Accurate measurement of crystallographic preferred orientation (CPO) is necessary to characterize anisotropic material properties. In geologic and engineered materials, crystal orientation datasets can be limited due to sample volumes or other practical constraints. To examine the effect of sample size on texture measurements, we generated large synthetic datasets (10 6 unique orientations) for a range of texture strengths and crystal symmetries. For each dataset, we measured texture strength (using the M-index) for 1,000 subsamples across a range of population sizes (n = 10 – 5,000). For datasets simulating olivine, the most abundant mineral in the upper mantle, we also calculated the seismic anisotropy of P-waves and S-waves and measured the position of maximum density for the seismically fast 100 axes for unimodal and girdled distributions. The M-index and the magnitude of seismic anisotropy are systematically overestimated at small population sizes but converge to “true” values when populations are sufficient. The uncertainty in a given measurement is reduced as population size increases. To help guide data acquisition by users of the electron backscatter diffraction (EBSD) technique, we establish two thresholds: a minimum sample size required for a meaningful result, and a greater sample size required to reduce uncertainty below 2%. In general, the number of data required to achieve these thresholds depends on crystal system, texture strength, and measurement quantity, and may vary by up to two orders of magnitude. To illustrate a use case for these data, we calculate the uncertainties associated with experimental and natural results that have been used to constrain numerical models of olivine CPO evolution.
Billings et al. (2026) studied this question.