A method and apparatus for generating attenuation-compensated images of subsurface region, including: computing an image of the region utilizing elastic wave propagation, based on field data and subsurface model; generating forward-modeled data utilizing forward viscoelastic wave propagation, based on the image; computing secondary image by migration; computing NMF based on the images; and applying the NMF to the image to generate the attenuation-compensated image. A method and apparatus includes: iteratively computing attenuation-compensated gradient of the region utilizing an elastic wave propagation operator in the back-propagation and a viscoelastic wave propagation operator in the forward modelling, based on field data and subsurface model; computing search direction based on the attenuation-compensated gradient, searching for an improved model, and checking the improved model for convergence.