高斯波包反射走时速度反演方法

Velocity inversion method with reflection travel-time based on Gaussian packet

扰动高斯波包理论指出,在Gabor域描述模型的扰动成分,且入射波场为短时宽带信号时,扰动波场可在时间域通过高斯波包算子描述.在此基础上通过拟合反射波的走时,提出一种速度反演方法.反射波走时残差利用地震道局部波形的互相关函数表示,以走时残差的二范数作为目标函数,优化目标函数实现对速度场的反演.基于一阶Born近似,利用扰动高斯波包理论推导出目标函数对速度场的梯度是本文理论部分的核心内容.梯度包括两部分:正传的背景波场与反传的扰动高斯波包之间的互相关,反传的背景波场和正传的扰动高斯波包之间的互相关.梯度表达式中背景波场和扰动波场均利用高斯波包算子模拟.计算梯度的具体算法中,如何模拟扰动波场,以及如何计算反射波的走时残差是两个要点,文中对此做了详细的讨论.数值实验进一步阐述了反演的实现策略,实验结果表明高斯波包反射走时速度反演方法和实现策略有效可行,并得到了理想的反演结果.

The scattering Gaussian packet theory tells that scattered waves can be calculated using the Gaussian packet operator with the perturbed model＇s spatial distribution of Gabor frames, and the precondition is that the signal of incident waves should be of short-duration in the time domain and broad-band in the frequency domain. Here a velocity inversion approach is proposed by fitting the travel-times of reflected waves based on the scatterring Gaussian packet theory, in which the travel-time residual is expressed by the cross-correlation of observed and simulated local seismic wave-forms, and then the objective function is defined as the L2-norm of travel-time residuals. Thus the velocity inversion can be implemented by the optimization of objective funcion. The key of the proposed inversion method is how to deduce the gradient of objective function with respect to the velocity field based on the first-order Born-approximation. The deduced gradient of the objective function includes two parts：one is the cross-correlation between forward-propagated background wave of source side and the backward-propagated scattered Gaussian packet, and the other is the cross-correlation between backward-propagated background wave of receiver side and the forward-propagated scattered Gaussian packet. Both of the background wave-field and scattered wave-field in the expression of gradients are simulated by the Gaussian packet operator. It is the key points that how to estimate the perturbed model and then to simulate the scattered wave-field, and how to calculate travel-time residual by considering the flexibility of Gaussian packet in the implementation of the proposed velocity inversion approach, which is discussed in details in this paper. The velocity inversion strategy is further illustrated by numerical experiments. The results show that the theory and algorithm of the reflection travel time velocity inversion method based on Gaussian packet are effective and feasible, which can achieve good inversion of data.