Uncertainty quantification for Wavefield-Reconstruction Inversion using a positive-definite approximated Hessian

We analyze the Hessian of wavefield reconstruction inversion (WRI) and propose a new approximated Hessian. Instead of requiring PDE solves, the matrix-vector multiplication action of the approximate Hessian can be achieved with several matrix-vector multiplications. The diagonal part of the approximated Hessian can be also calculated without additional PDE solves. We apply this approximated Hessian to uncertainty quantification and obtain statistical parameters such as standard deviation and confidence interval. Numerical example illustrate the accuracy of the estimated Hessian and the feasibility of the method to quantify uncertainties.

https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall...