Dimensionality Reduction in Full-Waveform Inversion Uncertainty Analysis

Abstract

The uncertainty of model parameters obtained by full-waveform inversion can be determined from the Hessian of the least-squares error functional. A description of uncertainty characterisation is presented that takes the null space of the Hessian into account and does not rely on the Bayesian formulation. Because the Hessian is generally too costly to compute and too large to be stored, a segmented representation of perturbations of the reconstructed subsurface model in the form of geological units is proposed. This enables the computation of the Hessian and the related covariance matrix on a larger length scale. Synthetic two-dimensional isotropic elastic examples illustrate how conditional and marginal uncertainties can be estimated for the properties per geological unit by themselves and in relation to other units.