Paleostress inversion refers to the determination of paleostress history from evidence found in rocks, based on the principle that past tectonic stress should have left traces in the rocks. Such relationships have been discovered from field studies for years: qualitative and quantitative analyses of deformation structures are useful for understanding the distribution and transformation of paleostress fields controlled by sequential tectonic events. 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. Inversions require assumptions in order to simplify the complex geological processes. The stress field is assumed to be spatially uniform for a faulted rock mass and temporally stable over the concerned period of time when faulting occurred in that region. In other words, the effect of local fault slip is ignored in the variation in small-scale stress field. Moreover, the maximum shear stress resolved on the fault surface from the known stress field and the slip on each of the fault surface has the same direction and magnitude. Since the first introduction of the methods by Wallace and Bott in the 1950s, similar assumptions have been used throughout the decades.
Fault slip analysis
Conjugate fault system
Anderson was the first to utilize conjugate fault systems in interpreting paleostress, including all kinds of conjugate faults (normal, reverse and strike-slip). 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. Therefore, a number of studies have been carried out by other researchers in assorted structural settings and by correlating with other deformation structures. Nonetheless, further development revealed the deficiency of the model:
1. Important geometrical properties absent in practical situation The geometrical properties of conjugate faults are indicative of the sense of stress, but they may not appear in the actual fault patterns.
Slickenside lineations normal to fault plane intersection Symmetrical sense of motion that gives the obtuse angle in the direction of lengthening Relation between the intersecting angle of fault planes and mechanical properties, with reference to information from rock mechanics experiments in lab 2. Observed fault patterns are far more sophisticated There are often oblique pre-existing faults, planes of weaknesses or striations to the fault slip, which do not belong to the conjugate fault sets. Neglecting this considerable amount of data would cause error in analysis.
3. Neglecting the stress ratio (Φ) This ratio provides the relative magnitude of the intermediate stress (σ2) and thus determines the shape of the stress ellipsoid. However, this model does not give an account on the ratio, save for some specific cases.
Reduced stress tensor This method was established by Bott 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. It gives more comprehensive and accurate results in reconstructing paleostress axes and determining the stress ratio (Φ) than the conjugate fault system. The tensor works by solving for four independent unknowns (three principal axes and Φ) through mathematical computation of observations of faults (i.e. attitude of faults and lineations on fault planes, direction and sense of slip, and other tension fractures). This method follows four rigorous steps:
Data Analysis Computation of Reduced Stress Tensor Minimization Check of Results
Data analysis Reconstruction of paleostress requires large amount of data to attain accuracy, so it is essential to organize the data in comprehensible format prior to any analysis.
1) Fault Population Geometry Attitude of fault planes and slickensides is plotted on rose diagrams, such that the geometry is visible. This is particularly useful when the sample size is enormous, it provides the full picture of the region of interest.
2) Fault Motion Fault movement is resolved into three components (as in 3D), which are vertical transverse, horizontal transverse and lateral components, by trigonometric relation with the measured dips and trends. Net slip is shown more clearly which paves the way to understanding the deformation.
3) Individual Fault Geometry Fault planes are represented by lines in stereonets (equal area lower hemisphere projection), while rakes on them are indicated by dots sitting on the lines. It helps to visualize the geometrical distribution and possible symmetry among individual faults.
4) P (pressure) and T (tension) Dihedra This is a concluding step of compiling all the data and check their mechanical compatibility, also could be seen a preliminary step in determining major paleostress orientations. 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. Since fault plane and auxiliary plane perpendicular to striations are considered the same in this method, the model can be directly applied to focal mechanisms of earthquakes. Nonetheless, due to the same reason, this method cannot provide accurate determination of paleostress, as well as the stress ratio.
Determination of paleostress
Reduced stress tensor
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