Synchrosqueezing Optimal Basic Wavelet Transform and Its Application on Sedimentary Cycle Division

Sedimentary cycle division is an important step for sequence stratigraphy analysis. For the division of sedimentary cycle using seismic data, a key issue is characterizing the changes of dominant frequencies caused by the changes of stratum thickness with high accuracy and high resolution. The synchrosqueezing transform (SST) can provide a time-frequency (TF) representation with high resolution by synchrosqueezing the TF spectrum, which helps the sedimentary cycle identification. Unfortunately, it is a hard task to choose an appropriate basic wavelet, which influences the accuracy of the SST to characterize the sedimentary cycle. To solve this issue, we construct a synchrosqueezing optimal basic wavelet transform (SOBWT) to optimally characterize the sedimentary cycle. We first propose a criterion to construct the basic wavelet of SST by deriving the dominant frequency location condition and defining the similarity coefficient condition of the basic wavelet. Then, we introduce the optimal basic wavelet (OBW) to construct the basic wavelet that satisfies the dominant frequency location condition and the similarity coefficient condition. Note that we term the SST with a basic wavelet that satisfies the dominant frequency location condition and the similarity coefficient condition as the SOBWT. Finally, we apply the proposed SOBWT to synthetic and field data to testify its validity and effectiveness and compare it with conventional SST-based methods. The application results illustrate that it is much more convenient and easier for the sedimentary cycle division based on the SOBWT results.