Kelvin-Voigt黏弹性介质井孔声场有限差分数值模拟与波形特征  

Numerical Simulation and Waveform Characteristics of Borehole Acoustic Field in Kelvin-Voigt Viscoelastic Medium Well

作　　者：岳崇旺[1] 王祝文[2] Yue Chongwang;Wang Zhuwen(College of Geological Engineering&Surveying,Chung'an University,Xi’an 710054,China;College of GeoExploration Science and Technology,Jilin University,Changchun 130026,China)

机构地区：[1]长安大学地质工程与测绘学院,西安710054 [2]吉林大学地球探测科学与技术学院,长春130026

出　　处：《吉林大学学报（地球科学版）》2021年第4期1268-1275,共8页Journal of Jilin University：Earth Science Edition

基　　金：国家自然科学基金项目(41874135,41504090)。

摘　　要：岩石介质具有黏滞性,黏弹性介质模型相对于弹性介质模型更为接近岩石介质的真实情况。根据Kelvin-Voigt黏弹性单元体模型本构关系,推导了柱坐标系下各向同性黏弹性介质时间域交错网格有限差分方程,进行了黏弹性介质井孔声场的数值模拟。模拟结果表明:品质因子和声源中心频率对黏弹性介质中的井内外声场均有影响:井外声场和井内声场的衰减均随品质因子的增大而减小,井外声波和井内反射波振幅随之增大;井外声场的衰减随声源中心频率的增大而减小,井外声波振幅随之增大,井内声场的衰减随声源中心频率的增大而增大,井内反射波振幅随之减小。The rock medium has viscous properties, and the viscoelastic medium model is closer to the real situation of the rock medium than the elastic medium model. According to the constitutive relationship of the Kelvin-Voigt viscoelastic element model, the staggered grid finite difference equations of the viscoelastic isotropic medium in the cylindrical coordinate system are derived, and the numerical simulation of acoustic field of the wellbore in viscoelastic medium are completed. The simulation results show that the rock quality factor and the acoustic source center frequency have effects on the acoustic field inside and outside the well in the viscoelastic medium: The attenuation of the acoustic field outside and inside the well decreases with the increase of the quality factor, and the wave amplitude outside the well and the reflected wave amplitude increase accordingly;The attenuation of the acoustic field outside the well decreases with the increase of the source center frequency, and the wave amplitude outside the well increases accordingly;The attenuation of the acoustic field in the well increases with the increase of the source center frequency, and the wave amplitude in the well decreases accordingly.

关 键 词：Kelvin-Voigt模型 黏弹性介质 交错网格有限差分 井孔声场 波形特征 

分 类 号：P631.8[天文地球—地质矿产勘探]