Pulse Propagation In Rocks

This discussion is confined to the first section of Professor Clark's paper entitled 'Elastic and Nonelastic Waves' and its application to wave propagation in rocks. Some published results by other investigators concerning measured decay of peak strain and variation of pulse duration with travel distance are cited, but the principal subject of this section is a detailed mathematical analysis of spherical (and, to a lesser extent, of plane) wave propagation in various homogeneous, isotropic media. The materials selected include an elastic substance, a Voigt and a 'modified' Voigt solid-the latter incorporating the assumption of a constant loss factor (defined here as the product of frequency and the ratio of the imaginary to the real part of the shear modulus)-and a solid friction model. While other possible representations of a solid continuum model are mentioned, corresponding solutions are not presented. The pulse inputs considered comprise exponential decay, a unit step, and steady- state sinusoidal excitation: the process of conversion from one solution to another in the operational plane is indicated. The basic problem relative to the analysis of wave propagation in rocks concerns the specification of the appropriate material behavior, since the equations of motion for a given geometry of the source and medium are well established. In principle, the required information can be deduced from two types of measurement: 1) field observations of underground explosions or seismic disturbances, and 2) laboratory tests on small samples of the pertinent rock. However, in practice both types of approaches are beset with difficulties and subject to valid criticism. Field observations must be carried out under relatively uncontrolled conditions, including, in general, a lack of knowledge of the precise arrangement of the medium, stratification, faulting. inhomogeneities, etc. Specimens investigated in the laboratory can not represent the environment found