A first comparison of the inverse scattering series non-linear inversion and the iterative linear inversion for parameter estimation

Abstract

The inverse scattering series (ISS) direct non-linear inversion and the iterative linear inversion for parameter estimation are examined and compared. The convergence and the rate of convergence of both the ISS inversion subseries and the iterative inversion method are tested for different velocity contrasts on a simple 1D one parameter acoustic model. The rate of convergence of the ISS inversion method is analytically and numerically studied. When the reflection coefficient R 0.618, the ISS inversion subseries still converges, but not monotonically. Numerical tests show that when the velocity contrast is small, both inversion methods converge and the ISS inversion method converges faster than the iterative inversion method. When the velocity contrast increases, the iterative inversion method will not converge when R > 0.5, while the ISS inversion method always converges.