基于流变体模型的波恩近似方程地震正演模拟

The seismic forward modeling using Born approximation equation based on rheological body

常规τ值法假设应力松弛时间与应变延迟时间近似相等,造成了常Q模型拟合精度低.本文利用精确的广义流变体模型Q值计算公式,研究改进的τ值法求解常Q模型参数.根据地震波散射理论,推导了基于广义流变体模型的黏滞性介质一阶波恩近似方程,结合位移-速度关系得到了含卷积完全匹配层边界条件的黏滞性介质应力-速度方程的一阶波恩近似表达式.通过数值实验验证并对比了黏滞性介质中全波波动方程、一阶波恩近似方程以及单程波波动方程的波场特征,讨论了基于流变体模型的黏滞性介质一阶波恩近似方程对速度扰动和Q扰动的适应性,以及对旅行时和振幅精度的影响.

The conventionalτmethod assumes that the stress relaxation time is approximately equal to the strain delay time,leading to the constant Q model with low precision.In this study,an improvedτmethod is proposed by an accu-rate equation of Q value based on generalized rheological body so as to solve the parameters of constant Q model.According to the seismic wave scattering theo-ry,the first-order Born approximation equation in viscoacoustic media is derived based on generalized rheological body and then the first-order Born approxima-tion of stress-velocity equation is obtained for the viscoacoustic media with con-volutional perfect matched layer （CPML ） boundary.The wave fields and records are compared through numerical simulation by full wave equation,first-order Born approximation equation and one-way wave equation.And it is also discussed that the precision of travel time and amplitude of the seismic wave obtained by the viscoacoustic first-order Born approximation equation with velocity perturbation and Q perturbation.