The Theory of Stress Wave Radiation from Explosions in Prestressed Media

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 particularly, 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

The Effect of Anelasticity on Periods of the Earth's Free Oscillations (Toroidal Modes)

It is known that the anelastic properties of the Earth characterized by a ‘Q’ structure will affect the periods of free oscillation. It is generally considered that the effect is negligible compared to the other perturbing effects due to rotation, ellipticity, and lateral inhomogeneities. Nevertheless, it is of some interest to investigate the precise magnitude of this effect for the observed free oscillation modes since it could provide us with another constraint in the determination of the Q structure of the Earth. An application of perturbation theory provides us with a good estimate of the magnitude of the changes in the periods of an elastic model due to inclusion of anelastic effects. Calculations based on currently accepted mean elastic and anelastic models for the Earth show that the shift in period due to anelasticity is at most 0·023 per cent for the toroidal modes from _0T_2 to _0T_(99), the maximum occurring near _0T_(60). For more extreme Q models, which may be locally applicable, period shifts of the order 0·1 per cent occur, with the maximum again near _0T_(60), corresponding to a period of approximately 150 s. Observational accuracy for the toroidal oscillations is around 0·1 per cent so that anelastic shifts in toroidal oscillation periods are at the present limit of observational accuracy. Viewed in terms of propagating surface waves, the dispersion due to anelasticity results in at most 0·005-0·01 km s^(−1) variations in the phase and group velocities. Such shifts are within the observational resolution of surface dispersion measurements using narrow band filtering techniques. Compared to other perturbing effects, anelasticity is significant for the toroidal oscillation only in the 50- to 300-s period range. In this range, lateral variations in structure generally cause larger perturbations. However, when viewed in terms of propagating surface waves in selected homogeneous regions, anelasticity becomes the dominating effect. Further, the frequency shift due to anelasticity is scaled by (1/Q)^2, so that the anelastic effect can be well within observational accuracy and comparable to any perturbing effect for more extreme, yet acceptable, Q models. In particular, when applied to surface waves propagating across a tectonic region with a strong low velocity zone in the upper mantle, the anelasticity induced dispersion on frequency shift can be significant and measurable. In such cases a joint inversion of elastic and anelastic properties is appropriate

Transient and residual strains from large underground explosions

Tectonic strain readjustments associated with large underground explosions have been observed at the Nevada Test Site. The BENHAM event of December 19, 1968 produced a peak quasi-static radial strain of 1.2 × 10^(−7) at a distance of 29 km. This strain transient was followed by an exponential return to the initial state with a time constant of 13 minutes, and is interpreted as the direct elastic response of the medium to a time varying pressure in the BENHAM cavity. An upper bound on the tectonic strain release was determined to be 0.7 × 10^(−8). Using these measurements it is estimated that the permanent and quasi-static strains associated with this explosion could significantly effect local earthquake occurrences out to distances of about 15 km. The size distribution of aftershocks of this explosion resembles that seen in model experiments of brittle fracture, in which the distribution is controlled by the dimensions of inhomogeneities in the medium

Elastodynamic source theory

The mathematical formulation and evaluation of the radiation field for general elastodynamic sources is given and applications of the theory to the description of source fields of geophysical interest are treated. The study was primarily undertaken to provide a theoretical basis for estimating the properties of the tectonic stress field and parameters of rupture phenomenon in the earth through observations of the radiation field from earthquakes and other tectonic sources. Thus the description of the tectonic source is particularly emphasized, both as to its physical origins and with respect to the radiation field to be expected from it. The mathematical description of the tectonic source field is achieved in terms of an elastic relaxation theory of radiation which corresponds to a generalized initial value problem involving the initial prestress field. As a consequence, the radiation field is obtained in terms of the rupture expansion rate (velocity of rupture), the rupture dimensions and orientation and the magnitude and orientation of the initial stress field. Inertial conditions are inherent in the relaxation theory so that the time dependence of the field is automatically specified. Careful attention is given to causality relationships so that the resulting field expressions contain the complicated space-time relationships associated with a tectonic source field. Energy and equilibrium relations are considered and expressions are obtained for the estimated energy release and the final static field in terms of the source parameters. Detailed properties of the radiation field are given in the form of source field amplitude and phase spectra. Spatial radiation patterns are obtained showing the direction properties as functions of frequency, prestress and other source parameters. Similar results are given for shock induced rupture under prestress conditions, along with estimates of tectonic energy release. It is concluded that the theoretical predictions for the properties of the radiation field from a spontaneous rupture source are in general agreement with the actual observations of the field from such a source, but that accurate estimates of the prestress and rupture parameters require a more complete coverage and analysis of the field than is usually the case. It is concluded from a preliminary analysis of the Ranier nuclear explosion that tectonic energy release did occur and that the anomalous radiation observed would correspond to a prestress shear field of the order of 20 bars. The most likely mechanism of rupture at depth in the earth is considered to be unstable creep phenomenon resulting in phase change (melting) and the rupture source models adopted are not inconsistent with this hypothesis

Earthquakes and Nuclear Detonations

The report by Emiliani et al. (1) asserts some statistical results which would be important if well substantiated. To the undersigned, their evidence appears inadequate. Since it is likely that the conclusions, if unchallenged, will be accepted as authoritative, and misapplied by readers not well versed in the subject, critical remarks are offered