Two New Gradient Precondition Schemes for Full Waveform Inversion

We propose two preconditioned gradient direction for full waveform inversion (FWI). The first one is using time integral wavefields. The Least square problem is formulated as the time integral residual wavefields, which can partially resolve the effect of high-passed filter in the traditional gradient formula; the convergence rate is greatly accelerated. The other one is localized offset Hessian inspired by the generalized imaging condition, which provides another redundancy in the Hessian. We compare the traditional conjugate gradient scaled by the shot illumination and localized offset Hessian (actually, only diagonal part is considered here), and contrast their performance for waveform inversion. The results demonstrate the localized offset Hessian (diagonal part) can provide much more information in the subsurface, and is preferred to the layer-strip inversion.