An improved algorithm of the fourth-order Runge-Kutta method and seismic wave-field simulation
四阶龙格-库塔方法的一种改进算法及地震波场模拟

In this article, we present an improved algorithm of the fourth-order Runge-Kutta (RK) method to solve the wave equations. We first change the original fourth-order Runge-Kutta method into a 2-stage scheme, and then introduce a weighting parameter in the first stage to obtain a weighted scheme. To study this new improved method, first of all, we analyze its stability condition for 1D and 2D cases. Secondly, we derive the dispersion relation for 1D problem and give the numerical dispersion results, and compare the method against the fourth-order Lax-Wendroff correction (LWC) and the displacement-stress staggered-grid methods. Thirdly, for 2D case we use the improved RK, LWC and staggered-grid methods to simulate the acoustic wave fields, and present some comparisons of the computational efficiency and numerical results for different methods. Finally, two layered-medium models are further selected to investigate the computational validity of the acoustic and elastic wave-field simulations. These numerical results show that the improved method has weak numerical dispersion, high computational efficiency, and great potentiality of application in seismic exploration.