Abstract
This paper describes numerical experiments for an inverse problem using the spectral and the adjoint variable methods. If the inverse problem is solved based on the adjoint variable method, the state equation which is introduced as the governing equation for the numerical model and the adjoint equation is computed by applying numerical methods. In this study, the spectral method is employed as the computational scheme for the state and the adjoint equations. In case that the spectral method is employed for the computation of the partial differential equation, the accuracy of the solution depends on the wave number. I therefore investigate the dependency of the solution for the wave number by numerical experiments. A waveform inversion problem is employed as the inverse problem.
