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摘要:
鉴于常规的傅里叶变换滤波及f-k滤波等压制面波的局限性，基于小波基函数的特点，提出一种基于二维小波变换的低频噪音压制方法：在对比分析各类型小波的基础上，选择利于低频面波压制的小波基函数；通过二维小波分解将地震数据转换到时间、空间、频率、波数四维域中，对含面波成分的低频高波数部分进行高通滤波；重构地震数据，得到压制面波后的处理结果。经理论模拟记录的试算和低频采集资料的处理证明，本方法去噪效果好，且在面波压制过程中较好地保护了低频有效波。
Abstract:Owing to the limitation of the conventional Fourier transform filtering and FK filtering methods in suppressing surface wave, we provided in this paper a surface wave suppression method based on two-dimensional wavelet transforms and the basic characteristics of the wavelet. Upon the basis of comparative analysis of various types of wavelet, we selected one from the others for low frequency surface wave suppression. Through the two-dimensional wavelet, decomposition can be used to convert seismic data into the four dimensional domains of time, space, frequency and wave number, and then conduct a high-pass filtering to the low frequency and high wave number component. As the result, reconstruction of seismic data and processing after the suppression of surface wave results are obtained. The theoretical simulation of the record and low frequency seismic data processing show that the denoising is effective. It can protect the low frequency effect wave effectively during the process to suppress the low frequency wave at the same time.
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Key words:
- two-dimensional wavelet transform /
- seismic data /
- surface wave /
- noise suppression
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表 1 常用小波的特性
Table 1. Characteristics of the common wavelet
小波类型 N阶表示形式 正交性 支撑长度 消失矩 对称性 Daubechies dbN 有 2N-1 N 较差(除了db1) Symmlet symN 有 2N-1 N 近似对称 Biorthogonal biorNr, Nd 双正交 分解：2Nd+1
重构：2Nr+12Nt 可以对称 Coiflets coifN 有 6N-1 小波函数2
N尺度函数2N-1近似对称 
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表 2 采用不同小波提取面波的性能比较
Table 2. Comparison of extracting surfacewave by using different wavelet
小波类型 消失矩 平均绝对误差 耗用时间/s 支撑度 反射波区域Er 面波区域Es db20 20 0.042 4 0.042 4 1.204 35 sym20 0.038 7 0.038 7 11.656 35 db10 10 0.043 1 0.043 1 0.641 17 sym10 0.039 3 0.039 3 0.907 17 coif5 0.038 1 0.038 1 0.906 7 db8 8 0.041 1 0.041 1 0.578 13 sym8 0.039 8 0.039 8 0.609 13 coif4 0.039 8 0.039 8 0.719 21 bior2.8 0.041 3 0.041 3 0.671 15 db5 5 0.040 5 0.040 5 0.515 7 sym5 0.039 9 0.039 9 0.516 7 db4 4 0.043 4 0.043 4 0.484 5 sym4 0.040 1 0.040 1 0.484 5 bior2.4 0.047 1 0.047 1 0.500 7 coif2 0.041 4 0.041 4 0.515 9
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