Inverse method applied to a sand wedge: Estimation of friction parameters and uncertainty analysis

We examine the fundamental mechanism of frontal accretion in a sand wedge from the occurrence of a forward thrust ramp evolving into a fault-bend fold to the jump of deformation to a new frontal ramp ahead. We use inverse problem theory to extract quantitative information on friction parameters from the systematic comparison of experimental observations and theoretical predictions. The observables are locations, dips and lifetime of thrust ramps, hinge and associated compression. The experimental values (observed data) are cast into statistical models describing the error bars. The theory of limit analysis provides calculated data, requiring five parameters : material density, friction coefficient of the décollement plane, friction coefficient of the bulk material, and the variation of friction with slip on the ramp as well as the distance for this variation. The misfit between observed data and calculated data is determined for all physically admissible values of the parameters. Values yielding a small misfit are interpreted as highly probable. The mean misfit per observable is within their error bars and therefore application of the theory reproduces the observables. Bulk and décollement friction coefficient values with high probability are compared to independent measurements. The inversion also reveals systematic discrepancies: the frictional weakening on the ramps is overestimated, while the force is underestimated, the calculated thrust sheet is longer than observed and the calculated jump to a second ramp occurs earlier than observed. These conclusions allow us to identify necessary improvements for the experimental set-up and of the theoretical assumptions