Fast Computation of Traveltimes for Multifold Seismic Data Solving the Double-Square-Root Eikonal Equation

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 traveltimes for the whole multifold acquisition in a one run. We also address an alternative form of the DSR equation which allows stepping in two-way time rather than in depth. We develop a WENO-RK numerical scheme for solving both forms of the DSR equation. The numerical scheme was also developed for curvilinear coordinates which allows traveltime computations for meshes fitting surface topography as well as the topography of interfaces which produce reflected and head waves. 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. The DSR equation is solved numerically providing all prestack traveltimes in one run which should be faster than computing traveltimes shot by shot. We plan to use this numerical scheme for speeding up forward modeling for iterative kinematic inversion of prestack data. One possible application can be migration velocity analysis based on picking residual moveouts in common-image gathers.