标量波方程广义有限差分正演模拟

Forward modeling of scalar wave equation with generalized finite difference method

常规有限差分法地震波场正演模拟受限于固定的网格步长,不可避免地会出现网格剖分与实际速度界面不一致的情形,进而带来起伏界面处的阶梯状绕射以及反射波旅行时不准确等问题。广义有限差分法是一种无网格方法,它基于泰勒函数展开和加权最小二乘拟合,将微分方程中未知参数的偏导数表示为相邻节点函数值的线性组合,可根据不同地质体模型建立适用的场节点分布形式,克服了传统有限差分法对网格的依赖性。文中采用沿层布置节点的非均匀剖分方法,使生成的节点与起伏的地表或边界贴合。针对不同模型的测试结果表明,广义有限差分法能有效解决虚假反射、反射波旅行时不准确等问题,且具有稳定性。

The forward modeling of seismic wavefields with the conventional finite difference method is constrained by fixed mesh spacing,and thus the mesh subdivision is inevitably inconsistent with the actual speed interface,which brings about problems such as stair diffraction in undulating interface and inaccurate travel time of reflection waves.The generalized finite difference method is a meshless algorithm based on Taylor function expansion and weighted least squares fitting.In this method,the partial derivative of unknown parameters in the differential equation is expressed as a linear combination of the function values of adjacent nodes,and suitable distribution forms of field nodes can be established according to different geological body models.Thus,it overcomes the problem of mesh dependence that the traditional finite difference method faces.In this paper,the non-uniform subdivision method which sets nodes along the layer is applied to make the generated nodes conform to the undulating surface or boundary.The test results of different models show that the generalized finite difference method can effectively solve the problems of the spurious reflection and inaccurate travel time of reflection waves,with stability.