Paleostress inversion

[2] Deformation ranges from microscopic to regional scale, and from brittle to ductile behaviour, depending on the rheology of the rock, orientation and magnitude of the stress, etc.

Therefore, detailed observations in outcrops, as well as in thin sections, are important in reconstructing the paleostress trajectories.

In other words, the effect of local fault slip is ignored in the variation in small-scale stress field.

Regional conjugate fault can be better understood by comparison to a familiar rock mechanics experiment, i.e. the Uniaxial Compressive Strength (UCS) Test.

Basics of their mechanisms are similar except the principal stress orientation applied is rotated from perpendicular to parallel to the ground.

The conjugate fault model is a simple way to obtain approximate orientations of stress axes, due to the abundance of such structure in the upper brittle crust.

This method was established by Bott[5] in 1959, based on the assumption that direction and sense of slip occurs on the fault plane are the same with those of the maximum resolved shear stress, hence, with known orientations and senses of movements on abundant faults, a particular solution T (the reduce stress tensor) is attained.

[5] It gives more comprehensive and accurate results in reconstructing paleostress axes and determining the stress ratio (Φ) than the conjugate fault system.

As this is a simple graphical representation of the fault geometry (being the boundaries of dihedra) and sense of slip (shortening direction indicated by black and extension depicted by grey), while it is able to provide good constraints on the orientation of principal stress axes.

The approximation is built upon the assumption that the orientation of maximum principal stress (σ1) most probably passes through the greatest number of P-quadrants.

Nonetheless, due to the same reason, this method cannot provide accurate determination of paleostress, as well as the stress ratio.

The reduced stress tensor is a mathematical computation approach to determining the three principal axes and the stress ratio, totally four independent unknowns, calculated as eigenvectors and eigenvalue respectively, so that this method is more complete and accurate than the mentioned graphical approaches.

This formulation is a deviator, which requires more computation to obtain information of the stress ellipsoid despite maintaining a symmetry in mathematical context.

[12] However, individual sense of motion is an effective reflection of orientation of stress axes in real situation.

Regarding the efficiency in computation, which is particularly significant in long iterative processes like this, tangent of angles is preferred to cosine.

The reduced stress tensor should best (hardly perfectly) describe the observed orientations and senses of movement on diversified fault planes in a rock mass.

This implies the variation in stress orientation and ratio Φ within a rock mass is overlooked yet always present in practical case, due to interaction between discontinuities at any scale.

Hence, the significance of this effect has to be examined to test the validity of the method, by considering the parameter: the difference between the measured slickenside lineation and the theoretical shear stress.

The average angular deviation is insignificant when compared with the total of instrumental (measuring tools) and observation (unevenness of fault surfaces and striae) errors in majority of the cases.

[11] In conclusion, the reduced stress tensor method is validated when Quantitative analyses cannot stand alone without careful qualitative field observations.

The above described analyses are to be carried out after the overall geologic framework is understood e.g. number of paleostress systems, chronological order of successive stress patterns.

Also, consistency with other stress markers e.g. stylolites and tension fractures, is required to justify the result.

A piezometer is an instrument used in the measurement of pressure (non-directional) or stress (directional) from strain in rocks at any scale.

Since these mechanisms primarily depend on flow stress and their resulted deformation is stable, the strained grain size or grain boundary are often used as an indicator of paleostress in tectonically active regions such as crustal shear zones, orogenic belts and the upper mantle.

The nucleation process is triggered at boundaries of existing grains only when materials have been deformed to particular critical values.

This process happens steadily over the strain history, thus the change in orientation is progressive but not abrupt as grain boundary bulging.

Therefore, grain boundary bulging and subgrain rotation are differentiated as discontinuous and continuous dynamic recrystallization respectively.

Such relation has been represented by an empirical equation between normalized value of grain size and flow stress, which is universal for various materials: d is the average grain size; b is the length of the Burgers vector; K is a non-dimensional temperature-dependent constant, which is typically in the order of 10; μ is the shear modulus; σ is the flow stress.

Therefore, the determination of the boundary zone between fields of these two creep mechanisms matter to know when the recrystallized grain size tends to stabilize, as to supplement the above model.

Before starting to infer flow stress magnitude, the mineral has to be calibrated carefully in laboratory.