【摘要】 总结了牛顿类地震反演方法中Hessian算子的作用,对其在地震反演成像中的数学物理含义进行了分析.Hessian算子是误差泛函对模型参数的二阶导数,反映了误差泛函对模型变化的二次型特征.分析声波方程下的Hessian算子的格林函数表达形式,发现其表达了整个观测系统和子波频带等因素对地震数据空间到模型空间投影过程的影响.提出了两种分别适用于最小二乘偏移和全波形反演的Hessian算子简化格式.平面波Hessian算子应用于最小二乘偏移能够得到相对保真的成像结果,改善了地震偏移成像的精度.地下偏移距Hessian算子应用于全波形反演能够加快反演迭代的计算效率.最后,对Hessian算子在地震反演成像中的价值进行了讨论和评价.更多还原

【Abstract】 In this paper,we summarize the influence of Hessian operator in seismic inversion methods and review the mathematical and physical meanings of the Hessian operator in the seismic inversion imaging.Hessian operator is the second derivation of the misfit function to the seismic model parameters.It can be seen by analyzing its Green’s function formulation under the acoustic wave approximation that the Hessian reflects the effects of the seismic acquisition system and wavelet frequency band during the projection of information from the data spaces to the model spaces.We propose two pseudo-Hessian forms for the least-squares migration and the full waveform inversion separately.The application of plane-wave Hessian operator can lead to an amplitude-preserved migration result.The sub-offset Hessian can be used to the full waveform inversion to enhance the efficiency of inversion.At last,we discuss and evaluate the Hessian operator in seismic inversion imaging.更多还原