Quantifying the intensity of crystallographic preferred orientation (CPO): some practical considerations and recommended practices

Andrew J. Cross 

Crystallographic preferred orientations (CPOs) commonly develop during the crystal-plastic deformation of rocks and minerals, and are widely used to infer strain intensity and geometry, reconstruct deformation conditions, and estimate mechanical anisotropy. Although CPO intensity is often quantified using scalar metrics that reduce the full orientation distribution to a single value, these measures can be highly sensitive to their calculation parameters and input data quality. Here, we examine the performance of two widely used metrics—the J-index and the M-index—using orientation data from a diverse suite of simulated, natural, and experimental specimens. We show that ODF-based measures of CPO intensity such as the J-index (and the ODF-derived variant of the M-index) can vary markedly with kernel parameters and may not converge to a unique value without careful treatment. In contrast, the M-index yields stable, reproducible results across a broad range of conditions when calculated in its original form using random-pair misorientation angle histograms. Monte Carlo resampling shows that M can be accurately estimated with 95% probability using ~500 orientations for moderate-to-strong CPOs (M ≥ 0.25), whereas weak CPOs (M < 0.1) may require up to ~3,000 unique orientation measurements. These results highlight the inherent limitations of reducing complex orientation distributions to one-dimensional metrics, and underscore the importance of consistent methodology, adequate sampling, and transparent reporting. Consequently, we propose a set of practical guidelines to improve the robustness, reproducibility, and comparability of CPO intensity estimates among specimens of similar type, mineralogy, and origin.