基于同步提取变换的地空频率域电磁信号幅度提取方法

Amplitude Extraction of Ground-Airborne Frequency-Domain Electromagnetic Signals Based on Synchroextracting Transform

地空频率域电磁法探测信号为多频非平稳信号,为了解决应用传统傅里叶变换方法提取其幅度时分辨率较差的问题,本文提出了基于同步提取变换(SET)的地空频域电磁信号幅度提取方法。该方法对电磁数据进行SET,得到高分辨率时频图,并利用能量算子使电磁数据时频谱能量更为集中;采用贪心算法提取脊线,得到时频图的高能量带;通过自回归模型自适应地补充了脊线中的0值,解决了由窗函数引起的端点效应问题。根据脊线位置的时频图复数值,得到各频率分量幅度随时间的变化,研究了不同信噪比情况下基于SET的地空频率域电磁信号幅度提取结果的准确性。结果表明:当信噪比≥10 dB时,幅度提取结果的平均相对均方根误差均小于5%;当信噪比<10 dB时,幅度提取结果的平均相对均方根误差在10%以内。提取效果良好。将此方法应用于新疆霍拉山隧道工程地空频率域电磁法探测中,成功提取了多频电磁信号各频率分量的幅度,与采用傅里叶变换提取非平稳信号幅度的方法相比,该方法有效地提高了幅度提取结果的分辨率。

The detection signal of the ground-airborne frequency-domain electromagnetic method(GAFDEM)is multi-frequency non-stationary signal,when extracting its amplitude using conventional Fourier transform methods,the resolution is poor.To solve the above problem,this paper proposes an amplitude extraction method of ground-airborne frequency-domain electromagnetic signal based on synchroextracting transform(SET).This method performs SET on the electromagnetic data to obtain high-resolution time-frequency graph,and uses energy operator to make the energy of time-frequency spectral electromagnetic data more concentrated.At the same time,the greedy algorithm is used to realize the ridge extraction method to obtain the high energy band of the time-frequency graph.By filling in zero values in the ridges adaptively through autoregressive model,the endpoint effect problem caused by the window function is solved.according to the complex value of the time-frequency-diagram at the ridge location,the variation of the amplitude of each frequency component with time is obtained,and the accuracy of the amplitude extraction of electromagnetic signals in the ground-airborne frequency-domain based on SET is investigated under different signal-to-noise ratios.Through calculation,when the signal-to-noise ratio is greater than or equal to 10 dB,the average relative root mean square error of the amplitude extraction result is less than 5%;When the signal-to-noise ratio is less than 10 dB,the average relative root mean square error of the amplitude extraction result is less than 10%,achieving good extraction results.This method is applied to the GAFDEM delection of the Huola Mountain tunnel project in Xinjiang,and the amplitude of each frequency component of the multi-frequency electromagnetic signal is successfully extracted.Compared with the method of extracting non-stationary signal amplitude using the Fourier transform,this method effectively improves the resolution of amplitude extraction results.