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Seismic data and analysis of geological structures

The orientation and relative intensity of the horizontal stresses can be inferred from seismic data and also from certain geological features and structures. For example, provided the dyke orientation is not controlled by joints or faults, it is reasonable to infer that the least principal stress acts normal to dykes, so that, when

Figure 2.11 (a) Simplistic representation of the force distribution of a disk with a hole, subjected to biaxial compression, at poles and equator of the disk. There is a three-fold force concentration of stress at the hole boundary in the direction of the applied forces p and q and a tensile stress of -p and -q as indicated in the diagram. With p>q, the biaxial forces acting at the 'pole' and 'equator' of the small hole become significantly enhanced. (b) When these enhanced forces, per unit area, are translated into stresses, it can be inferred that the walls of the borehole may spall or 'break-out'.

such features are vertical, it follows that the greatest horizontal stress acts in the plane of the intrusion. Similarly, the regional orientation of stresses can be inferred from studies of folds and faults. Earthquake data can also be used to infer orientation of stress axes. However, all such techniques, based on theory, require very careful application.

Fault movement and seismic data

When a fault is initiated in homogeneous and isotropic rock, it is reasonable to accept the theoretical concepts of brittle failure, and assume that the axis of intermediate principal stress lies in the plane of shear failure, and that the axis of maximum principal stress makes an angle with the fault plane which is determined by the physical properties of the rock. This angle is commonly close to 30°.

Once shear failure takes place, the magnitude of the stresses changes. If we are dealing with a normal fault, initiated when Sx is vertical, it can be shown that the erstwhile least principal stress (S3), adjacent to the fault plane, increases in magnitude, so that it becomes the intermediate principal stress (S2), while the erstwhile intermediate principal stress in the plane of the fault becomes (S3). Once a fault is initiated, it develops to reach its maximum extent. This development, requiring a number of slips on the fault, may take place in a relatively short period, during which the orientation of the principal stresses may remain reasonably constant. Over a longer period, the axes of principal stress and their magnitudes, although causing fault

Figure 2.12 Slip conditions on a fracture in the crust are determined by the orientation and magnitude of the principal stresses and their orientation relative to the given fracture plane. The diagrams a-h indicate the zones of failure (black) for a variety of stress directions. The reader is directed to Jaeger and Cook (1969), and Price and Cosgrove (1990) for a more detailed treatment (after Jaeger and Cook, 1969).

Figure 2.12 Slip conditions on a fracture in the crust are determined by the orientation and magnitude of the principal stresses and their orientation relative to the given fracture plane. The diagrams a-h indicate the zones of failure (black) for a variety of stress directions. The reader is directed to Jaeger and Cook (1969), and Price and Cosgrove (1990) for a more detailed treatment (after Jaeger and Cook, 1969).

movement, may undergo such rotation that all principal stress axes are oblique to the fault plane (Price and Cosgrove, 1990).

By postulating orientations of the axes of principal stress to a hypothetical plane, and by assuming one or more specific values for the coefficient of sliding friction and also the ratio of the magnitude of the principal stresses, it is possible to determine the conditions under which slip may take place on the hypothetical fault plane. Such an exercise is reported by Jaeger and Cook (1969), where the areas were determined in which the normal plane must fall if slip on the plane can take place, for the assumed conditions of friction and ratio of stress magnitudes (Figure 2.12).

From seismic data, one may infer the orientation of the axis of maximum principal stress, from first arrivals. However, frequently, the orientation of the fault plane is not known, nor are the orientations or relative magnitudes of the principal stresses. The fact that the seismic analyst is so frequently confronted with such 'unknowns' gave rise to the oft forgotten caution by McKenzie (1969), that the analyst can only expect to place the pole of the maximum principal stress in the correct quadrant!

Analyses of geological structures

These analyses embrace a number of techniques. The easiest of these is based on, for example, the reasonable assumption that dykes, sometimes in conjunction with alignment of volcanic vents, also provide good evidence for the orientation of the greatest horizontal stress. But these events are limited in occurrence and, moreover, the inferred stress data relate to the period when the dykes or vents were emplaced, and so may well be different from the current stress situation.

In recent studies of what has been termed neo-tectonics, the slip direction of recently active fault planes has become a favoured means of determining the orientation of the axis of maximum principal stress. This technique has been pioneered and developed by French structural geologists (e.g. Carey and Brunier, 1974; Carey, 1979; Angelier et al., 1982). In these studies, several adjacent fault planes are usually exposed, and the slip direction can be inferred from striations and slickenside. It is assumed that the axis of maximum principal stress acts at 30° to the fault plane, rather than the 45° favoured by geophysical analysts of seismic data. However, the problems outlined above in the section on Fault Movement and Seismic Data still hold.

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