Those properties that serve to describe the ability of a material to withstand stress without undergoing permanent deformation. All solid substances, including rocks, follow Hooke's law, that is, the proportionality relation between strain (or deformation) and stress (or force per unit area). The stress-strain ratio in simple linear compression or expansion is Young's modulus of elasticity (E),
where F/A is the force per unit area or stress, and ΔL/L is the strain or elongation or shortening per unit length under the application of expansion or compression.
The stress-strain ratio under hydrostatic compression or expansion is the bulk modulus of elasticity (K),
where ΔV/V is the volume expansion or shrinkage per unit volume under the application of expansion or compression.
The stress-strain ratio in shearing, or application of a force, tangential to the surface displaced, is the rigidity or shear modulus of elasticity (µ).
where F/A is the shearing stress and ΔL/L is the shearing strain or deformation without change in bulk volume.
Poisson's ratio (s) is a measure of the geometric change of shape
where W stands for width. It is always comprised between 0 and 1/2, its theoretical value being 1/4 for elastic bodies. The above-mentioned properties are responsible for the propagation of sound or acoustic waves through rocks.
Two types of body waves are propagated through elastic media:
(a) longitudinal or compressional waves wherein the back and forth oscillations of particles are in the direction of propagation, their velocities being given by
where rb is bulk density of rock.
(b) Transverse or shear waves wherein the back and forth oscillations of particles are in a direction perpendicular to the direction of propagation, their velocities being given by
The longitudinal waves always arrive before the transverse waves, and to the present time, the former only have been used extensively in well logging. (From Pirson.)