Wave-equation time migration

Step 2. Dix conversion

Applying equation 10 for converting RMS velocity $V_0(x_0,t_0)$ to Dix velocity $V_d(x_0,t_0)$ in practice requires special care because of possible noisy measurements. Large variations in RMS velocities produce rapid variations in interval velocities which leads to unstable Dix inversion. It helps to formulate Dix conversion as a linear estimation problem and use regularization for constraining its solution (Clapp et al., 1998; Valenciano et al., 2004; Fomel and Guitton, 2006; Fomel, 2007a). We use least-squares and shaping regularization for stable conversion of RMS velocities to interval velocities.