page_title: Paleostress inversion
section_title: Data analysis
hierarchical_section_title: Paleostress inversion / Fault slip analysis / Reduced stress tensor / Data analysis
caption_attribution_description: English: individual fault geometry
context_page_description: 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.
context_section_description: 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.
  4) Principle of P and T dihedra: incompatibility zones (white) are found by overlapping P (black) and T (grey) regions derived from fault sets
caption: 3) Individual fault geometry represented on a stereonet
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