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通过将地震波位移运动方程变换至Hamilton体系,引入广义动量和广义坐标,并定义系统动能和势能的Lie算子,构造了一类新的适用于高效长时间地震波模拟的二阶辛格式,同时将此格式用Baker-Campbell-Hausdorff(BCH)公式展开,基于截断误差原理极小得到了三组优化系数.在与常见辛格式对比中,从理论上和数值实验中分析了本文构造的这类优化二阶格式高精度高效率性;在与经典Newmark格式对比中,从长时间计算角度论证了本文格式具有长时间地震波计算能力;在非均匀介质地震波模拟中,本文格式与三阶辛格式得到了一致的地面合成地震记录和单道地震记录.
A new kind of second-order symplectic scheme suitable for high-efficiency long-term seismic wave simulations is constructed by transforming the motion equation of seismic wave into Hamiltonian system, introducing generalized momentum and generalized coordinates, and defining Lie operator of system kinetic energy and potential energy. Simultaneously, This format is developed by the Baker-Campbell-Hausdorff (BCH) formula, and three optimization coefficients are obtained based on the principle of truncation error. In comparison with the common symplectic scheme, this kind of optimization constructed in this paper is analyzed theoretically and numerically Second-order format, high-precision and high-efficiency. Compared with the classical Newmark format, this paper proves that the proposed scheme has the ability of long-term seismic wave calculation in long-term calculation. In the case of inhomogeneous seismic wave simulation, Consistent ground synthetic seismograms and single-channel seismograms.