Construction of Optimal Basic Wavelet via AIDNN and Its Application in Seismic Data Analysis

Continuous wavelet transform (CWT) is an effective tool for seismic time-frequency (TF) analysis. Selecting a matched wavelet to the analyzed seismic wavelet is a key issue for accurately characterizing TF features of seismic data. The three-parameter wavelet (TPW) can match different seismic wavelets by adjusting the three parameters. However, it is difficult to select appropriate parameters for matching TPW to seismic wavelets in real applications. In this letter, we propose a basic wavelet construction method by using the TPW and the deep learning network. The proposed workflow first builds a mapping relationship between seismic wavelet and seismic data by using the alternating iterative deep neural network (AIDNN). Based on this relationship, we then estimate a seismic wavelet. Using the estimated seismic wavelet, we can finally construct an analytical basic wavelet by matching the TPW to the extracted wavelet. Note that we named the TPW with optimal parameters as the optimal basic wavelet (OBW), and its wavelet transform is OBWT. To demonstrate the validity and effectiveness of the proposed approach, we apply it to synthetic traces and field data for characterizing their TF features. The results show that OBWT preserves the amplitude better and has a higher resolution than the CWT with mismatched basic wavelets to the seismic wavelet, which is helpful for seismic data analysis in the future.