Elastic least-squares reverse time migration is a state-of-the-art linear imaging technique used to retrieve high-resolution quantitative subsurface images. Its successful application requires many migration/modeling cycles. To accelerate the convergence rate, various pseudoinverse Born operators have been proposed, providing quantitative results within a single iteration, while having roughly the same computational cost as reverse time migration. However, these are based on the acoustic approximation, leading to possible inaccurate amplitude predictions as well as the ignorance of S-wave effects. To solve this problem, we have extended the pseudoinverse Born operator from acoustic to elastic media to account for the elastic amplitudes of PP reflections and provide an estimate of physical density P- and S-wave impedance models. We restrict the extension to marine environments, with the recording of pressure waves at the receiver positions. First, we replace the acoustic Green’s functions by their elastic version, without modifying the structure of the original pseudoinverse Born operator. We then apply a Radon transform to the results of the first step to calculate the angle-dependent response. Finally, we simultaneously invert for the physical parameters using a weighted least-squares method. Through numerical experiments, we first examine the consequences of the acoustic approximation on elastic data, leading to inaccurate parameter inversion as well as to artificial reflector inclusion. Then, we determine that our method can simultaneously invert for elastic parameters in the presence of complex uncorrelated structures, inaccurate background models, and Gaussian noisy data.