Rocscience International Conference 2025 is going to take place in Sydney, Australia Read more

Search Results

Fisher Distribution

A Fisher Distribution is commonly used for modeling the distribution of 3-dimensional orientation vectors [Fisher (1953)], such as the distribution of joint orientations (pole vectors) on a sphere. A Fisher Distribution describes the angular distribution of orientations about a mean orientation vector, and is symmetric about the mean. The probability density function can be expressed as:

Probability density function Eqn.1

where Angular deviation variable is the angular deviation from the mean vector, in degrees, and K is the "Fisher constant" or dispersion factor.

In RS2, joint orientations for the Baecher or Veneziano joint network models can be defined using a Fisher distribution.

Fisher K

The Fisher K value describes the tightness or dispersion of an orientation cluster. A larger K value (e.g. 50) implies a tighter cluster, and a smaller K value (e.g. 20) implies a more dispersed cluster, as shown in the following figure.

Stereonet plots showing the effect of Fisher K on a randomly generated joint set of 500 samples

Stereonet plots showing the effect of Fisher K on a randomly generated joint set of 500 samples

The Fisher K value can be estimated from Eqn. 2, for data sets with greater than approximately 30 vectors (poles) [Fisher (1953)].

Fisher K value equation Eqn.2

where N is the number of poles, and R is the magnitude of the resultant vector (i.e. the magnitude of the vector sum of all pole vectors in the set).

Standard Deviation

By analogy with a Normal distribution, it can be shown that the standard deviation of a Fisher distribution can be estimated from Eqn.3 [Butler (1992)].

Equation to estimate Fisher distribution Eqn.3

where is the "angular standard deviation" or "angular dispersion" of the Fisher Distribution, and K is the Fisher constant.

Rocscience logo, click here to return to the homepage Portal Account Portal Account Log In Log Out Home Shopping Cart icon Click here to search our site Click here to close Learning Tech Support Documentation Info Chevron Delete Back to Top View More" Previous Next PDF File Calendar Location Language Fees Video Click here to visit Rocscience's LinkedIn page Click here to visit Rocscience's YouTube page Click here to visit Rocscience's X page Click here to visit Rocscience's Facebook page Click here to visit Rocscience's Instagram page Click here to visit Rocscience's Reddit page Bookmark Network Scroll down for more Checkmark Download Print Back to top Single User Multiple Users RSLog RocFall3 CPillar Dips EX3 RocFall RocPlane RocSlope3 RocSupport RocTopple RS2 RS3 RSData RSPile Settle3 Slide2 Slide3 SWedge UnWedge RocTunnel RocSlope2 Commercial License Education License Trial License Shop safe & secure Money-back guarantee