Inversion Velocity Analysis via Differential Semblance Optimization in the Depth-oriented Extension

Migration velocity analysis (MVA) is an approach to solve a partially linearized variant of the waveform inversion problem, i.e. linear in short scales, nonlinear in long scales. The linear inversion part is often approximated by migration in practice, which is only adjoint of linearized Born modeling operator. In this abstract, we derive the gradient formulas for short scales and long scales separately from the two-term extended waveform inversion objective function, which contains data fitting and differential semblance term. As the reflectivity image inverted by Chebyshev iteration, instead of prestack migration approximation, is used to adjust velocity model, we call this new velocity analysis scheme inversion velocity analysis (IVA). Chebyshev iteration method rather than conjugate gradient method is justified in the derivation of gradient formula of long scales. The corrected gradient calculation is also proved to be more accurate than naive one. In this abstract, we focus on depth-oriented model extension in the acoustic constant density medium, but most of the formulas and algorithms can be extended into other model extensions and more complex medium. Numerical tests on Gaussian anomaly model demonstrates the effectiveness of our proposed method.