Nonlinear partial Functional Derivative and Nonlinear LS Seismic Inversion

Taylor expansion of the full nonlinear partial derivative (NLPD) operator is directly related to the full scattering series (Born series) which has a serious convergence problem for strong scattering. The renormalization procedure applied to the Taylor-Fréchet series leads to the De wolf approximation of NLPD, which changes the Fredholm type series into a Volterra type series so that renormalized Fréchet series has a guaranteed convergence. Numerical simulations demonstrate the different convergence behaviors of the two types of series for NLPD in the case of strong perturbations. Preliminary study on the LS inversion theory using the nonlinear kernel leads to an inversion scheme of simultaneous updating both the model parameters and propagators.