DESCRIPTION OF THE FIVE INTERPOLATION METHODS

The formula for Stolt migration is

$$model(x,z)=2DFT^{-1}\{data[k_x,\omega(k_x,k_z) ] \frac{d\omega} {dk_z}\}$$ (1)

We first Fourier transform the data set in the (t,x) domain into the $(\omega,k_x)$ domain, then map $\omega$ into k_z by the dispersion relation as follows:

$$k_z=\sqrt{\frac{\omega^2}{v^2} -{k_x}^2}$$ (2)

In this mapping step, we need to use an interpolation operator because of the discrete Fourier transform. Finally, we inverse Fourier transform the data in the (k_z,k_x) domain back to the (z,x) domain.

To compare the five interpolation methods, we implement them in a Stolt migration of three impulses at different depths in anelliptic anisotropy media Dellinger et al. (1993), which causes triplication at the corners of each impulse response. We use the same synthetic data and parameters for each interpolation method in order to compare the results of different interpolators.