  Sound propagation in the ocean is considered. We demonstrate a novel
algorithm for full wavefield reconstruction using pointwise measurements by
means of a vertical array. The algorithm is based on the so-called discrete
variable representation and can be implemented both for tonal and pulse
signals. It is shown that the algorithm is robust against array distortions and
ambient noise of moderate amplitude. Efficiency of reconstruction is verified
by means of numerical simulation with a model of a shallow-sea waveguide. It is
found that the effect of bottom sound attenuation enables accurate
reconstruction with arrays having relatively low density of hydrophones.
