantaneously and uniformly pressurize the source cavity. This approach yields a radiation pattern that is very different from the point source model. The compressional-wave radiation patterns have a large variation in signal strength and very strong shear waves when frequencies up to 200 Hz are included, but seismograms computed for frequency ranges of interest in regional wave propagation (around 1 Hz) have a nearly isotropic compressional-wave radiation pattern and a much smaller shear wave. This shear wave is largest for long, tunnel-like cavities or short, disklike cavities. When the cavity is located in a transversely isotropic medium, quasi-shear waves are generated, but, for the media we consider, their magnitude decreases for long, tunnel-like cavities and is larger for more equidimensional cavities. These somewhat counterintuitive results show that anisotropy can actually cause a radiation pattern to appear more isotropic than the corresponding wave fields in an isotropic medium.