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研究了抛物方程(PE)远场近似条件及起始场的计算,得到了容许误差和最小参考距离之间的关系。结果表明在最小参考距离以内,PE远场近似条件会通过PE传播算子的传递而引起较大的计算误差,因此,PE传播算子不能用于自起始场的计算。在此基础上,给出了没有远场近似条件限制的传播算子,该算子可以将起始场和远场计算统一起来,便于数值实现。对Pekeris波导的声传播问题(JASA标准PE测试问题)的数值计算结果表明,利用该算子可以精确地计算出PE自起始场和传播损失曲线。
The far field approximation conditions and initial field calculation of parabolic equation (PE) are studied. The relationship between the allowable error and the minimum reference distance is obtained. The results show that within the minimum reference distance, PE far-field approximation conditions will cause large computational errors due to the transfer of PE propagation operators. Therefore, PE propagation operators can not be used in the calculation of self-starting fields. On this basis, the propagator operator without the restriction of far field approximation is given, which can unify the initial field and the far field calculation, which is convenient for numerical realization. The numerical calculation of the acoustic propagation problem of Pekeris waveguide (JASA standard PE test problem) shows that this operator can accurately calculate the PE initial field and propagation loss curve.