Forward Modeling of the One-Way Acoustic Wave Equation by the Hartley Method

The conventional approach for prestack modeling has been to use a two-way wave equation which unavoidably produces multiple reflections. In this paper, a modeling method based on the one-way wave equation is discussed. In the method, the receivers are assumed buried under the surface only recording primary reflected waves, and the recorded data are extrapolated upward in depth up to the surface. The scheme economically produces synthetic sections containing primary energy only. We perform the depth extrapolations using the split-step operator in the frequency domain, so to provide the synthetic data for evaluating some migration methods or velocity estimation schemes, we can compute a certain frequency band of the data, which would accelerate the algorithm greatly especially when dealing with 3-D data. Furthermore, the split-step operator is developed in terms of the Hartley transforms in place of the Fourier transforms, this leads to a more efficient and economical program. The feasibility of the methods is demonstrated on numerical examples.