利用非线性最优化方法构建近似常Q黏弹模型

Constructing nearly constant-Q viscoelastic model using the nonlinear optimization method

目前通常采用的黏弹模型在描述介质品质因子对频率的依赖关系方面存在不足。基于广义标准线性固体,利用黏声或黏弹介质的品质因子公式建立超定非线性方程组,采用属于非线性最优化方法的Levenberg-Marquarat算法求解方程组来拟合近似常Q模型,并模拟二维均匀模型的地震响应,简要考察黏弹性的影响。该方法不用任何近似或假设,所得结果更精确,而且可以求解病态问题。拟合及模拟结果表明:Levenberg-Marquarat方法可以较精确地构建近似常Q模型,采用两个组元就已足够;黏弹性对地震波的振幅和频谱有显著影响,实际应用中应当考虑。

Current viscoelastic models have shortage in describing the relation between quality factor Q and frequency. Based on the generalized standard linear body, over-determined system of nonlinear equations was established using the Q formula of viscoacoustic/viscoelastic media and the Levenberg-Marquarat algorithm. The Levenberg-Marquarat algorithm being a nonlin- ear optimization method was adopted to directly compute the relaxation time to fit the nearly constant Q model. The seismic response of 2D homogeneous model was computed to investigate the effect of viscoelasticity briefly. This method does not involve any approximations or assumptions, so the results are more accurate. The ill-posed problems can also he solved by this method. The fitting and simulation results show that Levenberg-Marquarat algorithm can construct nearly constant Q model more accurately with only two elements. Viscoelasticity has a remarkable effect on the amplitude and frequency spectrum of seismic wave, and should be considered in practical applications.