刘财^1,2,3,4,,
胡宁^1,,,
郭智奇¹,
罗玉钦¹
1. 吉林大学地球探测科学与技术学院, 长春 130026
2. 吉林大学应用地球物理实验教学中心, 长春 130026
3. 吉林大学地质资源立体探测虚拟仿真实验教学中心, 长春 130026
4. 国土资源部应用地球物理重点实验室, 长春 130026

基金项目: 国家自然科学基金重点项目（41430322，41430322）、中央高校基本科研业务费专项资金和吉林大学高层次科技创新团队建设项目联合资助


详细信息

作者简介: 刘财, 男, 1963年生, 教授, 博士生导师, 主要从事地震波场正反演理论和综合地球物理等研究.E-mail:liucai@jlu.edu.cn

通讯作者: 胡宁, 男, 1987年生, 博士研究生, 主要研究方向为复杂介质弹性波传播机理.E-mail:jluhooning@163.com

中图分类号: P631

收稿日期:2018-02-01
修回日期:2018-04-12
上线日期:2018-06-05

Numerical simulation of the wavefield in a viscous fluid-saturated two-phase VTI medium based on the constant-Q viscoelastic constitutive relation with a fractional temporal derivative

LIU Cai^1,2,3,4,,
HU Ning^1,,,
GUO ZhiQi¹,
LUO YuQin¹
1. College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China
2. Central Lab of Applied Geophysics, Changchun 130026, China
3. Virtual Simulation Experiment Teaching Center of Stereo-Exploration of Geological Resource, Changchun 130026, China
4. Key Laboratory of Applied Geophysic, Ministry of Land and Resources, Changchun 130026, China


More Information

Corresponding author: HU Ning,E-mail:jluhooning@163.com

MSC: P631

--> Received Date: 01 February 2018
Revised Date: 12 April 2018
Available Online: 05 June 2018


摘要
摘要:分数阶微分算子具有描述历史依赖性和全域相关性的特质，本文利用这种特质描述双相介质固体骨架的黏弹性特征.基于Kjartansson常Q理论将含有分数阶时间导数的黏弹固体骨架各向异性本构关系与双相介质理论有机地结合起来，并引入流变学本构关系描述孔隙流体的黏滞性力学行为，提出一种新的基于分数阶时间导数常Q黏弹本构关系的含黏滞流体双相VTI模型.推导了相应的时间域波传播方程，然后对该方程进行了数值模拟.对整数阶导数采用高阶交错网格有限差分算法，对分数阶时间导数采用短时记忆中心差分算法，进行了不同相界、不同品质因子组及双层地质结构情况下该类介质中波场的数值模拟与特征分析.模拟结果表明：将含有分数阶时间导数的常Q黏弹固体骨架各向异性本构关系及孔隙流体的黏滞性本构关系引入双相介质理论是可行的，二者的结合能更好地反映地下介质的黏弹性特征，对于进一步认识波在黏弹各向异性孔隙介质中的传播机理具有重要意义，为反演和重构地下油气储层和结构奠定正演理论基础.
关键词: 常Q黏弹本构关系/
分数阶时间导数/
双相介质/
各向异性/
短时记忆

Abstract:Fractional differential operators have the trait of describing historical dependence and global correlation.In this paper, we use this trait to describe the viscoelastic characteristics of a two-phase solid matrix.Based on the Kjartansson constant-Q model theory, the anisotropic constitutive relation of the viscoelastic solid skeleton with fractional temporal derivative is combined with the two-phase medium theory, and the rheological constitutive relation is introduced to describe the viscous mechanical behavior of the pore fluid.A new VTI model of a vicious fluid-saturated two-phase VTI medium based on the constant-Q viscoelastic constitutive relation with a fractional temporal derivative is proposed, and the corresponding wavefield propagation equation is deduced in the time domain.In numerical simulation, the finite difference method on a high-order staggered grid is used for the integer order derivative, and the short time memory center difference algorithm is employed to discretize the fractional order temporal derivative.Following the equations, the wavefield in this medium model is simulated for different phase boundaries, different Q values, and a two-layer structure, and then the wavefield features are analyzed.The results of numerical modeling indicate that it is feasible to introduce the constant-Q viscoelastic solid anisotropic constitutive relation containing a fractional temporal derivative and the viscous constitutive relation of the pore fluid into the two-phase medium theory, and the combination of both the relations can better reflect the viscoelastic characteristics of the underground medium.These results are of importance for further understanding the propagation mechanism in a viscoelastic anisotropic porosity medium, and provide a theoretical basis for inversion and reconstruction of underground oil and gas reservoirs and structures.
Key words:Constant-Q viscoelastic constitutive relation/
Fractional temporal derivative/
Two-phase medium/
Anisotropic/
Short memory



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