Source-independent Q-compensated viscoacoustic least-squares reverse time migration

Abstract

The strong viscosity of the subsurface introduces amplitude absorption and phase-velocity dispersion. Incorrect compensation of the inherent attenuation (the strength of seismic attenuation can be quantified by the inverse of quality factor Q, which is defined as 2π times the ratio of the stored energy to the lost energy in a single cycle of deformation) can significantly affect imaging quality. While Q-least squares reverse time migration allows for the compensation of attenuation effects during the iterations, the traditional L2-norm-minimization, which is highly sensitive to the source wavelet, poses a challenge in accurately estimating source wavelet from field data. Thus, we develop a source-independent Q-least squares reverse time migration, in which a convolutional objective function is introduced to replace the L2-norm constraint in order to mitigate the source wavelet effect. According to the Born approximation, we first linearize the constant-order decoupled fractional Laplacian viscoacoustic wave equation to derive the demigration operator, then construct the corresponding adjoint equation and gradient based on the convolutional objective function, iteratively estimating the reflectivity images. The proposed method relaxes the sensitivity to the wavelet compared to the conventional L2-norm scheme due to the convolutional objective function, which has the ability to construct the same new source for simulated and observed data. Numerical tests on a layered model, the Marmousi model, and field data demonstrate that the proposed source-independent Q-least squares reverse time migration enables us to obtain high quality reflectivity images even when using incorrect source wavelets.