Methods for wavefield extrapolation using measurements of a wavefield quantity and a component of the gradient of the wavefield quantity are disclosed. The methods use "exact" representations of scattering reciprocity. The methods can yield "exact", nonlinear, "true-amplitude" receiver wavefields that are beyond the receiver measurement boundary. Methods of evaluating/validating the extrapolated data are also disclosed. Some methods may also evaluate the accuracy of models for the areas where data are extrapolated or measured. These methods can be used in any industries involving imaging, such as geophysical/seismic exploration, bio-medical imaging, non-destructive remote sensing, acoustic space architecture, design and engineering.
