時空合域連續小波轉換應用於近海波場影像的波速與群波速度分析

Coastal Wave Image Analysis by Spatio-Temporal Continuous Wavelet Transform on Deriving Wave Celerity and Wave Group Speed

莊士賢(Laurence Zsu-Hsin Chuang) ； 吳立中(Li-Chung Wu) ； 董東璟(Dong-Jiing Doong) ； 高家俊(Chia-Chuen Kao)

《中國土木水利工程學刊》 23卷4期 (2011/12) Pp. 417-427

https://doi.org/10.6652/JoCICHE.201112_23(4).0007

摘要

本文藉由含速度轉換因子的「時空合域連續小波轉換」(STCWT)理論，發展出利用該數學理論分析數位化波場影像序列的演算方法，藉以瞭解STCWT應用於分析非均勻及非定常之波場影像的可行性，以便描述波浪於空間波場的演變特性，並避免波場的非均勻性及影像之邊界與解析度影響波浪特性計算結果的正確性。本文從波場影像中先選擇波浪速度與群波速當作分析與討論的焦點，經由波浪在近岸淺化過程中波譜、波速與群波速的特性演變的模擬與分析結果之比較，可初步證實本研究方法應用於非均勻波場分析的可行性。

關鍵字

時空合域連續小波轉換 ； 近海波場影像 ； 波速 ； 群波速度

並列摘要

The aim of this research was to study wave field analysis by applying spatio-temporal continuous wavelet transform (STCWT) in order to understand the features of non-homogeneity when discussing wave propagation on a varying topography. For the sake of applying wavelet theory to extract wave information from the inhomogeneous wave field, the algorithm of STCWT was developed. The relationships between wave parameters and the wavelet analyzed results were also derived from this study. The numerical algorithm of STCWT was tested in a simulated wave field of irregular waves in order to understand the practicability and accuracy of wave calculation from a wave field by wavelet transform. This is the first time wavelet transform has been used to analyze a non-homogeneous wave field, the influences of the wave image features and the wavelet function upon wave field analysis. It could, therefore, be concluded that the use of STCWT in analyzing non-homogeneous wave fields of random waves was feasible, even in coastal areas.

並列關鍵字

spatio-temporal continuous wavelet transform ； coastal wave image ； wave celerity ； wave group velocity