ABSTRACT
Over the past 12 years, many different computational methods or variations of existing methods have been proposed for determining paleostress tensors from fault populations and their slip directions. These methods are all based upon well-known relationships between stress and shear and use iterative, non-linear mathematical algorithms which seek to minimize the angles between the calculated maximum shear stress direction and the observed movement directions on each fault plane in a population. The solution returned is the best-fit paleostress tensor for the population.
By taking the Coulomb failure criterion into account, several paleostress analysis programs have been able to use linear, rather than non-linear, methods to solve for a paleostress tensor. The advantages of using linear equations is that they are less computationally-intensive and are far easier to solve.
A major problem with computational methods of paleostress analysis is that very little work has been done on evaluating their effectiveness and/or possible limitations. If the techniques return results consistent with other methods of estimating paleostress directions, or with various kinematic analysis methods, they are often used by geologists. If not, an attempt may be made to explain why, but geological explanations are usually sought rather than criticizing the paleostress analysis methods. This study is an attempt to formulate the problem and to begin systematically examining it.
For my thesis project, I obtained several working versions of paleostress analysis computer programs. After much work, I decided to test two of the methods – those developed by Angelier and Reches. Artificial fault populations were created for these tests with a slip vector calculation program which I wrote specifically for that purpose. The artificial fault populations were created using exactly the same initial assumptions that the paleostress analysis programs used.
An artificial fault population is a set of fault orientations and their associated slip directions consistent with a predetermined stress field. For all of the fault populations created, the most compressive principal stress axis was vertical with a relative magnitude of +1.0 and the least compressive principal stress axis was oriented north-south with a relative magnitude of -1.0. Entering these populations into a paleostress analysis program should have, theoretically, returned the same orientations for the principal stress axes.
With this in mind, I chose to create several different types of artificial fault populations to test possible limitations in paleostress analysis. I used randomly-oriented fault populations, special-case fault populations, and fault populations which had data added or removed from them.
The results of these tests are that the two paleostress analysis programs I examined may work sufficiently well for certain types of well-constrained fault populations, but often give large errors when examining special types of fault sets such as conjugate faults, orthorhombic symmetry faults, and fault populations where all of the faults have very similar orientations. The paleostress analysis programs may also be sensitive to measurement errors and/or extraneous data depending upon several factors, including the orientations of the faults in question.
In conclusion, much more work is currently needed to further examine this topic and to begin to formulate general guidelines for applying paleostress analysis methods to fault populations gathered by geologists in the field.

Schimmrich, S.H., 1991. Evaluation of computational methods of paleostress analysis using fault-striation data.  Unpublished MSc. thesis, State University of New York at Albany. 394 pp., +xix
University at Albany Science Library call number:  SCIENCE Oversize (*) QE 40 Z899 1991 S35

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