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For quantitative seismic imaging, iterative least-squares reverse timemigration is the recommended approach. The existence of an inverse of theforward modelling operator would considerably reduce the number of requirediterations. In the context of the extended model, such a pseudo-inverse exists,built as a weighted version of the adjoint and accounts for the deconvolution,geometrical spreading and uneven illumination. The application of thepseudo-inverse Born modelling is based on constant density acoustic media,which is a limiting factor for practical applications. To consider densityperturbation, we propose and investigate two approaches. The first one is ageneralization of a recent study proposing to recover acoustic perturbationsfrom angle-dependent response of the pseudo-inverse Born modelling operator.The new version is based on weighted least-squares objective function. Themethod not only provides more robust results, but also offers the flexibilityto include constrains in the objective function in order to reduce theparameters cross-talk. We also propose an alternative approach based on Taylorexpansion that does not require any Radon transform. Numerical examples basedon simple and the Marmousi2 models using correct and incorrect backgroundmodels for the variable density Born modelling, verify the effectiveness of theweighted least-squares method when compared with the other two approaches. TheTaylor expansion approach appears to contain too many artifacts for asuccessful applicability.

From constant to variable density inverse extended Born modelling