The Transformed Hessian Operator in Seismic Inversion Imaging

AbstractIn this paper, we summarize the influence of the Hessian operator in seismic inversion methods and review the mathematical and physical meanings of the Hessian operator in the seismic inversion imaging. The Hessian operator is the second derivation of the misfit function to the seismic model parameters. Its Green's function formulation under the acoustic wave approximation shows that the Hessian operator reflects the effects of the seismic acquisition system and wavelet frequency band during the projection of information from the data spaces to the model space. We propose two pseudo‐Hessian forms for the least‐squares migration and the full waveform inversion separately. The application of the plane‐wave Hessian operator can lead to an amplitude‐preserved migration result. The sub‐offset Hessian can be used to the full waveform inversion to enhance the efficiency of inversion. At last, we discuss and evaluate the Hessian operator in seismic inversion imaging.