The numerical simulation of wave propagation in heterogeneous media involves very significant computational costs that can be considerably reduced by using finite elements whose order is adapted to the characteristics of the medium. In this paper, we show that we can further reduce these costs by using a mixed time scheme, combining two discrete formulas and using local time steps. We illustrate the effectiveness of the new scheme considering an application to seismic imaging treated by reverse time migration. We also show that the new scheme greatly reduces the numerical dispersion problems that appear frequently when adapting the orders of approximation in space only.