Density distribution techniques and strained length methods for determination of finite strains

Abstract

For a homogeneously deformed rock composed initially of an isotropic distribution of object shapes, finite strain may be determined from the correlation between the orientations of either two-dimensional or one-dimensional sample cuts and the frequencies with which they intersect marker objects. Mimran previously published an incorrect method for planar samples under the heading ‘density distribution technique’. Methods are described by which the three-dimensional strain may be directly determined from six general samples, either linear or planar. Construction of two-dimensional ellipses as an intermediate step is unnecessary and enforces practical difficulties. These methods may be simplified by use of samples parallel to known principal axes or planes of the finite strain. In this case the same large errors may arise from slight misorientation of samples as with other methods of strain measurement. A new quick method is proposed, combining linear and planar measurements of frequencies of intersected objects, which is thought to be the first method to circumvent a large part of the error from this error source. For example, if true X:Z ratio is 9 : 1, and orientations in the XZ plane are misjudged by 8°, normal methods give 38% error where the new method gives, with care, an error of 1.9%. For methods of strain measurement such as are described here the concept of strain ellipsoid is unnecessarily limiting, and should be abandoned.