Estimating accurate and precise strain in low-magnitude penetratively deformed rocks: Integrating forward strain modeling and natural data

Abstract

Estimating grain-scale strain using commonly used strain methods from a low-magnitude penetratively deformed rock is typically fraught with uncertainties as the measured strain is influenced by the pre-deformed grain shapes and grain-scale strain partitioning. Therefore, developing kinematic and mechanical models of orogenic wedge evolution based on such strain data can be misleading without knowing how accurate and precise those data are. To determine accuracy we created five 2-D synthetic rock images and deformed them with known strain under pure shear, simple shear, and general shear. We generated 4160 strain ratio (Rs) and long-axis orientation (φ) data. To determine precision we calculated 2σ (95%) uncertainties in Rs and φ from 102 quartz-rich rocks in Sikkim and generated 977 uncertainty data. Results show that the shape matrix eigenvector and stereographic projection methods record the lowest root mean square error, mean absolute error, and 2σ uncertainty values suggesting they are the most accurate and precise, regardless of strain ratio and deformation types. However, the accuracy and precision of φ deteriorate at Rs < 1.5. For most accurate and precise results, using the above mentioned methods, we recommend a minimum of 100 and 75 markers for Rs < 1.5 and Rs > 1.5, respectively.