Accuracy-constrained optimisation methods for staggered-grid elastic wave modelling

The classical finite-difference methods for seismic wave modelling are very accurate at low wavenumbers but suffer from inaccuracies at high wavenumbers, particularly at Nyquist wavenumber. In contrast, the optimisation finite-difference methods reduce inaccuracies at high wavenumbers but suffer from inaccuracies at low wavenumbers, particularly at zero wavenumber when the operator length is not long and the whole range of wavenumbers is considered. Inaccuracy at zero wavenumber means that the optimisation methods only have a zeroth-order accuracy of truncation and thus are not rigorously convergent. To guarantee the rigorous convergence of the optimisation methods, we have developed accuracy-constrained optimisation methods. Different-order accuracy-constrained optimisation methods are presented. These methods not only guarantee the rigorous convergence but also reduce inaccuracies at low wavenumbers. Accuracy-constrained optimisation methods are applied to staggered-grid elastic wave modelling.