In reflection seismology one places sources and receivers on the Earth’ssurface. The source generates elastic waves in the subsurface, that are reflected wherethe medium properties, stiffness and density, vary discontinuously. In the field, often,there are obstructions to collect seismic data for all source-receiver pairs desirable orneeded for data processing and application of inverse scattering methods. Typically,data are measured on the Earth’s surface. We employ the termdata continuationtodescribe the act of computing data that have not been collected in the field. Seismic dataare commonly modeled by a scattering operator developed in a high-frequency, singlescattering approximation. We initially focus on the determination of the range of theforward scattering operator that models the singular part of the data in the mentionedapproximation. This encompasses the analysis of the properties of, and the constructionof, a minimal elliptic projector that projects a space of distributions on the data acqui-sition manifold to the range of the mentioned scattering operator. This projector canbe directly used for the purpose of seismic data continuation, and is derived from theglobal parametrix of a homogeneous pseudodifferential equation the solution of whichcoincides with the range of the scattering operator. We illustrate the data continuationby a numerical example