The Theory of Stress Wave Radiation from Explosions in Prestressed Media

Abstract

Stress wave radiation from underground explosions has been observed to contain an anomalous shear wave contribution which is most likely of tectonic origin. In this paper the theoretical radiation field to be expected from an explosion in a prestressed medium is given under the assumption that no secondary low symmetry faulting on a large scale occurs and that the total tectonic component of the field is due to stress relaxation around the roughly spherical fracture zone created by the explosive shock wave. Evidence for the occurrence of this simple kind of tectonic source is considered, and it is concluded that this model is appropriate in many, if not most, instances involving underground explosions. Expressions for the spectrum of the radiation field and its spatial radiation pattern are given in terms of multipole expansions for the components of the rotation potential and the dilatation potential. Several possible rupture formation models are treated. All models show that the tectonic radiation is of simple quadrupole form, as has been observed. The energy radiated due to stress relaxation is considered in detail, and it is also shown that, in terms of the energy released, a dislocation source can be used as an equivalent for the stress relaxation effects.The theoretical energy partition between compressional and shear waves for the tectonic field is in the ratio of (approximately) 1 to 10, so that tectonic stress release does not affect the direct compressional body wave particulariy, but gives rise to totally anomalous SH polarized waves (e.g. Love waves) and affects Rayleigh type surface waves significantly, as is also observed. The theory can be applied to obtain estimates of source dimensions and the orientation and magnitude of the initial prestress field in the region of the explosion. In addition, application of this particular form of the general tectonic source theory to deep earthquakes and volcanic earthquakes also appears to be reasonable in view of the probable high symmetry of the failure or phase transition regions for such events.

Theoretical Rayleigh and Love waves from an explosion in prestressed source regions

“…which is the same result obtained from the approximate solutions to this problem given by Randall (1966) and Archambeau (1972) (Ald and Tsai, 1972;Randall, 1973a, b;Harkrider, 1976;Minster and Suteau, 1977;Minster, 1979). Also,…”

Very High Performance Organic Photonic Devices

“…Now, since the source corner frequency in the Mueller/Murphy P wave model is proportional to the compressional wave velocity divided by the elastic radius, it follows from the comparisons shown in Figure 18 that the S wave sources for these explosions must have characteristic lengths comparable to those of the corresponding P wave sources. One physical mechanism for S wave generation that would be consistent with this inference is the tectonic model proposed by Archambeau (1972) and Stevens (1980), in which an explosion in a prestressed medium causes a stress release in the nonlinear zone surrounding the explosion in which the medium is crushed and cracked by the outgoing compressional shock wave out to a range approximately equal to the elastic radius characteristic of the P wave source. If such a mechanism is in fact responsible for S wave generation by explosions, then it would be expected that the observed S/P ratios would depend on the strength of the individual explosion-induced tectonic release in some systematic fashion.…”

Isotropic and Nonisotropic Components of Earthquakes and Nuclear Explosions on the Lop Nor Test Site, China

“…There appears to be general agreement that the long-period part of the nonisotropic radiation is caused by tectonic release due to existing tectonic stresses in the source region (MUELLER and MURPHY, 1971;ARCHAMBEAU, 1972;MASSE, 1981;WALLACE et al, 1985;DAY and STEVENS, 1986;STEVENS, 1986;DAY et al, 1987;PATTON, 1991;STEVENS et al, 1991;HARKRIDER et al, 1994;EKSTRoÈ M and RICHARDS, 1994;LI et al, 1995).…”