Due to the absorption and attenuation effects caused by the inelastic properties of the Earth, the seismic waves cause amplitude attenuation and phase distortion during propagation. Compared with the conventional reverse time migration, the least squares migration can improve the imaging resolution and obtain the amplitude-fidelity imaging result. In this study, based on an unified viscoacoustic wave equation expressed in forward and backward directions, the Green’s function of the forward and backward propagation of viscoacoustic media is realized. By analyzing the mathematical and physical characteristics of Hessian kernel function, the inverse of Hessian matrix is solved by using non-stationary matching filter, and the inverse of the estimated Hessian matrix is directly applied to the conventional imaging result, thus the least square inversion result of the image domain is obtained. This method greatly reduces the computational cost of least-squares offset and effectively improves the image resolution in inverse imaging.


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