ADI-SGS scheme on ideal magnetohydrodynamics

In this paper, we construct numerical algorithms for the solution of inverse scattering problems in layered acoustic media. Our inverse scattering schemes are based on a collection of so-called trace formulae. The speed c of propagation of sound, the density ρ , and the attenuation γ are the three parameters reconstructed by the algorithm, given that all of them are laterally invariant. For a medium whose parameters c , ρ , and γ have m ⩾ 1 continuous derivatives, and data measured for frequencies between 0 and a > 0 , the error of our scheme decays as 1 / a m - 1 as a → ∞ . In this respect, the algorithm is similar to the Fourier Transform. Our results are illustrated with several numerical examples.