Practical schemes for distributed video coding with side information at the decoder need to consider non-standard correlation models in order to take non-stationarities into account. In this paper we introduce two correlation models for Gaussian sources, the Gaussian- Bernoulli-Gaussian (GBG) and the Gaussian-Erasure (GE) models, and evaluate lower and upper bounds on their rate-distortion functions. Provided that the probability of impulse noise or of erasures remains small, these bounds remain close to the rate-distortion function for Gaussian correlation. Two practical schemes for the GE correlation model are also presented, with performance about 1.5 dB away from the lower bound.