滑动最小二乘法求解地震波波动方程

本文首次将固体力学领域中的滑动最小二乘拟合法用于求解地震波波动方程.与有限差分法相比，该方法所采用的拟合思想使得解在全空间域更加连续，同时仍然保持高精度的特性；与有限元法相比，该方法绕过变分原理，经过算法的有限差分化之后，其所需的计算量及数据存储量均可大大降低.薄膜震动的数值算例表明了该方法的上述特点.最后，通过对几个模型的合成地震模拟试验，进一步证明了滑动最小二乘法用于波动方程数值模拟的可行性.

Solving seismic wave equation by moving least squares (MLS) method

In this paper,the moving least squares(MLS) fitting criterion commonly used in solid mechanics is discussed for solving seismic wave equations.The fitting in MLS instead of interpolation in finite difference method(FDM) makes the solution more continuous in the whole space domain without any loss of accuracy.On the other hand,although the absence of variational principle which is necessary in finite element method(FEM) save little computational volume,the cost could further be cut down greatly by a differentiated method.An example of vibrant film shows the merits of the MLS method.Furthermore,some synthetic seismograms obtained by MLS method prove its effectivity for wave equation seismic modeling.