In the context of elastic wave propagation, the non-periodic homogenization asymptotic method allows to find a smooth effective medium and equations that correspond to the wave propagation in a given complex elastic or acoustic medium down to a given minimum wavelength. By smoothing all discontinuities and fine scales of the original medium, the homogenization technique considerably reduces meshing difficulties as well as the numerical cost associated with the wave equation solver, while producing the same waveform as for the original medium (up to the wanted accuracy). We present here a variation of the original method, allowing to homogenize the difference, or residual, between an original medium and a reference medium. This makes it possible to, for example, homogenize some specific parts of a model or to leave unchanged a specific interface while homogenizing the rest of the model. We present two examples of applications, one implying a complex geological shallow structure and the other involving the combination of deterministic and stochastic elastic models