Second-Order Approximate Reflection Coefficient of Thin Interbeds with Vertical Fractures
Second-Order Approximate Reflection Coefficient of Thin Interbeds with Vertical Fractures
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DOI：
10.3390/math12020232
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发表时间：
2024-01
期刊：
影响因子：
2.4
通讯作者：
Shiwei Cui;Ya Sun;Pu Wang
中科院分区：
文献类型：
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作者：
Shiwei Cui;Ya Sun;Pu Wang
在上覆岩层的压实作用下，岩层中的水平裂隙闭合，而垂直裂隙广泛发育，可等效为HTI（横向各向同性，具有水平对称轴）介质。当横波传播到HTI介质中时，横波将分为两种类型的波：快横波和慢横波。当HTI地层薄且重叠时，称为薄互层模型，波场表现出复杂的一次反射、转换波和多次波。在薄互层HTI介质中，当入射角小于临界角时，采用递推算法，提出了一种新的全反射系数的二阶近似。通过多次波能量的分析，验证了二阶近似的有效性。将将HTI介质退化为各向同性的二阶近似解与肯内特的精确解进行比较，发现在P波入射时，当入射角小于临界角时，我们的解在任意方位角的精度都超过99.9%.然而，我们的SP波场的解适用于入射方位角在0-75°和120-180°之间，其中最低精度发生在入射角为25°时，相对误差为6.4%。SS波场的近似解与SP波场的近似解具有相同的适用范围，最大误差发生在入射角为1°时，为6.3%。这种新的二阶近似的HTI薄互层的全反射系数公式有助于我们了解复杂薄互层的反射特性。也为岩性、地层油气藏AVO（Amplitude Versus Offset）分析和反演技术的发展奠定了理论基础。
The horizontal fractures in the strata will close in the compaction effect of overlying strata, while the vertical cracks are widely developed, which can be equivalent to HTI (transverse isotropy with a horizontal axis of symmetry) medium. When an S-wave propagates into HTI media, the shear wave will divide into two types of waves: a fast S-wave and slow S-wave. When the strata of HTI are thin and overlapping, called the thin interbeds model, the wave field exhibits complex primary reflections, converted waves, and multiples. We introduce a new second-order approximation of the total reflection coefficient, with the incidence angle lower than the critical angle in thin-interbed HTI media using a recursive algorithm. We verify the effectiveness of the second-order approximation by analyzing the energy of multiples. Comparing the second-order approximate solution that degenerates the HTI medium into isotropic and Kennett’s exact solution, we find that our solution has an accuracy of over 99.9% in any azimuth, with the incidence angle lower than the critical angle under P-wave incidence. However, our solution of the SP wave field is suitable for incidence azimuth angles between 0–75° and 120–180°, with the lowest accuracy occurring at an incidence angle of 25° and a relative error of 6.4%. The approximate solution in the SS wave field has the same applicable range as the SP wave, with the maximum error of 6.3% occurring at the incident angle of 1°. This new second-order approximate formula for the total reflection coefficient of thin interbeds composed of HTI helps us to understand the reflection characteristics of complex thin interbeds. It also lays a theoretical foundation for the development of AVO (Amplitude Versus Offset) analysis and inversion techniques for lithological and stratigraphic oil and gas reservoirs.