Least squares staggered-grid finite-difference for elastic wave modelling

Staggered-grid finite-difference (SFD) methods have been used widely in seismic wave numerical modelling and migration. The conventional way to calculate the high-order SFD coefficients on spatial derivatives is the Taylor-series expansion method, which generally leads to great accuracy on just a small frequency zone. In this paper, we first derive the SFD coefficients of arbitrary even-order accuracy for the first-order spatial derivatives by the dispersion relation and the least-squares method, which can satisfy the specific numerical solution accuracy of the derivative on a wide frequency zone. Then we use the SFD coefficients based on the least-squares to solve the first-order spatial derivatives and analyse the accuracy of the numerical solution. Finally, we perform elastic wave numerical modelling with the least-squares staggered-grid finite-difference (LSSFD) method. Meanwhile, the numerical dispersion, the modelling accuracy and the computing costs of the new method are compared with that of the Taylor-series expansion staggered-grid finite-difference (TESFD) method. The numerical dispersion analysis and elastic wavefield modelling results demonstrate that the LSSFD method can efficiently suppress the numerical dispersion and has greater modelling accuracy than the conventional TESFD method under the same discretisations and without extra computing costs.