A method of estimating the stress exponent in the flow law for rocks using fold shape

On the basis of experiment and theory, we expect rocks to deform in a linear fashion when diffusive processes control deformation, and nonlinearly in most other situations. The geometric characteristics of buckle folds in layered materials are dependent on rheological parameters, and in particular depend strongly on the stress exponent, n_L, of the stiff layers involved. Thus, information about the deformation rocks have undergone and their rheological state during deformation can be obtained by studying fold shapes and strain distributions. This is important because there is uncertainty in extrapolating laboratory-derived flow laws to the very slow natural strain rates and large strains found in nature. We have studied the development of buckle folds in linear and nonlinear materials using finite-element modeling, and interpolated the numerical results to construct plots relating several geometric parameters to variations in power-law exponent, n_L, and viscosity ratio, m, of layer to matrix. Such plots allow for a comparison of the results of numerical models with data for many natural and experimentally-produced folds, and there is consistency among the data for folds produced in physical models, using both linear and nonlinear materials and the numerical simulations. data for folds from the Appalachian Mountains, the Alps and elsewhere, however, suggest high values of n_L in the flow laws for a number of rock types. The unexpectedly high estimates of n_L suggest that other factors, such as strain softening or anisotropy, may influence fold shape, and thus complicate the estimation of the rheological properties of rocks.