The wide-angle PE method is applied to the prediction of sound propagation in a range-dependent environment. The finite-difference model treats the sloping ground by a staircase approximation. The method allows impedance and slope angle variations to be taken into account. The implementation of sloping interfaces in one-way PE models introduces a fundamental problem of energy conservation. This is generated at the lower boundary condition. The ground is assumed to be a locally reacting surface where the ground impedance is defined as the ratio of pressure to the normal component of particle velocity at the surface. The staircase PE method approximates the normal at the slope surface with the vertical component at the stair-step surface. A numerical correction can be included. Using a scale model facility [K. B. Rasmussen, 3617–3620 (1994)], a series of measurements is carried out. The results are compared with the PE calculations. The magnitude of the error due to the interface condition is evaluated.
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机译：广角PE方法应用于范围相关环境中声音传播的预测。有限差分模型通过阶梯近似法处理倾斜地面。该方法允许考虑阻抗和倾斜角变化。单向PE模型中倾斜接口的实现引入了一个基本的节能问题。这是在下边界条件下生成的。假定地面是局部反应表面，其中接地阻抗定义为压力与该表面处粒子速度的法向分量之比。阶梯PE方法在坡面处近似法线，而在阶梯面处垂直分量。可以包括数字校正。使用比例模型工具[K. B. Rasmussen，3617–3620（1994）]，进行了一系列测量。将结果与PE计算进行比较。评估由于界面条件引起的误差的大小。
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