均匀介质、复杂各向同性介质和各向异性介质中的地震波传播过程 ,可用统一形式的标量声波方程描述 .考虑到在无损耗条件下 ,地震波方程描述了地震波场这一个无穷维的哈密顿体系随时间的演化过程 ,该过程为一个单参数连续辛变换 ,因而可以在其哈密顿形式表述下导出其辛格式 .与显式辛算法相比 ,隐式辛格式对应的隐式辛几何算法具有无条件稳定的特点 ,可以允许较大的计算步长 .但是由于隐式算法不可避免地面临高阶矩阵的求逆 ,其每一步的计算速度较慢 .为实现矩阵快速求逆 ,文中采用了螺旋边界条件下谱因式分解的方法 .在螺旋边界条件下 ,需要求逆的矩阵化为带状矩阵 ,而且其各列非零元素的位置和大小具有非常好的相似性 ,因而可以采用谱因式分解的方法实现快速LU分解 .文中采用二阶精度的隐式蛙跳辛格式和谱因式分解方法 ,计算了常速度、层状介质和Marmousi模型中的波场 .计算表明 ,隐式辛算法不失为波场计算的一种好方法 The propagation of seismic waves in homogeneous medium, complex isotropic medium and anisotropic medium can be described by a uniform form of scalar sound wave equation. Considering that under the condition of no loss, the seismic wave equation describes an infinite dimension Hamiltonian of seismic wave field Compared with the explicit symplectic algorithm, implicit symplectic symplectic symplectic symplectic algorithm has the following properties: (1) Because of the unconditional stability, larger computational steps can be tolerated, but implicit algorithms are inevitably subject to high-order matrices for each step of the calculation .In order to achieve fast matrix inversion, a spiral The method of spectral factorization under the boundary condition, under the helical boundary conditions, the inverse matrix matrix is ​​required to be a strip matrix, and the positions and sizes of non-zero elements in each column have very good similarity, Decomposition of the method to achieve rapid decomposition of LU.This paper uses implicit leapfrog Symplectic Scheme and spectral factorization method of second order precision, Wavefield layered medium and Marmousi model calculation shows that a good way wavefield calculation algorithm may well be implicit oct