The double-square-root (DSR) equation can be viewed as a Hamilton-Jacobi equation describing kinematics of downward data continuation in depth. It describes simultaneous propagation of source and receiver rays which allows computing reflection wave prestack traveltimes (for multiple sources) in a one run thus speeding up solution of the forward problem. Here we give and overview of different alternative forms of the DSR equation which allows stepping in two-way time and subsurface offset instead of depth. Different forms of the DSR equation are suitable for computing different types of waves including reflected, head and diving waves. We develop a WENO-RK numerical scheme for solving all mentioned forms of the DSR equation. Finally the extended exploding reflector concept can be used for computing prestack traveltimes while initiating the numerical solver as if a reflector was exploding in extended imaging space.