position using the following expression equivalently a wavefield u i x y t and its crossline derivative u2202 u i x y t u2202 y both sampled at the positions y y k with k 1 2 3 can be reconstructed at any y position using the following expression where t is time u03b4x and u03b4y are the existing inline and crossline spatial sampling either in the source or receiver domain for source side interpolation the wavefield u i are organized as common receiver gathers x and y corresponding to source point positions for receiver side interpolation the wavefield u i are organized as common shot gathers x and y corresponding to receiver point positions while conventional recordings require two acquisition points per wavelength to allow proper sampling of the wavefield the additional gradients enable interpolation of any recorded wavefield u i at any position between two acquisition points up to a wavelength apart note that equation 1 and 2 theoretically allows for interpolation of uniformly sampled data but algorithms also exist for non uniform random sampling that can interpolate even more aliased data like the mimap technique vassallo et al 2010 by including the gradient s in the interpolation process larger irregularities in the acquisition geometry due to any kind of obstacles can be accurately reconstructed note also that interpolation direction is not limited to the inline and crossline directions only but in any direction in between for example if one want to interpolate along the u03c6 direction e g with a u03c6 angle with respect to the inline direction the desired gradient is given by g u03c6 g x u00b7 cos u03c6.