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我们利用动态射线理论计算了当震源和检波器位于同一点时一个弯曲界面的反射响应。这个响应曾经由 Cohen 和 Bleistein 根据 Kirchhoff 近似的赫姆霍尔兹公式和多维稳相法计算过。这种近似曾由 Hilterman 推导过,它还可以用 Hubral 的简单公式计算。射线方法还可以用于近似计算具有复杂构造非均匀介质的反射响应。这种以赫姆霍尔兹积分的 Kirchhoff 近似为基础的方法并不是那么容易做到的。
We use the dynamic ray theory to calculate the reflection response of a curved interface when the source and detector are at the same point. This response was calculated by Cohen and Bleistein based on the Kirchhoff approximation of the Helmholtz equation and the multidimensional stationary phase method. This approximation was derived by Hilterman and can also be calculated using Hubral’s simple formula. The ray method can also be used to approximate the reflection response with heterogeneous media with complex configurations. This method based on Kirchhoff approximation of Herm Holz points is not easy to do.