小波变换与地震信号特征分析

Wavelet transform and seismic signal analysis

地震波的瞬时信号 ,如瞬时振幅、瞬时频率及瞬时相位等 ,是研究地球介质的重要参数。根据小波定义 ,对 Morlet小波进行了修正 ,并对修正后的小波形态进行了深入讨论。理论分析表明 ,小波变换效果受到整形参数、小波长度、中心频率、频带宽度及小波个数等参数的制约 ,特别是整形参数与小波中心频率及频带之间关系对小波变换起到决定性作用。在地震波信号的实际处理中 ,可选取恰当的整形参数 ,同时采用合适的小波中心频率以避免小波变换对信号产生的遗漏和冗余。文中给出了实际地震记录处理的示例。

The instantaneous parameters of seismic wave, such as instantaneous amplitude, instantaneous frequency, and instantaneous phase, are of very important role in studying properties of the earth. Based on the definition of wavelet, the authors revised the Morlet wavelet and discussed the characteristics of revised wavelet in detailed. Theoretically analysis shows that the effect of wavelet transforms is restricted by the parameters such as shape, length of wavelet, central frequency, bandwidth, as well as the number of wavelets, especially the relationship among shape, central frequency, and bandwidth play a key role in wavelet transform. In the actual treatment of seismic records, we can choose proper parameter of shape. At mean time, we need give correct central frequency of wavelet to avoid omitting and redundancy of original message during wavelet transform. At the end of the article, the field record is demonstrated as result of wavelet transform according to the concept of instantaneous amplitude and instantaneous phase.