Earth's Free Surface Research Articles

Calculation of explosion-produced craters-high-explosive sources

A simple two-dimensional model is developed of cratering physics for high-explosive sources in alluvium during the surface gas-acceleration phase of excavation. The required initial conditions for the model are knowledge of the earth's free-surface topography and motion at the time the surface gas acceleration begins (tG) and knowledge of the cavity pressure and volume. At tG the overburden material—that material between the cavity and the earth's free surface—is assumed to be homogeneous, incompressible fluid. At this time the cavity is approximated as follows: (a) the radius of the lower hemisphere is calculated by a one-dimensional hydrodynamic plastic-elastic model of the response of a geologic medium to an explosive source, and (b) the cavity configuration above the shot horizon is calculated from mass conservation of the overburden material and the calculated free-surface topography at the time tG. In the model, the upper cavity surface is subdivided into elemental surface areas, and mass zones are defined which subtend these elemental surface areas. Newton's second law of motion with a simple phenomenological frictional force (calibrated on the Scooter event) is applied to each mass element. The cavity gas is assumed to behave adiabatically. The physical laws, assumptions, and initial conditions cited above provide a basis for the numerical simulation of the cavity evolution, mound development, and formation of the lip through up-thrust during the surface gas-acceleration phase of excavation. With the development of a calibrated numerical simulation model of excavation processes during the surface gas-acceleration phase, it is appropriate to explore the use of the model for estimating the apparent crater radii and depth for 0.5-kt high-explosive sources at various emplacement depths. Assuming a reasonable angle of repose for alluvium (45°), we have prepared estimates of the apparent crater radii for scaled depth of burst from about 10 to 65 m/kt1/3.4. These estimated crater radii compare very favorably with the observed (scaled) crater radii for high explosives in alluvium. The apparent (scaled) crater depths, for certain types of craters, are also calculated. Perhaps the most significant contribution of the study is the development of a physical model for calculating the time history of the mound, the lip formation, and the cavity geometry during the surface gas-acceleration phase of cratering.

On the determination of the polarization angle of the S wave

Abstract This study is concerned with determining the minimum epicentral distance for which it is permissible to obtain the value of the polarization angle of the S wave by measuring the angle between the great circle path at the station and the direction of the horizontal component of the S wave particle motion obtained from the seismograms. This critical distance can be determined by the fact that at smaller distances the particle motion of the earth's surface due to the incidence of S will be nonlinear (the SH and the horizontal and vertical components of SV will be out of phase with respect to one another) while at larger distances the particle motion will be linear. An analysis of the S motion recorded by the Galitzin-Wilip seismographs at Florissant indicates that the critical distance is 42 degrees. The periods of these S waves are of the order of 10 second. The analysis also shows that the effective P wave velocity of teleseismic waves at the earth's free surface is 7.74 km/sec, and the effective value of Poisson's ratio and the effective S wave velocity at the earth's surface are 0.25 and 4.46 km/sec, respectively. By effective values are meant the values of the velocities and Poisson's ratio that govern the angle of incidence of the waves at the earth's surface.