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Preface. It is a pleasure and a honour to be included in this issue commemorating the centenary of Robert Stoneley's birth. I was, I believe, the last of the small number of research students supervised by Stoneley, and it gives me great pleasure that most of my research has been, by chance, in a field he initiated-(azimuthal) seismic anisotropy. Bob Stoneley was one of the first seismologists to consider azimuthally anisotropic seismic waves (specifically surface waves) in cubic (Stoneley 1955) and orthorhombic symmetries (Stoneley 1963). Although, he considered these papers 'essentially as a development in the theory of elasticity', they were invaluable references to me when I first began to calculate surface waves in an anisotropic Earth. Bob would have been gently amused that a large part of the Earth is now recognized as having orthorhombic anisotropic symmetry. S U M M A R YThe shear-wave splitting observed along almost all shear-wave ray paths in the Earth's crust is interpreted as the effects of stress-aligned fluid-filled cracks, microcracks, and preferentially oriented pore space. Once away from the free surface, where open joints and fractures may lead to strong anisotropy of 10 per cent or greater, intact ostensibly unfractured crustal rock exhibits a limited range of shear-wave splitting from about 1.5 to 4.5 per cent differential shear-wave velocity anisotropy. Interpreting this velocity anisotropy as normalized crack densities, a factor of less than two in crack radius covers the range from the minimum 1.5 per cent anisotropy observed in intact rock to the 10 per cent observed in heavily cracked almost disaggregated near-surface rocks.This narrow range of crack dimensions and the pronounced effect on rock cohesion suggests that there is a state of fracture criticality at some level of anisotropy between 4.5 and 10 per cent marking the boundary between essentially intact, and heavily fractured rock. When the level of fracture criticality is exceeded, cracking is so severe that there is a breakdown in shear strength, the likelihood of progressive fracturing and the dispersal of pore fluids through enhanced permeability. The range of normalized crack dimensions below fracture criticality is so small in intact rock, that any modification to the crack geometry by even minor changes of conditions or minor deformation (particularly in the presence of high pore-fluid pressures) may change rock from being essentially intact (below fracture criticality) to heavily fractured (above fracture criticality). This recognition of the essential compliance of most crustal rocks, and its effect on shear-wave splitting, has implications for monitoring changes in any conditions affecting the rock mass. These include monitoring changes in reservoir evolution during hydrocarbon production and enhanced oil recovery, and in monitoring changes before and after earthquakes, amongst others.

A new technique is presented for modelling the elastic constants of cracked structures with application to systems with weak concentrations of parallel cracks, and of simple biplanar and triplanar cracks. The velocities and V,lVs ratios of these anisotropic structures are used to provide quantitative models for some earthquake precursors. These results indicate the great importance of crack geometry to the behaviour of precursors. The velocities of saturated cracks appear to favour the dilatancy-diffusion model of precursory phenomena. Synthetic seismograms are calculated for propagation through possible dilatancy zones. The seismograms show some characteristic features which may be useful for the investigation of earthquake dilatancy .

This paper studies the effect on the overall properties of a cracked solid of the existence of connections between otherwise isolated cracks and of small-scale porosity within the 'solid' material. The intention is to provide effective medium models for the calculation of elastic wave propagation with wavelengths greater than the dimensions of the cracks. The method follows that of earlier papers in which the overall elastic properties are directly related to parameters governing the microstructure, such as crack number density and the mean radius and spacing distance of the cracks. Expressions derived by the method of smoothing are evaluated to second order in the number density of cracks, thereby incorporating crack-crack interactions through both the strain field in the solid and the flow field of fluids in the pores.Flow of interstitial liquids tends to weaken the material; the limit of zero flow is equivalent to isolating the cracks and the limit of free flow is equivalent to dry (gasfilled) cracks. It also introduces additional attenuation. The inclusion of small-scale porosity gives a model of 'equant porosity' which is more closely constrained by the details of crack dynamics than earlier models.

Theoretical developments of Hudson demonstrate how to calculate the variations of velocity and attenuation of seismic waves propagating through solids containing aligned cracks. The analysis can handle a wide variety of crack configurations and crack geometries. Hudson associates the velocity variations with effective elastic constants. In this paper we associate the variation of attenuation with the imaginary parts of complex effective elastic constants. These complex elastic constants permit the simulation of wave propagation through two-phase materials by the calculation of wave propagation through homogeneous anisotropic solids.