Second-order Central Difference Finite-difference Wave Equation Datuming Formulation

Several methods of referencing seismic reflection data to a new datum have been researched and presented in the literature, that differ in the approach used to implement the calculation of datumed wavefields. The implementation time determines, in part, the efficiency of such a method. In this paper, a simple finite-difference approach for extrapolating seismic data from one datum to another for seismic near-surface irregularity correction is derived. Kirchhoff’s integral forms the basis on which the formulation is based. The Kirchhoff summation method is used, in a novel way, in agreement with summation theory by considering a single trace as an input wavefield to the algorithm. The approach is considered time-saving in computing the output wavefields as only a single trace serves as an input in any occasion of producing every output trace. For prestack data, the method consists of two steps; calculating the wavefields referenced to the output datum for a source and receivers and time- shifting the resulting data along the mean travel-time ray paths. The algorithm is successfully applied to real data and synthetic shot gathers. For a horizontally layered earth model with a planar surface, mathematical analysis shows that the gradient of the locus of the reflection travel time increases with offset, for a shot-on-end reflection profiling, in conformity with the synthetic data obtained for such a model. In the said analysis, considering parabolic, hyperbolic, and nonhyperbolic travel-time approximations, the gradient forms a useful tool for normal moveout velocity determination. The implementation of the algorithm on field data samples suppressed coherent noise, including the long-wavelength type such as ground roll, in contrast with the static correction method. The normal moveout corrections show that shift along ray-path produced less normal moveout stretch than shift along vertical for near-surface events for the same normal moveout parameters.