Theoretical Rayleigh and Love Waves from Explosions in Nonspherical Cavities and from Tectonic Release in Compressive Stress Fields

Abstract

Ben‐Menahem and Mikhailov (1995) developed a spherical mapping approximation to compute displacement fields due to explosions in nonspherical cavities embedded in elastic media. The explosion‐generated stress distribution was mapped onto the surface of an equivalent virtual spherical cavity. In this article, we use these techniques to analyze Rayleigh‐ and Love‐wave radiation patterns for a horizontal cylinder cavity, modeling an explosion in a tunnel for diameter‐to‐length ratios ranging from a line source (zero diameter) to that of a disk (zero length). The equivalent tectonic release is that created in a horizontal direction tensile stress field. With this orientation, the Love‐wave radiation pattern is identical to that of a vertical strike‐slip fault with a strike of 45° from the axis of symmetry. Assuming temporal step-function pressures and ignoring near-field nonlinear elasticity, shock waves, and reverberations in the air-filled cavity, we express the displacement fields for either explosion or tectonic release, in terms of a multipole expansion of spherical eigenvectors. This is done for both axisymmetric ellipsoidal and right cylindrical cavities. As in Ben‐Menahem and Mikhailov, at long wavelengths the dominant spherical harmonics are found to be, at most, second order. This is true even for extreme geometries such as the finite-length line source and the disk. For long-period surface waves, the first two terms suffice. At very long periods, the radiation field is the same as that due to the rapid formation of a spherical cavity in the presence of tensile stress, and differs by only a sign in case the initial stress is compressive instead. The two sources differ only in their respective second-order moment tensor time functions.