Image-domain least-squares reverse time migration (IDLSRTM) through point-spread functions (PSFs) has been proven to be a feasible approach to improve the spatial resolution and amplitude fidelity of reflection images recovered by reverse time migration (RTM). However, it usually ignores the earth’s Q-effects, which may lead to an unfocused reflection image with an undesired spatial resolution. In this paper, we develop a Q-compensated IDLSRTM approach (denoted as Q-IDLSRTM) through PSFs, in which we use the viscoacoustic wave equation based on the generalized standard linear solid model to simulate inherent subsurface attenuation and the linear inversion to compensate for the amplitude attenuation. The PSFs are estimated by a round of modeling-migration computation and spatial interpolation on the fly. There are two key points in the developed Q-IDLSRTM approach. The first is that we must apply the deblurring filter as a preconditioner to compensate for the attenuation of image amplitude of PSFs and RTM in a viscoacoustic medium, before the iterative solution. The preconditioned PSFs and RTM images can help us to construct a less ill-posed image-domain inverse problem that can produce an improved image quality and a faster convergence rate, compared with the conventional Q-IDLSRTM approach without the deblurring filter. The second key point is that we can impose the L1-norm constraint and total variation regularization on the reflection image to stabilize the solution of the ill-posed inverse problem. Several 2D and 3D experiments verify that the developed approach can achieve better imaging quality in terms of amplitude fidelity and spatial resolution relative to the conventional Q-IDLSRTM and acoustic IDLSRTM approaches.

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