Quasi-P wave forward modeling in viscoelastic VTI media in frequency-space domain

The finite difference is an important method of wavefield numerical simulation. It can calculate recursively by time slice, and the round-off errors of each time slice may accumulate to the next time slice in time domain, eventually, which will lead to too large accumulated error when the time slice is enough. However, solving all equation set in frequency domain is based on the frequency slice on the space grid, whose error is assigned to each grid point, it is without accumulated error and easier to simulate the attenuation of the viscoelastic anisotropic media in frequency-space domain. In order to overcome the numerical dispersion of routine finite-difference operators, 25-point optimized finite-difference operators are applied. This paper derives firstly the formula of quasi-P wave in viscoelastic VTI media in frequency-space domain, and then constructs the difference format using 25-point optimized finite difference operators, so it implements forward modeling. A case study of fault model compares and analyzes the crosswell seismic quasi-P wavefield stimulated with the finite difference method for both elastic VTI media and viscoelastic VTI media. In the end, it comes to the conclusion that the amplitude of seismic wave is relatively smaller and the main frequency is decreased in viscoelastic media.