From Tomography to FWI with a Single Objective Function
From Tomography to FWI with a Single Objective Function
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DOI：
10.3997/2214-4609.20130413
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发表时间：
2013-06
期刊：
影响因子：
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通讯作者：
T. Alkhalifah;Y. Choi
中科院分区：
文献类型：
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作者：
T. Alkhalifah;Y. Choi
我们的地震资料中的反射引起了全波形反演（FWI）目标函数的严重非线性行为。因此，如果没有一个好的初速度模型，可以在反演所用频率的一个周期内产生反射，则很难收敛到解。这种速度模型通常是从迁移速度分析或走时断层扫描等方法中提取的，这些方法不能保证符合FWI的要求。因此，我们提出了一个目标函数，该函数基于观测数据和建模数据之间瞬时旅行时间的失配。波场的相位属性及其相位展开特性提供了频率相关的走时函数。由于合成的低频数据具有很强的阻尼，因此该属性允许将首次到达的旅行时间与从观测数据中挑选出来的旅行时间进行比较，例如在波动方程层析成像中。当我们放松合成数据和观测数据的阻尼时，目标函数测量相位中的失配，但在FWI类型的反演中展开。因此，它提供了一个单一的目标函数和从旅行时断层成像到全波形反演的自然过渡。一个Marmousi实例证明了该方法的有效性。
Reflections in our seismic data induce serious nonlinear behavior in the objective function of full waveform inversion (FWI). Thus, without a good initial velocity model, that can produce the reflections within a cycle of the frequency used in the inversion, convergence to the solution becomes hard. Such velocity models are usually extracted from migration velocity analysis or traveltime tomography, among other means, that are not guaranteed to adhere to the FWI requirements. As such, we promote an objective function based on the misfit in the instantaneous traveltime between the observed and modeled data. This phase based attribute of the wavefield, along with its phase unwrapping features, provide a frequency dependent traveltime function. With strong damping of the of the synthetic, potentially low frequency, data, this attribute admits first arrival traveltime that could be compared with picked ones from the observed data, like in wave equation tomography. As we relax the damping on the synthetic and observed data, the objective function measures the misfit in the phase, however unwrapped in an FWI type inversion. It, thus, provides a single objective function and a natural transition from traveltime tomography to full waveform inversion. A Marmousi example demonstrates the effectiveness of the approach.