基于高斯束与高斯波包的Gabor框架散射波模拟方法

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.

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

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-scatterer is simulated with the finite-difference (FD for short) method and Gaussian packet. The two are almost the same in the time domain and very similar with each other in the frequency domain. The accuracy of scatter Gaussian packet is higher as the scatter angle becomes smaller, and vice versa. The scattered waves of a synthetic model are examined, and the common shot gathers calculated using FD method and Gaussian packet are comparable, except boundaries of shot gather. For comparing details of wavefields simulated using the above two methods, two groups of traces are extracted from common-shot-gathers. Comparison of waveforms show that amplitudes of different methods are almost the same while phases of wavelets are distinguishable. Accuracies of waveforms calculated with Gaussian packet are lower when offset becomes bigger.Calculation of the wavefield scattered by Gabor-scatterer using Gaussian beam and Gaussian packet are deduced for constant-density acoustic medium. Compared with scatter wave modeling in an anisotropic elastic medium, the number and initial amplitudes of scatter Gaussian beams/packets are both distinguishable here. Scatter Gaussian beam/packet's initial amplitudes are disparate in 2- and 3-dimensional media. With the proposed scatter theory, wavefields scattered by Gabor-scatterer calculated using the Gaussian packet and FD method are compared. They are comparable with each other in the time domain while there is a little difference in the frequency domain, and the reason has been analyzed in this article. Accuracy of simulation using Gaussian packet is influenced by scatter angles. The accuracy is higher when scatter angle becomes smaller and vice versa. Common-shot-gathers observed on the earth surface of a general model are simulated with the proposed Gaussian packet approach. Comparison of the presented scheme and FD method shows that our method is effective, although waveforms of common-shot-gathers simulated using Gaussian packet are slightly different from that simulated using the FD method.