多子波分解与重构中子波的优选

Optimization of wavelets in multi-wavelet decomposition and reconstruction method

在地震信号的多子波分解与重构中,子波类型与子波分辨率的选择是十分重要的。针对这一问题,首先计算了复数Paul子波和复数Morlet子波的时频谱,并讨论了频率域内子波宽度控制参数对频率域分辨率的影响;然后应用匹配追踪算法对实际地震数据进行多子波分解与重构,从理论上确定了控制复数Paul子波和复数Morlet子波频率域分辨率的最佳子波宽度,对两种子波分解重构地震剖面的差异性进行了对比分析。理论和实际计算结果表明:复数Paul子波与复数Morlet子波的分辨率和频谱能量分布有所不同,在实际应用中需针对不同的研究目的选择不同类型的子波。基于复数Paul子波的重构剖面保留了更多的低频能量,适用于反射同相轴连续的地下构造研究;基于复数Morlet子波的重构剖面高、低频频谱差异大,更适用于地震波吸收衰减研究。

It is very important to select the wavelet and its resolution in multi-wavelet decomposition and reconstruction method.In order to well select wavelet,firstly,we calculate the time-frequency spectrums of complex Paul wavelet and complex Morlet wavelet,and discuss the influence of wavelet width controlling parameters on resolution in frequency domain.Then,matching pursuit algorithm is applied to carry out multi-wavelet decomposition and reconstruction on actual seismic data,and theoretically identify best wavelet width controlling the frequency-domain resolution of complex Paul wavelet and complex Morlet wavelet;meanwhile,the difference of the seismic sections reconstructed from the two wavelets is analyzed.Theoretical model and actual data computation results indicate that the two wavelets have different resolution and different shape of frequency spectrum.In actual application,we should select the wavelet in terms of the target:the reconstruction profile based on complex Paul wavelet preserves more low-frequency energy,which is suitable to study the sub-structures with continuous reflection events;the reconstruction profile based on complex Morlet wavelet has large contrast between low-frequency and high-frequency spectrum,which is more suitable to study the seismic wave absorption and attenuation effect.