Laboratory Investigation of the R Factor: Geomechanical Insights into Time-Lapse Seismic Signatures of Permian Aeolian Clashach Sandstone, Morayshire, Scotland

This work investigates the coupling of seismic velocity variations to strain within geomechanically active systems, using controlled laboratory experiments on Clashach sandstone to strengthen the empirical foundations for the use of time-lapse seismic monitoring for geomechanical model calibration. The R factor, also known as the dilation factor, expresses the sensitivity of seismic velocity variations to vertical strain. The fundamental goal of this study is to understand the behaviour of R factors during deformation in an effort to improve predictive models for subsurface deformation, hence increasing the safety and efficiency of geoengineering applications. Stór Mjölnir is a state-of-the-art triaxial deformation equipment capable of real-time X-ray imaging and acoustic emission (AE) monitoring, used in laboratory testing of rocks. Clashach sandstone samples were tested using two experimental protocols: (a) constant strain rate loading, and (b) constant acoustic emission rate loading, whereby stress is increasing monotonically or modulated, respectively. The evolution of differential stress, axial strain, P-wave velocity, and porosity was tracked and studied to determine R factor behavior under various deformation regimes, such as compaction, linear elasticity, strain hardening and softening. This method allows for controlled monitoring of geomechanical transformations, gathering high temporal-resolution data that would be difficult to obtain under field conditions. The results show that material stiffness has a considerable influence on the sensitivity of the R factor, even across samples with the same lithology. The R factor increased logarithmically during the compaction-dominated period, peaking before falling as the material reached its yield point. Stiffer samples had higher peak R values and moved through the compaction phase faster. The observed discrepancy between predicted P-wave velocity trends and porosity evolution indicates the presence of anisotropy, implying that anisotropic factors contribute to fluctuations in the R factor. These findings demonstrate the R factor's effectiveness in tracking deformation stages while also emphasizing its sensitivity to differences in stiffness, lithology, stress-state circumstances, and potentially anisotropy, limiting its general applicability for quantitative strain prediction. This study improves the use of the R factor in 4D seismic monitoring and geomechanical modeling by describing its complex behavior within a single lithology. Understanding the limits of the R factor can help build safer and more effective subsurface engineering solutions, reducing hazards associated with reservoir compaction, hydrocarbon production, CO₂ storage, and other geoengineering projects. Future research that includes a larger range of lithologies and stress regimes may improve the dependability of the R factor in subsurface geomechanical studies. In addition, considering tensorial nature of stress and strain, along with velocity anisotropy measurement may lead to the predictability of R factor beyond assumptions for uniaxial strain conditions.