Imaging the two acoustic medium parameters density and compressibility requires the use of both the acoustic pressure and velocity wave fields, described via integral equations. Imaging is based on solving for the unknown medium parameters using known measured scattered wave fields, and it is difficult to solve this ill-posed inverse problem directly using a conjugate gradient inversion scheme. Here, a contrast source inversion method is used in which the contrast sources, defined via the product of changes in compressibility and density with the pressure and velocity wave fields, respectively, are computed iteratively. After each update of the contrast sources, an update of the medium parameters is obtained. Total variation as multiplicative regularization is used to minimize blurring in the reconstructed contrasts. The method successfully reconstructed three-dimensional contrast profiles based on changes in both density and compressibility, using synthetic data both with and without 50% white noise. The results were compared with imaging based only on the pressure wave field, where speed of sound profiles were solely based on changes in compressibility. It was found that the results improved significantly by using the full vectorial method when changes in speed of sound depended on changes in both compressibility and density.