中文摘要：

在复杂山地和复杂海底条件下,地表和海底的剧烈起伏对地震波数值模拟提出了更高的要求.常规有限差分法采用矩形网格对模型进行网格剖分,由于矩形网格自身的限制,起伏地表或起伏海底只能由一系列阶梯状折线代替,从而引起人为虚假绕射波.此外,在模拟液-固界面的反射波时,如果界面与网格线不一致,则需要更密的网格才能得到精确的结果.为了解决上述问题,本文将自适应网格生成技术引入到起伏海底速度模型的网格剖分中,采用高阶仿真型有限差分法（MFD）对曲线坐标下的声波方程波进行了数值模拟.利用自适应网格生成技术对速度模型进行网格剖分不仅可以准确地描述模型边界,而且可以有效消除虚假绕射波.高阶仿真型有限差分法可以有效压制频散提高计算精度.模型试算结果表明,本文方法对复杂海底模型具有很好的适应性.

英文摘要：

The drastic fluctuation of the earth′s surface and the sea bottom put forward a higher requirement to the numerical simulation of seismic waves.In the conventional finite difference methods,the rectangular mesh is used to divide the model.However,the rugged sea bottom and earth surface can only be represented by staircase lines,which will causes purious diffractions.Furthermore,when simulating the waves reflected at liquid-solid interfaces,denser meshes are needed to obtain sufficient accurate results for the interface does not coincide with the grid line.Thus,for the conventional finite difference method,denser meshes should be adopted in the whole study region,which will cause the increase of the computational cost and the memory.To solve the above problems,we first introduce the adaptive mesh generation technique to divide the velocity model with rugged sea bottom.Then,we employ high-order mimetic finite difference（MFD）method to simulate the acoustic equation under the curvilinear coordinate system.The adaptive mesh generation technique can not only represent the boundary of the model precisely but also suppress the spurious diffractions effectively.The high-order mimetic finite difference method can suppress the dispersion effectively and improve the computational precision.The numericalresult show that the proposed method has a good adaptability to the complex sea bottom model.