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. Numerous methods have been proposed to quantify CPO intensity as a scalar metric, but these metrics 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 electron backscatter diffraction (EBSD) for a diverse suite of simulated, natural, and experimental specimens. We show that ODF-based measures of CPO intensity, such as the J-index, can vary markedly with kernel parameters and may fail to converge to a unique value. In contrast, the M-index, when calculated from random-pair misorientation angle histograms, yields stable, reproducible results across a broad range of conditions. Monte Carlo resampling demonstrates that M can be accurately described 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 findings form the basis of a recommended, standardised practice to ensure that CPO intensity values are both reproducible and comparable across similar geological and experimental contexts.