Toledo B A, Chian A C-L, Rempel E L, Miranda R A, Muñoz P R, Valdivia J A
Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), CTA/ITA/IEFM, São José dos Campos-SP 12228-900, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Feb;87(2):022821. doi: 10.1103/PhysRevE.87.022821. Epub 2013 Feb 28.
We study general multifractal properties of tidal gauge and long-wave time series which show a well defined transition between two states, as is the case of sea level when a tsunami arrives. We adopt a method based on discrete wavelets, called wavelet leaders, which has been successfully used in a wide range of applications from image analysis to biomedical signals. First, we analyze an empirical time series of tidal gauge from the tsunami event of 27 February 2010 in Chile. Then, we study a numerical solution of the driven-damped regularized long-wave equation (RLWE) which displays on-off intermittency. Both time series are characterized by a sudden change between two sharply distinct dynamical states. Our analysis suggests a correspondence between the pre- and post-tsunami states (ocean background) and the on state in the RLWE, and also between the tsunami state (disturbed ocean) and the off state in the RLWE. A qualitative similarity in their singularity spectra is observed, and since the RLWE is used to model shallow water dynamics, this result could imply an underlying dynamical similarity.
我们研究验潮仪和长波时间序列的一般多重分形特性，这些序列在两种状态之间呈现出明确的转变，海啸来袭时海平面的情况就是如此。我们采用一种基于离散小波的方法，称为小波首元，该方法已成功应用于从图像分析到生物医学信号等广泛的应用领域。首先，我们分析了2010年2月27日智利海啸事件的验潮仪经验时间序列。然后，我们研究了受驱动阻尼正则化长波方程（RLWE）的数值解，该方程表现出开关间歇性。这两个时间序列的特征都是在两个截然不同的动力学状态之间突然变化。我们的分析表明，海啸前和海啸后的状态（海洋背景）与RLWE中的开状态之间存在对应关系，海啸状态（受干扰的海洋）与RLWE中的关状态之间也存在对应关系。观察到它们的奇异性谱存在定性相似性，并且由于RLWE用于模拟浅水动力学，这一结果可能意味着存在潜在的动力学相似性。
