各向异性黏弹性介质波场数值模拟
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摘要
地层不仅表现为各向异性,还表现为内在的黏弹性特征.为准确描述地震波在地球介质中的传播特征,选取的模型应该能够模拟岩石的各向异性特征和衰减特征.基于玻尔兹曼叠加原理,考虑本构方程,建立二维黏弹性VTI介质的波动方程及其差分格式,利用交错网格有限差分法分别对弹性和黏弹性VTI介质进行数值模拟,并且分析不同品质因子组合对波场能量衰减和频率吸收作用的影响.数值模拟结果表明:膨胀滞弹性形变的品质因子主要影响qP波衰减,并且品质因子越小,qP波衰减越大;剪切滞弹性形变的品质因子主要影响qSV波的能量衰减,并且品质因子越小,qSV波衰减越大;各向异性黏弹性中qP波、qSV波主频向低频方向移动,高频吸收明显,有效频带变窄.
In view of the fact that layers not only show anisotropic behavior,but also show intrinsic viscoelastics,thus an accurate description of wave propagation in earth medium requires a model that accounts for the anisotropic and viscoelastic behavior of rocks. This paper established a wave equation and the difference scheme of 2D viscoelastic VTI media based on the Boltzmann superposition principle,starting from the constitutive equations. The simulation wave field propagation in elastic and viscoelastic VTI medium used grid high order finite difference,and compared and analyzed the effects of energy attenuation and frequency absorption related to different Q factor pair. The results of numerical simulation show:the Q factor related to dilation inelastic deformation affects energy attenuation of qP wave,and the smaller the Q factor is,the greater the qP-wave attenuation. The Q factor related to shear inelastic deformation affects energy attenuation of qSV wave,and the smaller the Q factor,the greater the qSV-wave attenuation. While the frequency of qP wave and qSV wave in the anisotropic viscoelastic tend to be of low frequency,absorption of high frequency is obvious and the effective frequency band narrows. The research work is useful for further understanding of seismic wave propagation in anisotropic viscoelastic media.
In view of the fact that layers not only show anisotropic behavior,but also show intrinsic viscoelastics,thus an accurate description of wave propagation in earth medium requires a model that accounts for the anisotropic and viscoelastic behavior of rocks. This paper established a wave equation and the difference scheme of 2D viscoelastic VTI media based on the Boltzmann superposition principle,starting from the constitutive equations. The simulation wave field propagation in elastic and viscoelastic VTI medium used grid high order finite difference,and compared and analyzed the effects of energy attenuation and frequency absorption related to different Q factor pair. The results of numerical simulation show:the Q factor related to dilation inelastic deformation affects energy attenuation of qP wave,and the smaller the Q factor is,the greater the qP-wave attenuation. The Q factor related to shear inelastic deformation affects energy attenuation of qSV wave,and the smaller the Q factor,the greater the qSV-wave attenuation. While the frequency of qP wave and qSV wave in the anisotropic viscoelastic tend to be of low frequency,absorption of high frequency is obvious and the effective frequency band narrows. The research work is useful for further understanding of seismic wave propagation in anisotropic viscoelastic media.
引文
[1]刘莲莲.各向异性黏弹性孔隙介质伪谱法波场正演模拟[D].北京:中国石油大学,2007.
[2]杜启振,王延光,付水华.方位各向异性黏弹性介质波场数值模拟[J].地球物理学进展,2006,21(2):502-504.
[3]刘财,张智,邵志刚,等.线性黏弹体中地震波场伪谱法模拟技术[J].地球物理学进展,2006,21(2):360-369.
[4]杜启振,杨慧珠.方位各向异性黏弹性介质波场有限元模拟[J].物理学报,2003,52(8):2010-2015.
[5]谭末一,赵兵,张中杰.黏弹性VTI介质地震波模拟特征分析[J].地球物理学进展,2007,22(4):1305-1311.
[6]单启铜,乐友善.PML边界条件下二维黏弹性介质波场模拟[J].石油物探,2007,46(2):126-130.
[7]牟永光,裴正林.三维复杂介质地震数值模拟[M].北京:石油工业出版社,2005.
[8]瑞克.N.H.黏弹性介质中的地震波[M].许云,译.北京:地质出版社,1981.
[9]周光泉,刘孝敏.黏弹性理论[M].合肥:中国科技大学出版社,1988.
[10]Carcione J M.Attenuation and quality factor surfaces in anisotropic viscoelastic media[J].Mechanical of Material,1995,19(2):311-327.
[11]杜启振,杨慧珠.具有水平对称轴的横向各向同性线性黏弹性介质波场特征[J].石油大学学报:自然科学版,2003,27(1):14-18.
[12]尹陈.地震波衰减与流体预测研究[D].成都:成都理工大学,2008.
[13]Carcione J M.Wave fields in real media:Wave propagationin anisotropic,an elastic and porous media[M].American:Elsevier Sci-ence Ltd,2001.
[2]杜启振,王延光,付水华.方位各向异性黏弹性介质波场数值模拟[J].地球物理学进展,2006,21(2):502-504.
[3]刘财,张智,邵志刚,等.线性黏弹体中地震波场伪谱法模拟技术[J].地球物理学进展,2006,21(2):360-369.
[4]杜启振,杨慧珠.方位各向异性黏弹性介质波场有限元模拟[J].物理学报,2003,52(8):2010-2015.
[5]谭末一,赵兵,张中杰.黏弹性VTI介质地震波模拟特征分析[J].地球物理学进展,2007,22(4):1305-1311.
[6]单启铜,乐友善.PML边界条件下二维黏弹性介质波场模拟[J].石油物探,2007,46(2):126-130.
[7]牟永光,裴正林.三维复杂介质地震数值模拟[M].北京:石油工业出版社,2005.
[8]瑞克.N.H.黏弹性介质中的地震波[M].许云,译.北京:地质出版社,1981.
[9]周光泉,刘孝敏.黏弹性理论[M].合肥:中国科技大学出版社,1988.
[10]Carcione J M.Attenuation and quality factor surfaces in anisotropic viscoelastic media[J].Mechanical of Material,1995,19(2):311-327.
[11]杜启振,杨慧珠.具有水平对称轴的横向各向同性线性黏弹性介质波场特征[J].石油大学学报:自然科学版,2003,27(1):14-18.
[12]尹陈.地震波衰减与流体预测研究[D].成都:成都理工大学,2008.
[13]Carcione J M.Wave fields in real media:Wave propagationin anisotropic,an elastic and porous media[M].American:Elsevier Sci-ence Ltd,2001.
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