优化的近似解析离散化（ONAD）方法是近年来发展的一种新的数值方法。与广泛应用的有限差分方法相比，这种方法充分利用了位移梯度所包含的波场信息，使得该方法在粗网格条件下或介质速度反差较大时能够有效地压制数值频散。本文将ONAD方法推广到球坐标系下，给出了求解球坐标系下SH波方程的ONAD方法。为了调查球坐标系下该算法的精度和计算效率，本文选取均匀介质模型和IASP91非均匀介质模型进行数值模拟实验，分别给出了ONAD方法、精确解以及高阶Lax-Wendroff修正（LWC）方法的模拟结果，并进行了比较。结果表明，ONAD方法在求解球坐标系下SH波方程时具有弱数值频散、储存量小以及计算速度快的优点。作为应用，本文模拟了SH波在地表和地幔边界（CMB）之间的传播，得到了不同时刻的波场快照和合成地震记录，并对波场快照和地震记录进行了分析。

The optimal nearly-analytic discrete (ONAD) method is a new numerical method developed in recent years for solving the wave equation. Compared with other methods，such as finite-difference methods used popularly, the ONAD method can effectively suppress numerical dispersion when coarse grids are used. In this paper, the ONAD method is extended to solve the SH wave equation in spherical coordinates. To investigate the accuracy and the efficiency of the ONAD method, this paper compares the results simulated by the ONAD method and other methods for homogeneous model and inhomogeneous IASP91 model. The comparisons indicate that the ONAD method can suppress the numerical dispersion effectively. On the other side, the ONAD method requires less computation storage and has the advantage of fast calculation. As an application, we use the ONAD method to simulate the SH wave propagation in Earth’s surface and the core mantle boundary. Meanwhile, we analyze the SH wave propagating in the heterogeneous medium through the snapshots and synthetic seismograms.