Determination of fabric and strain ellipsoids from measured sectional ellipses — theory

Calculating a ‘fabric ellipsoid’ from sectional fabric ellipses is a common requirement in studies of rock fabrics. There may be any number, N≥3 of sections, with arbitrary orientations, and absolute or relative sizes of the sectional ellipses are often not known. In the method presented here, the solution is shown to be that of a system of linear equations, and that solution can always be found. An ‘incompatibility index’ permits an assessment of how well sectional data fit with each other, and allowance can also be made for different levels of confidence for the different sectional ellipses.