Probabilistic analysis and comparison of stress-dependent rock physics models

Abstract

A rock physics model attempts to account for the nonlinear stress dependence of seismic velocity by relating changes in stress and strain to changes in seismic velocity and anisotropy. Understanding and being able to model this relationship is crucial for any time-lapse geophysical or geohazard modelling scenario. In this study, we take a number of commonly used rock physics models and assess their behaviour and stability when applied to stress versus velocity measurements of a large (dry) core data set of different lithologies. We invert and calibrate each model and present a database of models for over 400 core samples. The results of which provide a useful tool for setting a priori parameter constraints for future model inversions. We observe that some models assume an increase in VP/VS ratio (hence Poisson’s ratio) with stress. A trait not seen for every sample in our data set. We demonstrate that most model parameters are well constrained. However, third-order elasticity models become ill-posed when their equations are simplified for an isotropic rock. We also find that third-order elasticity models are limited by their approximation of an exponential relationship via functions that lack an exponential term. We also argue that all models are difficult to parametrize without the availability of core data. Therefore, we derive simple relationships between model parameters, core porosity and clay content. We observe that these relationship are suitable for estimating seismic velocities of rock but poor when comes to predicting changes related to effective stress. The findings of this study emphasize the need for improvement to models if quantitatively accurate predictions of time-lapse velocity and anisotropy are to be made. Certain models appear to better fit velocity depth log data than velocity–stress core data. Thus, there is evidence to suggest a limitation in core data as a representation of the stress dependence of the subsurface. The differences in the stress dependence of the subsurface compared to that measured under laboratory conditions could potentially be significant. Although potentially difficult to investigate, its importance is of great significance if we wish to accurately interpret the stress dependence of subsurface seismic velocities.