基于归一化能量谱目标函数的全波形反演方法

基于L2范数的常规全波形反演目标函数是一个强非线性泛函，在反演过程中容易陷入局部极小值.本文提出归一化能量谱目标函数来缓解全波形反演过程中的强非线性问题，同时能够有效地缓解噪声和震源子波不准等因素的影响.能量谱目标函数是通过匹配观测数据与模拟数据随频率分布的能量信息来实现最小二乘反演的，其忽略了地震数据波形与相位变化的细节特征，这在反演的过程中能够有效缓解波形匹配错位等问题.数值测试结果表明，基于归一化能量谱目标函数在构建初始速度模型、抗噪性和缓解震源子波依赖等方面都优于归一化全波形反演目标函数.金属矿模型测试结果表明，即使地震数据缺失低频分量，基于归一化能量谱目标函数的全波形反演方法在像金属矿这样的强散射介质反演问题上同样具有一定的优势.

Full waveform inversion based on normalized energy spectrum objective function

The L2 norm-based conventional Full Waveform Inversion (FWI) method is a strong nonlinear functional, it is easy to fall into a local minimum during the inversion process. In this paper,the Normalized Energy Spectrum based Full Waveform Inversion (NESFWI) is proposed to alleviate the strong nonlinear problem and reduce the dependence of high Signal to Noise Ratio (SNR) seismic data and source wavelet. The objective function of NESFWI is to match the energy spectrum of the observed and synthetic data in the frequency domain,which ignores the waveform and phase oscillation characteristics of the seismic data. It can effectively mitigate the waveform mismatching problem during the inversion process,while reducing dependence of seismic source wavelet and high SNR seismic data. Numerical examples show that NESFWI results are better than the Normalized Full Waveform Inversion (NFWI) in building an initial velocity model,noise immunity and source wavelet dependence. Tests on a metallic deposit model show that even if the seismic data lack low frequency components,it still can get better inversion results than the conventional FWI method.