A study of Fresnel volume under a curved interface based on grid traveltime computation
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摘要:
为了研究弯曲界面曲率变化对分辨率的影响，首先推导了垂直入射下来自弯曲界面的反射波和透射波界面菲涅尔带近似的解析公式，证明了公式中曲率为零恰好对应已经被推导的平界面菲涅尔带的解析公式，然后给出了利用网格走时计算方法计算弯曲界面下反射波和透射波菲涅尔体的数值实现策略，这一实现策略同时保证了网格走时计算的精度和菲涅尔体计算的精度，最后对比了不同弯曲界面（不同曲率）下的菲涅尔体相对于平界面（曲率为零）下菲涅尔体的变化.研究结果表明，界面下高速时，向斜弯曲造成菲涅尔体在界面附近变宽，使得分辨率降低；背斜弯曲造成菲涅尔体在界面附近变窄，使得分辨率提高.并且向斜弯曲对分辨率的影响程度要明显大于背斜弯曲.而界面下低速时，结论正好相反.
Abstract:In order to study the influence of the curvature of a curved interface on resolution, we deduce the approximate analytic formulas of Interface Fresnel Zone for reflected and transmission waves from a curved interface. Then we verify these formulas correspond to those from a planar interface which are already derived by others when the curvature in our formulas equals zero. At the same time, we develop a numerical method to compute the Fresnel volume for reflection and transmission under a curved interface based on grid traveltime computation, with the accuracy of grid traveltime computation and Fresnel volume acceptable. Finally, we compare these Fresnel volumes under different curved interfaces with a Fresnel volume under a planar interface whose curvature equals zero. Computational results show that a syncline-curved interface makes Fresnel volume wider near the interface than a planar interface and lowers the resolution, while an anticline-curved interface makes Fresnel volume narrower near the interface and enhances the resolution, with high speed under the interface. Moreover, the influence of a syncline-curved interface on resolution is obviously greater than that of an anticline-curved interface. The conclusion is opposite, with low speed under the interface.
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Key words:
- Traveltime computation /
- Fresnel volume /
- Interface Fresnel Zone /
- Curvature /
- Resolution
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图 10
反射波界面菲涅尔带(IFZ)随界面曲率的变化
Figure 10.
IFZ for reflection from a curved interface changing with different curvatures
图 12
透射波界面菲涅尔带(IFZ)随界面曲率的变化
Figure 12.
IFZ for transmission from a curved interface changing with different curvatures
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