3D wavefield extrapolation in laterally-varying tilted TI media

We develop a new 3D wavefield-extrapolation method for a transversely isotropic (TI) medium with a symmetry axis. The wavefield extrapolation is done by an implicit isotropic extrapolation operator with an explicit correction operator. The explicit correction is a 2D convolution operator in the space domain, whose coefficients are estimated by a weighted least-squares method in the Fourier domain. The extrapolation operator is stable and suitable for laterally-varying 3D TI media. This new method can be used to extrapolate wavefields in a 3D transversely isotropic medium with a vertical symmetry axis (VTI) in tilted coordinates. We also discuss the effects of the filter length on its accuracy and shorten the filter by changing the least-squares weighting function. We present the impulse response of our algorithm and compare it with the anisotropic phase-shift method.