Open Access
 Issue JNWPU Volume 37, Number 5, October 2019 878 - 885 https://doi.org/10.1051/jnwpu/20193750878 14 January 2020

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## 1 抛物方程简介

PE大多情况下使用直角坐标系xyzO下的表达式, 假设电波以向+x方向很小角度方向传播, 那么从二维标量Helmholtz方程推导出的PE在Taylor展开取前2项近似后得到标准抛物方程

## 2 误差分析及复杂环境下的步长选择

### 2.1 SSFT的误差分析

 图 1相对误差与步进步长、频率关系

### 2.2 复杂环境下步长选择

1) 步进步长至少满足对相对误差的要求;

2) 复杂环境等级高, 选择较小步进步长;

3) 复杂环境等级低, 选择较大步进步长。

 图 2不同环境所对应不同步长的传播因子曲线

## 3 仿真实验

### 3.1 仿真条件

1) 地表高程的变化采用如图 3所示的类正弦地形, 地形的变化分布在20~25 km之间。

2) 不同距离范围内, 地表介质变化如表 2所示。

3) 大气环境变化

 图 3不规则地形剖面示意图

### 3.2 仿真结果

 图 4变步长与固定步长在不同水平距离的传播因子曲线

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## All Figures

 图 1相对误差与步进步长、频率关系 In the text
 图 2不同环境所对应不同步长的传播因子曲线 In the text
 图 3不规则地形剖面示意图 In the text
 图 4变步长与固定步长在不同水平距离的传播因子曲线 In the text

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