Application of the Laguerre integral transforms for solving dynamic seismic problems

When solving the forward seismic problems in inhomogeneous media it appeared effective to use algorithms based on a combination of finite integral Fourier, Fourier-Bessel or Legendre transforms along one or two spatial coordinates with the finite difference technique along the remaining coordinate. The development of such an approach for vertically and radially inhomogeneous media was considered earlier, for 2D and 3D inhomogeneous media in. When modeling seismic fields in the media with attenuation the Fourier transform along the temporal coordinate was used, and the obtained boundary problem was solved by the sweep method. In the given paper, the efficiency of application of the Laguerre integral transform along the temporal coordinate for the equations of the first and second order with respect to time is considered. An aspect of exact satisfaction of the initial data for these equations is investigated also. The analytical solution for wave fields propagation in the homogeneous media is obtained. The solution is represented as a series of the Laguerre functions. Advantages of the Laguerre integral transform as compared to the Fourier transform are discussed when solving the forward seismic problems in 2D inhomogeneous media.