Stuart Crampin

A review of wave motion in anisotropic and cracked elastic-media

Abstract Recent developments in the theory and calculation of wave propagation in anisotropic media have been published in the geophysical literature and refer specifically to seismological applications. Anisotropic phenomena are comparatively common, and it is the intention of this review to present these developments to a wider audience. Few of the results are new, but the opportunity is taken to tidy up a few loose ends, and present consistent theoretical formulations for the numerical solution of a number of propagation problems. Such numerical experiments have played a large part in our increasing understanding of wave motion in anisotropic media. It now appears that the solution of most problems in anisotropic propagation can be formulated, if the corresponding solution exists for isotropic propagation, and may be solved at the cost of considerably more numerical computation. There are two significant results from these developments: the recognition of the importance of body- and surface-wave polarizations in diagnosing and estimating anisotropy; and the recognition that many two-phase materials, particularly cracked solids, can be modelled by anisotropic elastic-constants. This last result opens up a new class of materials to wave-motion analysis, and has applications in a variety of different fields.

Evaluation of anisotropy by shear‐wave splitting

The polarizations of three‐component shear wavetrains carry unique information about the internal structure of the rock through which they pass: specifically, commonly observed shear‐wave splitting may contain information about the orientation of crack distributions. This information cannot usually be recovered from shear waves recorded at the free surface because of interference with the interaction of the shear wave with the surface, even for nearly vertical incidence. However, shear‐wave splitting in synthetic three‐component vertical seismic profiles, in some cases, may be interpreted directly in terms of the direction of strike of vertical cracks. Because the human eye is not skilled at identifying the phase relationships between three‐component seismograms played out conventionally as parallel time‐series, the polarizations are displayed in orthogonal sections of the particle displacements to facilitate recognition and evaluation of the shear‐wave splitting. Estimating the orientations of cracks, an...

Calculable fluid–rock interactions

This paper introduces a model of rock deformation (anisotropic poro-elasticity or APE), where the response of fluid-saturated rock to changing conditions, prior to fracturing, can be calculated. The driving mechanism for deformation is fluid migration along pressure gradients between neighbouring intergranular microcracks and pores at different orientations to the stress field. The parameters that control changes to microcrack geometry also control the splitting (birefringence) of seismic shear-waves, so that changes in deformation can be directly monitored by analysing the shear-wave splitting which is observed in almost all rocks. Analysis of shear-wave splitting in the Earths crust and APE-modelling show that distributions of, mostly intergranular, cracks in the crust are always geometrically close to fracturing with the implication that shear-wave splitting is sensitive to comparatively minor changes of stress and minor changes of in situ conditions. This has important implications for the state of criticality of the rockmass and, as a consequence, changes in shear-wave splitting have been observed before larger earthquakes on those few occasions when suitable source–receiver geometry coincides with appropriate seismic activity. APE also has implications for monitoring changing conditions in reservoirs during hydrocarbon recovery.

Neotectonics of the Marmara Sea region of Turkey

Seismological investigations in Western Anatolia, NW Turkey have identified linear patterns of earthquake epicentres outlining a wedge-shaped block in the area of the Marmara Sea. This block shows different seismic characteristics from the rest of Western Anatolia and appears to act as a separate tectonic unit. Earthquake fault-plane mechanisms show that the Marmara block is being rotated and sheared in order to accommodate the right-lateral motion of the north Anatolian Fault and the extensional tectonics of the southwestern Anatolia. Investigations of the behaviour of seismic shear-waves suggest that neotectonic stress aligns water-filled microcracks throughout the upper (brittle) 10–20 km of the crust and that in situ stress directions can be monitored by analysis of shear waves recorded on three-component instuments.

Estimating the internal structure of reservoirs with shear‐wave VSPs

In the past 10 years, vertical seismic profiles (VSPs) have played an increasingly important role in identifying and delineating in situ layers. Such VSPs have usually recorded P-wave data. Three‐component shear wave trains carry three or four times more information about the source and structure of the rocks along the raypath than the equivalent P-wave train so, in principle, shear‐wave VSPs should be a particularly valuable technique for examining in situ layers.

Microcracks in the Earth's crust

The presence or absence of cracks within in situ crustal rocks is open to wide misunderstandings because of the inaccessibility of the material and the difficulty of reproducing in situ conditions in the laboratory. There is now evidence from a wide range of results that most crustal rocks are pervaded by aligned liquid-filled microcracks, where the liquid is usually water but may be oil in hydrocarbon reservoirs. The recognition that there are aligned liquid-filled microcracks deep within the crust ties together a number of previously contradictory phenomena. Liquid-filled cracks in the Earths crust, although generally recognised as being present (Brace 1972, 1980), are little understood and the implications of their behaviour have not been explored. This is partly because it is impossible to reproduce in laboratory conditions more than a few of the large range of independent phenomena controlling the existence and behaviour of cracks in rock in situ. The liquid in these cracks is usually a water solution but may be oil in hydrocarbon reservoirs. The other major source of misunderstandings about cracks in the crust is that the principal technique for examining the properties of rocks at depth in the crust has been the analysis of travel times of seismic bodywaves, and reflection and refraction experiments by the exploration industry yield consistent structural interpretations without any need to assume the existence of widespread cracking. We now recognise that this is because almost all seismic experiments in the past have used P-waves, and P-wave travel-times are very little affected by liquid-filled cracks with low aspect-ratios. In contrast, shear-wave splitting (shear-wave birefringence) is very sensitive to distributions of aligned cracks (Crampin 1978). Recent observations of shear-waves (Crampin et al. 1980; Crampin 1985a) suggest that parallel, vertical, water-filled micro cracks pervade much of the brittle, upper 10-20 km of the crust. We call such distributions of aligned fluid-filled cracks extensive dilatancy anisotropy (EDA) (Crampin, Evans and Atkinson 1984). EDA is a unifying concept that allows a variety of phenomena from geology, geophysics and the rock-mechanics laboratory to be correlated for the first time. The existence of such cracks has wide implications for all deformatory processes in the crust, and the ability to monitor crack geometry by shear-wave propagation has applications to many currently important activities ranging from determining preferred directions of flow in hydrocarbon reservoirs to earthquake prediction.

