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构造紧支集小波正交基时发现：紧支集正交小波基函数与地震波极为相似，比较适合地震资料处理．利用快速小波变换及小波变换的正交分解性将仿真地震记录在时间域分解成不同尺度下的地震记录．原始记录的频谱和重建记录的频谱表明：数字信号按小波变换进行正交分解重建具有很好的保真性．为检验快速小波变换去噪效果，对仿真地震记录加入随机噪音，利用快速小波变换去噪，即求取Ｌ２（Ｒ）空间各正交基的投影，比较去噪前后的仿真地震记录，随机噪音得到压制，且信号不失真．
It is found that when the orthogonality of the compact support set wavelet orthogonal basis is found, the orthogonal wavelet basis function of the tight support set is very similar to the seismic wave, which is more suitable for seismic data processing. The seismic data are decomposed into seismic records with different scales by using the fast wavelet transform and orthogonal decomposition of wavelet transform. The spectrum of the original record and the spectrum of the reconstructed record show that the digital signal has good fidelity for orthogonal decomposition reconstruction by wavelet transform. In order to test the denoising effect of fast wavelet transform, random noise was added to the simulated seismograms and the noise was removed by fast wavelet transform, that is, the projection of each orthonormal basis in L2 (R) space was obtained. The simulated seismograms before and after de-noising Get suppressed, and the signal is not distorted.