A homotopy method for well-log constraint waveform inversion
A homotopy method for well-log constraint waveform inversion
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DOI：
10.1190/1.2387117
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发表时间：
2007
期刊：
影响因子：
3.3
通讯作者：
B. Han;H. Fu;Hong Liu
中科院分区：
文献类型：
--
作者：
B. Han;H. Fu;Hong Liu
声波方程波形反演方法的主要困难是目标函数存在局部极小值。波形反演无法收敛到全局最小值，除非波场包含非常低的频率，或者初始模型非常接近真实模型。约束可以提高方法的收敛性;然而，如果初始模型远离正确的模型，正常的迭代方法仍然会陷入局部极小值。我们设计了一种同伦方法来提高波形反演的鲁棒性;它可以自然地使用约束，例如测井曲线。此外，为了进一步条件的反问题，我们将标准的Tikhonov正则化。我们通过一个合成的例子表明，我们的方法是更有可能找到一个全球最小比正常的迭代方法。
The primary difficulty posed by the method of waveform inversion for the acoustic-wave equation is the presence of local minima of the objective function. Waveform inversion fails to converge to the global minimum unless the wavefield contains very low frequencies, or the starting model is very close to the true model. Constraints can improve the convergence of the method; however, if the starting model is far from the correct model, normal iterative methods will still get trapped in local minima. We designed a homotopy method to improve the robustness of waveform inversion; it makes natural use of constraints, such as well logs. In addition, to further condition the inverse problem, we incorporate standard Tikhonov regularization. We demonstrate through a synthetic example that our method is more likely to find a global minimum than normal iterative methods.