Strain determination from the measurement of pebble shapes |
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| Authors: | Gerhard Oertel |
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| Institution: | Department of Earth and Space Sciences, UCLA, Los Angeles, Ca 90024 U.S.A. |
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| Abstract: | Cross-sections of pebbles or other near-ellipsoidal bodies in rocks can be measured in three planes, conveniently chosen orthogonal to each other, but otherwise oriented arbitrarily. The three sets of measurements, referred to a single Cartesian coordinate system, can in principle be used to calculate the average pebble shape. Some of these measurements, however, are necessarily redundant and, generally, not compatible without adjustments for the distribution of an error. The calculation of the average ellipsoid is developed, as is that of the strain which transforms an original sphere into such an ellipsoid. This calculation involves the distribution by a weighted least-squares method of the error due to redundancy and leads to the assignment of an estimated error to each of the second-rank tensor components of the strain. The assumption is made that, after being referred to the common coordinate system, the measured values for each tensor component have a normal distribution. This assumption may not always be correct but could be tested before this method is used. |
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