A simple approximation to the P-wave reflection coefficient and its implication in the inversion of amplitude variation with offset data
A simple approximation to the P-wave reflection coefficient and its implication in the inversion of amplitude variation with offset data
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DOI：
10.1190/1.1443437
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发表时间：
1993-04
期刊：
影响因子：
3.3
通讯作者：
S. Mallick
中科院分区：
文献类型：
--
作者：
S. Mallick
推导出平面P波反射系数随射线参数变化的近似公式。近似表明，P波反射系数在非垂直入射角下的行为主要由两个参数控制：（1）Rf，流体-流体反射系数（即，当两种介质中的S波速度均设为零时的反射系数）和（2）Δμ/ρ，剪切模量的对比度与平均体积密度的比值。我还证明了由R. Bortfeld和R. Shuey可以近似地从我的公式中推导出来。最后给出数值例子来证明公式的准确性。使用反射系数理论值的最小二乘反演，我证明了在振幅与炮检距数据的线性反演中，Δμ/ρ比泊松比Δσ的对比度更好地估计。最后，将精确反射系数与Shuey近似进行了比较。
I derive an approximate formula for the plane P‐wave reflection coefficient as a function of ray‐parameter. The approximation shows that the behavior of the P‐wave reflection coefficient at nonnormal angles of incidence is mainly controlled by two parameters: (1) Rf, the fluid‐fluid reflection coefficient (i.e., the reflection coefficient when the S‐wave velocities in both media are set to zero) and (2) Δμ/ρ, the ratio of the contrast in shear moduli to the average bulk density. I also show that the other formulas for the P‐wave reflection coefficient given by R. Bortfeld and R. Shuey can be approximately derived from my formula. I give numerical examples to demonstrate the accuracy of the formula. Using a least‐squares inversion of theoretical values for the reflection coefficients, I demonstrate that, in a linear inversion of amplitude versus offset data, Δμ/ρ is better estimated than the contrast in Poisson’s ratio, Δσ. Finally, comparing the exact reflection coefficient with Shuey’s approximation for ...