It has been shown that the effects of multipath propagation in a mobile wireless communications system can be mitigated if the receiver can make predictions about the multipath fading. In this paper, we introduce a novel scheme for extrapolating multipath fields outwards in space, given field observations within a limited region. Whereas previous work has concentrated on simple multipath propagation with a finite number of plane wave scatterers, we use a less restrictive continuous model of scattering. The extrapolation scheme is based on a information-weighted modal expansion of the field, where modes containing too little information are penalized to minimize the extrapolation error. The performance of this scheme is shown to be far better than pessimistic error bounds derived in previous work.