基于CPML-RML组合边界条件粘弹TTI介质旋转交错网格有限差分正演模拟  

Rotated staggered grid finite difference forward modeling for wave propagation in viscoelastic TTI media based on CPML-RML combined boundary condition  

(1.中国地质大学(武汉)地球物理与空间信息学院,地球内部多尺度成像湖北省重点实验室,湖北武汉430074;2.中海油研究总院有限责任公司,北京100028)  

(1.Hubei Subsurface Multi-sacle Imaging Key Laboratory,Institute of Geophysics and Geomatics,China University of Geosciences,Wuhan 430074,China;2.CNOOC Research Institute Co.Ltd.,Beijing 100028,China)

实际地下介质中因充满流体、裂缝和裂隙等而同时表现出粘滞性特征和各向异性特征,传统的分裂式完全匹配层(SPML)吸收边界条件不能有效吸收低频和大角度入射波。为此,提出将非分裂式卷积完全匹配层(CPML)吸收边界条件与随机介质层(RML)边界条件相结合的策略来改善边界吸收效果,并将其应用于粘弹TTI介质有限差分正演模拟。为提高正演模拟的稳定性和精度,采用了旋转交错网格有限差分算法,并推导出了适用于粘弹TTI介质的CPML吸收边界条件公式及相应的旋转交错网格有限差分格式;采用随机介质建模理论并结合CPML吸收边界条件,建立了CPML-RML组合边界条件。利用二维均匀介质模型和二维复杂Hess模型对组合边界条件的吸收效果进行了测试,结果表明:相比SPML吸收边界条件与CPML吸收边界条件,CPML-RML组合边界条件在不增加计算量的情况下,具有更好的吸收效果,能有效减少人工边界反射、提高数值模拟精度;粘弹TTI介质中的地震波场表现出明显的振幅衰减和相位延迟,地震记录表现出浅部能量强、深部能量弱的特征,验证了CPML-RML组合边界条件对复杂介质的适应性及正确性。

 

The actual subsurface medium exhibits both viscoelasticity and anisotropy due to fluids,cracks and fissures.Traditional split perfectly matched layer (SPML) absorption boundary condition cannot effectively absorb low-frequency and large-angle incident waves.A strategy combining non-split convolutional perfectly matched layer (CPML) absorbing boundary conditions with random medium layer (RML) boundary condition is proposed,which will be applied to finite-difference forward modeling of viscoelastic TTI media.A rotated staggered grid finite difference algorithm is adopted to improve the stability and accuracy of forward modeling.Meanwhile,a CPML formula for TTI media and the corresponding rotated staggered grid difference format are derived.CPML-RML combined boundary conditions are established by combining stochastic medium theory modeling with CPML.Tests on 2D homogeneous model and Hess model showed that compared with SPML and CPML,CPML-RML combined boundary condition has better absorption effect without increasing the calculation amount,which can effectively reduce artificial boundary reflection and improve the accuracy of numerical simulation.The seismic wave field in viscoelastic TTI media exhibits amplitude attenuation and phase delay.The viscosity of underground media is characterized by strong shallow energy and weak deep energy in seismic records,verifying the adaptability and effectiveness of CPML-RML combined boundary conditions.

 

国家科技重大专项“南海深水区油气勘探地球物理关键技术”(2016ZX05026-001)资助。

 

10.3969/j.issn.1000-1441.2019.02.004