Quadratic wavefront and traveltime approximations in inhomogeneous layered media with curved interfaces
Quadratic wavefront and traveltime approximations in inhomogeneous layered media with curved interfaces
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具有弯曲界面的非均匀层状介质中的二次波前和走时近似
DOI：
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发表时间：
1982
期刊：
影响因子：
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通讯作者：
B. Ursin
中科院分区：
文献类型：
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作者：
B. Ursin
给出了由具有弯曲界面的非均匀层组成的三维介质从源区域到接收区域的走时平方的二次逼近。旅行时的平方，作为源和接收者坐标的函数，是围绕参考源和接收者点的泰勒级数展开的。给出了走时参数与射线参数和波前曲率矩阵的关系。与仅在参考源点和参考接收点重合（零偏移近似）的情况下使用源-接收机坐标相比，使用中点、半偏移坐标给出了简化的旅行时间函数。对于具有平面倾斜界面的均匀介质，进一步简化了走时近似。推导出的走时近似对于均匀介质中平面倾斜界面的反射是精确的。tr…的显式表达式
A quadratic approximation for the square of the traveltime from a source region to a receiver region is given for a three‐dimensional (3-D) medium consisting of inhomogeneous layers with curved interfaces. The square of the traveltime, being a function of source and receiver coordinates, is developed in a Taylor series around a reference source and receiver point. The relationships of the traveltime parameters to the ray parameters and the wavefront curvature matrices are shown. Using midpoint, half‐offset coordinates gives a simplified traveltime function compared to using source‐receiver coordinates only in the case that the reference source point and the reference receiver point coincide (zero‐offset approximation). For a medium consisting of homogeneous layers with plane dipping interfaces, the traveltime approximation is further simplified. The derived traveltime approximation is shown to be exact for a reflection from a plane dipping interface in a homogeneous medium. Explicit expressions for the tr...