在频率域基于小波变换和Hilbert解析包络的CSEM噪声评价

A noise evaluation method for CSEM in the frequency domain based on wavelet transform and analytic envelope

传统CSEM一般只提取主频信号,或以谐波与主频的振幅比为依据提取部分低阶谐波信号,但缺乏判断标准,实际操作中存在很大的不确定性.本文基于小波变换和希尔伯特解析包络提出一种新的CSEM信号噪声评价方法,首先在时间域中基于混合基快速傅里叶变换获得原始信号准确功率谱;其次在频率域中根据CSEM频率位置相邻频率幅值进行频谱预处理,基于离散小波变换将预处理后的频谱分成低频部分和高频部分,基于希尔伯特变换识别高频部分的上包络线,并与低频部分重构得到频谱的整体上包络线;最后根据包络线与对应CSEM频率振幅的比值估计噪声的影响幅度,根据阈值筛选出高信噪比的主频和谐波信号.本方法不需增加野外工作量即可提取大量的频率信号,特别是高阶谐波信号,实现频率加密,提高CSEM的纵向分辨能力和能源利用率.

In the conventional CSEM exploration method, only main frequencies of signal are used, or some lower-order harmonics information is extracted based on experiences. But such a procedure has no criteria to valid information extracted. In this paper we present an effective method for evaluating noise influence in the frequency domain, which makes it possible to extract frequency coefficients with high SNR, including both the main frequency and its harmonics. The spectrum of raw data is obtained from time domain data by using the mix-radix fast Fourier transform. Then it puts the amplitude of CSEM frequency into the average of adjacent two frequencies to output a modified spectrum. This pre-processed spectrum is divided into low frequency part （trend） and high frequency part （oscillation） by using discrete wavelet transform. The analytic envelope of the high frequency part is obtained based on Hilbert transform. The upper bound curve of the total spectrum is reconstructed with the low frequency part and the envelope of high frequency part. The maximum influence amplitudes （MIA） of noise at CSEM frequencies are estimated. Noise evaluation number is calculated based on MIA and raw amplitude in CSEM frequency. By this noise rating number, it will be possible to screen out frequency coefficients with high SNR from raw spectrum. By applying this method, amount of frequency coefficients, including many high-order harmonics, are extracted without increasing any field work. Vertical resolution of CSEM is also improved by this method since more frequency coefficients are extracted.