基于高斯束与高斯波包的Gabor框架散射波模拟方法  

A scattering wave modeling method using Gaussian beam and Gaussian packet in the Gabor domain

作　　者：李辉[1] 王华忠[1] 

机构地区：[1]同济大学海洋与地球科学学院波现象与反演成像研究组,上海200092

出　　处：《地球物理学报》2015年第4期1317-1332,共16页Chinese Journal of Geophysics

基　　金：国家自然科学基金(41374117);国家重点基础研究发展计划(973计划)项目(2011CB201002);国家重大专项项目(2011ZX05003-003;2011ZX05005-005-008HZ和2011ZX05006-002);中国石化地球物理重点实验室开放基金(33550006-14-Fw2099-0026)共同资助

摘　　要：在给出真实模型和相应光滑背景模型的情况下,如何计算扰动模型(散射体)产生的散射波场是一个有实际意义的正演问题.在Gabor变换域描述散射体,且入射波场为短时宽带信号时,散射波场可以在频率域用高斯束或时间域用高斯波包描述.相对于波动方程方法,高斯束和高斯波包的计算效率更高;背景模型光滑时,高斯束和高斯波包方法的精度也接近波动方程方法.文中导出了声波假设下应用高斯束和高斯波包计算散射波的方法.测试分析了高斯波包的计算精度.给出了一般散射体的散射波模拟策略.同时针对一个理论模型完成了本文方法计算散射波的实验,实验结果表明高斯波包散射波计算方法是有效可行的.How to calculate the wavefield that scattered by a perturbed model （scatterers） in a smooth background model is a practical problem. If scatterers are described in the Gabor domain, and the incident waves are short-duration and broad-band, then the scatter wavefield can be calculated using Gaussian beam in the frequency domain or using Gaussian packet in the time domain. Compared with wave-equation, Gaussian beam/packet shares higher efficiency. Moreover, the accuracies of Gaussian beam/packet are comparable with wave-equation in the case of smooth media. The method that calculates scatter waves using Gaussian beam and Gaussian packet in an acoustic medium is proposed. The accuracy of the modeling method is also analyzed.The incident waves and Green＇s function can be both written as the expressions with amplitude and travel-time under WKBJ approximation. Substituting these expressions into the formula of Born approximation of scatter waves in the acoustic medium, then the analytic expression of scatter waves that are scattered by Gabor-scatterer is deduced.The initial Hessian of scatter Gaussian beam＇s travel-time with respect to space coordinates is the same as that in Klime？＇s work （2012）. We present the initial values of Gaussian beam＇s dominate frequency, ray parameters, and amplitude in 3-dimensions, respectively. The initial amplitude of scatter Gaussian beam in 2-dimensions is also presented.Similar to scatter Gaussian beam, the initial Hessian of scatter Gaussian packet＇s travel-time is the same as that of Klime？＇s work （2012）, too. Scatter Gaussian packet＇s dominant frequency and initial ray parameters can be calculated with the same formulas as the scatter Gaussian beam. Both formulas for calculating initial amplitudes of scatter Gaussian packets in 3-dimensions and 2-dimensions are deduced.Finally, the strategy of simulating scatter wave with Gaussian beam and Gaussian packet can be concluded as a flow chart in the main body of the paper. The wavefield scattered by a Gabor

关 键 词：散射体 散射波场 GABOR函数 高斯束 高斯波包 

分 类 号：P631[天文地球—地质矿产勘探]