Wave-equation-based redatuming is expensive and requires a detailed knowledge of the shallow velocity field. We derive the analytical expression of a new prestack wavefield extrapolation operator, the Topographic Datuming Operator (TDO), which applies redatuming based on straight-rays approximation above and below a chosen datum. This redatuming operator is directly applied to common-source gathers to downward continue the source and the receivers, simultaneously, to the datum level without resorting to common-receiver gathers. As a result, the method is far more efficient and robust than the conventional wave-equation-based redatuming and does not require an accurate depth-domain interval velocity model. In addition, TDO, unlike wave-equation-based redatuming, requires effective velocities above datum, and thus can be applied using attributes valid for static correction methods. Effective velocities beneath the datum permit us to replace the surface integral, which is needed for wave-equation redatuming with a line integral. In the particular case of infinite (in practice, very high with respect to the shallow layers) velocity beneath the datum, the TDO impulse response collapses to a point, and TDO redatuming is equivalent to conventional static correction, which may, therefore, be regarded as a special case of the newly derived operator. The computational cost of applying TDO is slightly larger than static corrections, yet provides higher quality results partially attributable to the ability of TDO to suppress diffractions emanating from anomalies above datum. Since TDO is an operation based on geometrical optics approximation, velocity after TDO is not biased by the vertical shift correction associated with conventional static correction. Application to a synthetic data set demonstrates the features of the method.