An energy approach to seismic coupling analysis

Abstract

The explosion process is modeled by a step change in cavity pressure. The cavity is assumed to be spherical and embedded in an ideal elastic solid. This model represents a fully decoupled explosion in a cavity. It can also be used as an equivalent seismic‐wave source representing a tamped explosion. A decoupling cavity existence and operating region is defined in terms of cavity and overburden pressures and the rock yield strength. The upper limit for seismic coupling efficiency for an ideal monoatomic gas is given by Ew/Ex = 2Y/3μ, where Ew is the radiated seismic‐wave energy, Ex is the explosion yield, Y is the rock yield function, and μ is the shear modulus. This equation may be a good approximation for the seismic‐coupling efficiency of a tamped explosion, because it agrees well, perhaps fortuitously, with observations for tamped nuclear explosions in salt and granite. The seismic‐energy radiation from a spherical cavity in an elastic medium is given by Ew = 2πPχ, where P is a step change in cavity pressure and χ is the final value of the reduced displacement potential. This equation shows that the seismic‐coupling efficiencies of French nuclear explosions in Sahara granite may be about equal to those of U.S. shots in Nevada granite, even though the cavity radii, elastic radii, and reduced displacement potentials for these two sets of explosions (assuming equal yields) are quite different. The theoretical seismic‐energy spectra for the Nevada and the Sahara explosions are consistent with the measured spectrum for the 5‐kT Hardhat explosion and overlap to a significant degree. This overlap is centered in the 0.5‐ to 5‐Hz bandwidth and may partially explain why nuclear explosions in Nevada and Sahara granites appear to have the same magnitude‐yield relation. The possibility of regional variation of seismic‐signal attenuation in the upper mantle of the United States and the Sahara should also be investigated to complete the explanation of seismic coupling in Nevada and Sahara granite.

Inelastic processes in seismic wave generation by underground explosions

“…The scaling relation for these explosions in Algeria included the effect of rock strength as well as depth of burial (Michaud 1968). Computer calculations based on quasistatic rock strength measurements indicate that the relative absence (Algeria) or presence (Nevada) of water in preexisting fractures may be responsible for this difference in scaled cavity size (Rodean 1972). On the other hand, dynamic experiments with shock waves do not indicate any loss of shear strength because of the presence of water in Westerly granite (Larson and Anderson 1979b).…”

“…It can be shown (Rodean 1972) by means of Has. (8)- (16) that the cavity pressure change is limited to Contained in this table also means "tamped"; that is, the explosive assembly was in close proximity to the surrounding rock.…”

Calculations on seismic coupling of underground explosions in salt

“…Since the inductive displacement varies as 2 1/r , moving back to the original observation poirit introduce? an additional 2/3 factor of E , giving the final result that the displacement associated with the inductive field at a fixed observation point varies directly as E. •m 16^ ' (E " 7) The values Y…”