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Hessian Based Reflection Waveform Inversion

Summary The reflection full waveform inversion (RWI) is a promising method to recover the low-to-intermediate wavenumber of the model with reflection data. However, it is very difficult to precondition this highly nonlinear problem for robust convergence. The second-order derivative of the objective function, i.e. Hessian, implies the information of acquisition geometry, parameter trade-offs and the resolution ability from the observed data. In full waveform inversion (FWI), the Hessian matrix plays an important role to precondition the gradient and make the FWI converge faster. But there are few discussions about the preconditioning on the RWI gradient from the viewpoint of Hessian. In this abstract we will derive the Frechet kernel and Hessian of RWI problem. By including the Hessian information, we prove that the Hessian based RWI method can provide better results through the synthetic examples.