黏弹性VTI介质中敏感度核函数:地震波复走时关于弹性模量及Q值偏导数的计算

Sensitive kernel of complex traveltime of seismic wave with respect to elastic moduli and Q-factors in viscoelastic VTI media

实际地层中地震波传播普遍存在速度和衰减各向异性现象,研究黏弹各向异性介质中高频地震波传播理论有助于揭示地震波的传播特征.本文针对黏弹性VTI介质,从Christoffel矩阵的解析特征值出发推导出qP、qSV和qSH波的复相速度和复射线速度的解析表达式,并应用实射线追踪方法确定出均匀复射线速度矢量,由此计算出实射线速度和实射线衰减以及实射线品质因子.基于非均匀复相速度和均匀复射线速度的解析表达式,推导了实射线慢度和实射线衰减关于黏弹性模量(包括弹性模量和Q值)的敏感度核函数,该敏感度核函数反映各个黏弹性模量对地震波复走时的影响程度.不同岩石样本的数值计算结果显示,实走时对弹性模量更为敏感,而射线衰减(虚走时)对弹性模量和Q值的敏感程度相当.本研究可为黏弹性VTI介质中地震射线追踪和复走时层析成像提供理论基础.

Anisotropy of velocity and attenuation is often observed in seismic data.Investigation of high-frequency seismic wave propagation in viscoelastic anisotropic media helps understand seismic wave propagation in such media.Based on the analytic eigenvalues of Christoffel matrix for viscoelastic VTI media,we demonstrate the real ray-tracing method to calculate the ray velocity,ray attenuation,and ray quality factor.Then the sensitivity kernels of the real traveltime and imaginary traveltime(attenuation)with respect to elastic moduli and Q-factors are discussed.We apply these theoretical formulas to rock samples.The computational results of the sensitivity kernels indicate that the real traveltime is more sensitive to elastic moduli,while the ray attenuation is almost equally sensitive to elastic moduli and Q-factors.This study can provide the theoretical foundation for seismic ray tracing and traveltime and attenuation tomography in viscoelastic VTI media.