A three-dimensional Laguerre one-way wave equation solver

A finite difference algorithm based on the integral Laguerre transform in time for solving a three-dimensional one-way wave equation is proposed. This allows achieving high accuracy of calculation results. In contrast to the Fourier method, the approach does not need to solve systems of linear algebraic equations with indefinite matrices. To filter the unstable components of a wave field, Richardson extrapolation or spline approximation can be used. However, these methods impose additional limitations on the integration step in depth. This problem can be solved if the filtering is performed not in the direction of extrapolation of the wave field, but in a horizontal plane. This approach called for fast methods of converting the Laguerre series coefficients into the Fourier series coefficients and vice versa. The high stability of the new algorithm allows calculations with a large depth step without loss of accuracy and, in combination with Marchuk-Strang splitting, this can significantly reduce the calculation time. Computational experiments are performed. The results have shown that this algorithm is highly accurate and efficient in solving the problems of seismic migration.