海面波場資訊是呈現波浪於時間域以及空間域特徵的重要工具之一。有關海面波
場的研究，前人已提出一些波場分析的演算法，能有效的從均勻波場中解析出波浪的
特性。然而考慮到水深對波浪的影響，近岸波場往往是非均勻的。為能從非均勻波場
中取得完整且準確的波浪資訊，一套適合的數學方法是不可或缺的。
近年來，一套分析非定常以及非均勻訊號的數學理論-「小波轉換」已被許多研究
應用於不同領域的訊號分析。根據其數學特性，該理論應適用於解析非均勻波場，藉
以求得空間域中波浪傳遞期間之演變。本研究之目標為將時空合域小波轉換
(spatio-temporal wavelet transform)此一數學工具應用於分析海面波場，藉以解析出波浪
的非均勻特徵。
本研究率先嘗試將時空合域小波轉換理論引入作為分析非均勻波場之工具，為能
將此一數學理論應用於分析數位的波場資料，文中發展了連續小波轉換的離散型演算
法，並推導出小波轉換計算結果與波浪譜之間的關係。為了驗證小波理論於波場分析
的適用性以及本文方法發展過程的正確性，數值模擬波場在研究中被應用作為驗證的
工具。為能獲得準確的波浪分析結果，本文也討論各種可能會影響小波理論分析波場
結果準確度之因子，並嘗試提出最適用於波場分析的參數值。
經驗証分析流程正確性以及最佳化討論之後，本研究進一步利用小波轉換的分析
結果來量化波場的非均勻性，並提出一量化指標-「non-homogeneity index」。從不同波
場案例的分析結果發現，non-homogeneity index 確實與波場的非均勻程度有關，其值
會受到波場所處海底床斜率以及波浪週期所影響，且底床斜率對non-homogeneity
index 的敏感程度較高。
除了模擬波場的分析之外，本研究嘗試使用X-band 雷達影像作為海面波場資料進
行小波分析。結果顯示出近岸波場的能譜具有較明顯二階非線性波之能量存在。此外，
經由對不同季節的雷達影像進行分析後發現到颱風期間海面波場會呈現較明顯的非均
勻性。經由上述的分析與討論，本研究證實了時空合域小波轉換確實能有效應用於分
析非均勻的海面波場，獲得波場中不同位置的波浪譜資訊。

A sea surface wave field is a useful way to present wave features in both time and
space domains. Several algorithms have been proposed for analyzing the wave field so as to
obtain significant wave parameters. Due to the non-homogeneity of the wave field in space
domain, the algorithms which assume the wave field non-homogeneous may not be suitable
for discussing the spectral characters of the non-homogeneous wave field.
The wavelet transform is now recognized as a useful, flexible and efficient technique to
analyze intermittent, non-stationary and non-homogeneous signals as well as remote sensing
images. It should be workable to discuss a non-homogeneous wave field using wavelet
transform although, previously, this issue has received little attention. The aim of this
research was to study wave field analysis by applying spatio-temporal wavelet transform, 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
non-homogeneous wave field, the algorithm of spatio-temporal wavelet transform was
developed. The relationship between wave parameters and the wavelet analyzed results
were also derived from this study.
The numerical algorithm of spatio-temporal wavelet transform was tested in a
simulated wave field of regular and 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.
In order to understand the non-homogeneity of sea areas, the non-homogeneity of
different wave field cases were quantized using the wavelet transform. It was revealed that
the higher the sea bed slopes and the wave periods, the higher the non-homogeneity indexes.
The influence of the wave period on the non-homogeneity indexes was less than the
influence of bathymetry. In addition, the non-homogeneity index was also influenced by the
wave nonlinearity which is obvious in the shallow water area.
Finally, wave field images, acquired from X-band radar, were applied to the analysis.
For the areas near shore, it was revealed that the observed spectral energy deviated from the
linear dispersion relation. The primary spectral energy distribution agreed with the
relationship between the harmonic frequency and wave number which presents the
nonlinear dispersion relation It could, therefore, be concluded that the use of
spatio-temporal wavelet transform in analyzing non-homogeneous wave fields of random
waves was feasible, even in coastal areas.

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