Investigation of regularization parameters and error estimating in inverse elasticity problems

The method of Tarantola1 based on Bayesian statistical theory for solving general inverse problems is applied to inverse elasticity problems and is compared to the spatial regularization technique presented in Schnur and Zabaras.2 It is shown that when normal Gaussian distributions are assumed and the error in the data is uncorrelated, the Bayesian statistical theory takes a form similar to the deterministic regularization method presented earlier in Schnur and Zabaras,2 As such, the statistical theory can be used to provide a statistical interpretation of regularization and to estimate error in the solution of the inverse problem. Examples are presented to demonstrate the effect of the regularization parameters and the error in the initial data on the solution.