Calc(ulation)s Tab Functions


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Calc tab controls
  1. General Comments about the Calc Tab
  2. Sigmas/Stresses
  3. Angle of Friction
  4. Statistics on Hemispherical vs Spherical Data
  5. On Visible Data
  6. Mean(hem)
  7. Mean(Sphere)
  8. Selected Set
  9. Weighted Mean (hem)
  10. Weighted Mean (sphere)
  11. Fit Plane
  12. Apparent Dip on Selected plane
  13. Intersection of 2
  14. Intersection of three cones
  15. Data on Planes
  16. Random Data

General Comments about the Calc Tab

This tab contains calculations (those not found under the sets tab).
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Sigmas/Stresses

If two planes are taken to be complementary fracture planes, then from them the principal stress axes can be calculated, together with the internal angle of friction. Sigma 2 the intermediate stree direction is easily found as the intersection of the two fracture planes. Sigma 1, the most crompressive axis, is in the centre of the acute angle between these planes, Sigma 3, the least compressive or most tensile, direction is in the middle of the obtuse angle. The three sigmas are necessarily mutually perpendicular.
To perform this analysis you must first select (click on) the two data points to be considered complementary fracture planes (they may be planes or poles). Clicking the sigma/stresses button will create a new set containing three points, the remarks of these data points indicate which is which.
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Angle of Friction

Whenever the Sigmas /stresses function is used a comment appears under the Calc tab indicating the internal angle of friction of the material.
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Statistics on Hemispherical vs Spherical Data

 When computing statistics, it is often important to distinguish between what we will call 'spherical data' and what we will call 'hemispherical data'. We take 'spherical data' to refer to objects that have an absolute sense of direction, such as the way up of a bed. Such data required both hemisheres of the unit sphere to represent it. On the otherhand, objects such as poles to joints will be termed 'hemispheric data' because turning them through 180 degrees, or multiplying their vectors by -1, does not change their meaning.
Finding the 'mean' value or central tendancy of directional data is straightforward for spherical data, one simply adds the position vectors and normalises the result. A problem arises, however, for 'hemispheric data' . Consider poles to nearly vertical joints: a joint dipping 89 degrees west is close to a bed dipping 89 degrees east. Treated as ordinary directional data these poles are 178 degrees apart and have a mean direction which is straight down. This is not what is wanted. Cauldron uses a simple fudge, which works well for reasonably clustered data. When a 'hemisphere' option is selected, vectors are summed as with spherical data, however, if a vector to be added is more than 90 degrees from the current total then it's inverse is added instead. In the above example, the joint dipping 89 degrees east would be treated as one dipping 'up' 89 degrees west, their poles would thus be only two degrees apart and their 'mean' would lie between them on the horizontal plane.
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On Visible Data

 The ‘On Visible Data’ option means that a statistic is computed for all visible data, ignoring data that is temporarily invisible.
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Mean(hem)

 The central tendancy of a set of data can be found by considering each data point to be a vector. Adding them together and then normalising the result gives an 'average'.
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Mean(Sphere)

 The central tendancy of a set of data can be found by considering each data point to be a vector. Adding them together and then normalising the result gives an 'average'.
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Selected Set

 The ‘On Visible Data’ option means that a statistic is computed for the first selected set only.
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Weighted Mean (hem)

 The central tendancy of a set of data can be found by considering each data point to be a vector. Adding them together and then normalising the result gives an 'average'.
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Weighted Mean (sphere)

The central tendancy of a set of data can be found by considering each data point to be a vector. Adding them together and then normalising the result gives an 'average'.
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Fit Plane

 This function fits a plane through data. For example if your data consists of poles bedding planes folded in a cylindrical fold, then this function will draw a plane normal to the fold axis, that 'fits' the data best. The function operates by looking at each pair or data points and computing the normal. The mean of these normals is computed and a great circle entered about this pole.
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Apparent Dip on Selected plane

 A classic problem from structural geology classes is the "apparent dip", the dip that would be observed on a vertical rock face. Since exposures are seldom, in practice obediently vertical, the practical problem should be generally solved using the 'intersection of 2' function (find the direction common to the plane of the exposure and the plane of the bedding plane). However, in deference to tradition Cauldron provides a function that lets you select a planar structure enter the bearing (along) the vertical exposure plane, and then tells you the apparent dip (the use of negative numbers is supposed to indicate that the direction chose will go 'up dip'.
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Intersection of 2

 If two structures (great circles and or small circles) are selected, then this button creates two new points that represent the intersection of these structures. Note that 2 planes have two common points that appear at the same point on the plot, however, one is in the upper hemisphere and one in the lower. In this case you will often wish to delete one of them.
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Intersection of three cones

This option is designed to help solve problems such as the 'three borehole problem'. If three small circles are selected (Cauldron will remember up to three picks under the edit window) selecting this option will create up to 6 points in a new set. These new points each represent the directions common to two of the small circles. The 'three borehole problem' is one where three inclined, non parallel boreholes each intersect a planar structure at an angle which is known (but the bearing isn’t). Thus for each borehole the possible orientations of the structures pole lies on a small circle. Ideally the 'true' orientation of the structure would be where three small circles intersect at a single point. In practice errors mean that the answer will be near a small triangle formed by the small circles. If an accurate estimation of this result is required then go to the 'edit' tab and select and delete the three new points that do not form the vertices of this triangle. The go to the 'sets' tab to make sure that this set (now with only the three clustered points in) is selected. Then return to the 'calcs' tab and from the 'on selected set' box use the 'mean sphere' button. This will produce new point in the centre of the triangle, which will be a good estimate of the pole to the planar structure.
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Data On Planes

 Entering data on planes (e.g. the direction of lineations) is easily performed. First select the plane (by picking it in the edit tab pick box). The enter the plunge or pitch in degrees in the edit box provided. Clicking the pitch or plunge button will cause two data to be entered -its up to you to delete the one which is not intended. Hint: go the edit tab and select the two bottom points in turn, use Delete Pick. If, as is often the case, you are entering many such data to may wish to gather them together using the 'Merge Sets' function on the sets tab.
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Random Data

 This function enables the addition of a given number of random points. You choose upper, lower or both hemispheres and the number of points to add.
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Copyright: The copyright (2001) of this page is owned by Dr Nigel Stuart of Resource Dynamics, Alberta, Canada. You are welcome to use, reproduce it in part or in whole. Should you reproduce it in part please ensure that credit/blame for authorship is given. A link to the Resource Dynamics home page would be appreciated.