柱坐标声波方程正演两种PML边界加载方式的对比

Comparation of the Two PML Boundary Conditions for Acoustic Wave Modeling in Cylindrical Coordinates

分析了地震波场模拟中直角坐标系下一阶声压速度方程完全匹配层边界的两种不同的添加方式,讨论了其等价性。进而针对柱坐标系下一阶声压速度方程的特殊形式,推导出在柱坐标系下进行波场模拟的完全匹配层边界的特殊形式,指出柱坐标一阶方程中两种完全匹配层添加方式的不等价性。最后通过数值试验对两种不同的边界条件的实际应用效果进行了比较,结果表明变量复值化这一吸收边界实现方式在相同参数设置下的实际应用效果要优于直接引入衰减系数。

Two implementation approaches of perfectly matched layer （PML） boundary conditions for pressure velocity equation modeling are proved to be equivalent in Cartesian coordinates. According to the particularity of acoustic equation in cylindrical coordinates, PML boundary conditions are then derived into two different formulas in two implementation ways and two different algorithms are presented for acoustic equation modeling in cylindrical coordinates. Numerical simulations are used to compare the practical performances of the two formulas, which indi- cate that the two approaches are in-equivalent. The way of using complex variables shows better behavior than that using direct damping term under the same conditions.