A four-year study of shear-wave splitting in Iceland: 2. Temporal changes before earthquakes and volcanic eruptions

Abstract This chapter reports temporal variations in the time-delays between split shear-waves before both earthquakes and volcanic eruptions in Iceland. The hypothesis is that during a build-up of stress, crack distributions in a large volume surrounding the immediate source zone are modified until the level of cracking reaches fracture criticality, when shear strength is lost, rocks fracture, and earthquakes, or some types of eruptions occur. In one two-year period, when volcanic and magmatic activity appeared to be low, changes in shear-wave splitting in SW Iceland were observed routinely before earthquakes with magnitudes between M3.5 and M5.1. Assuming a linear relationship between earthquake magnitude and the rate of increasing crack aspect-ratio in this comparatively narrow amplitude range, the time and magnitude of a M5 earthquake was successfully stress-forecast. These results confirm a new understanding of pre-fracturing deformation of in situ rock that has implications over a wide range of situations where the crust undergoes changes at low levels of deformation below those at which rocks fracture. Potential applications of this new understanding include monitoring hydrocarbon production, as well as stress-forecasting earthquakes and some volcanic eruptions.

Diffraction of seismic waves by cracks with application to hydraulic fracturing

The authors describe a method of modeling seismic waves interacting with single liquid-filled large cracks based on the Kirchhoff approximation and then apply it to field data in an attempt to estimate the size of a hydraulic fracture. They first present the theory of diffraction of seismic waves by fractures using a Green`s function representation and then compute the scattered radiation patterns and synthetic seismograms for fractures with elliptical and rectangular shapes of various dimensions. It is shown that the characteristics of the diffracted wavefield from single cracks are sensitive to both crack size and crack shape. Finally, they compare synthetic waveforms to observed waveforms recorded during a hydraulic fracturing experiment and are able to predict successfully the size of a hydraulically induced fracture (length and height). In contrast to previously published work based on the Born approximation, the authors model both phases and amplitudes of observed diffracted waves. The modeling has resulted in an estimation of a crack length 1.1 to 1.5 times larger than previously predicted, whereas the height remains essentially the same as that derived using other techniques. This example demonstrates that it is possible to estimate fracture dimensions by analyzing diffracted waves.

Shear-wave splitting above small earthquakes in the Kinki district of Japan

Abstract We have identified shear-wave splitting, diagnostic of the effective anisotropy induced by aligned microcracks, in the wavetrains of micro-earthquakes at four stations of the Abuyama network in the Kinki District of Japan. We find that the directions of polarization of the faster split shear-waves are nearly parallel for all azimuths of arrival, and for all angles of incidence less than the critical angle at three of the four stations. These directions of polarization are consistent with the axis of maximum compression obtained from earthquake fault-plane mechanisms, and also agree with the directions of the general trends of geological structures which represent the orientations of the cleavage or lamination. These results suggest that crack-induced anisotropy is present in the brittle upper crust beneath Japan, as has been found elsewhere, but we could not distinguish whether this reflects the distributions of cracks induced by the present stress field, or results from the general trends of surface geology. Although the delay times between faster and slower shear waves are difficult to estimate reliably, because of their high sensitivity to internal interfaces, the delay times can be interpreted as the result of a distribution of parallel vertical cracks with a crack density of about 0.04. The consistency or lack of consistency of the directions of the shear-wave polarizations at the four stations demonstrates the effects of surface topography and near surface layering on the shear-wave polarizations.

A four-year study of shear-wave splitting in Iceland: 1. Background and preliminary analysis

Abstract A four-year study of seismic shear-wave splitting in Iceland was designed to seek temporal variations before earthquakes. Shear-wave splitting is observed routinely in Iceland whenever shear-waves arrive within the shear-wave window of seismic stations, and whenever adequate data are available, temporal and spatial variations in shear-wave splitting are observed before both earthquakes and volcanic eruptions. Shear-wave splitting is caused principally by the stress-aligned fluid-saturated microcracks and pore throats in almost all in situ rocks. Fluid-saturated microcracks are the most compliant elements of the rock mass, and changes in splitting can be directly interpreted and modelled as the effects of changing stress on the microcrack geometry in the rock mass often at considerable distances from the immediate earthquake source zone. Such changes were found and are reported in Part 2 of this study. This chapter presents the background, preliminary observations, and analysis of shear-wave splitting in Iceland.