  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.
