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《Chinese Journal of Geophysics》 2015-08
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Accurate identification for the electromagnetic impulse response of the earth with pseudo random coded waveforms

WU Xin;XUE Guo-Qiang;DI Qing-Yun;ZHANG Yi-Ming;FANG Guang-You;Institute of Electronics,Chinese Academy of Sciences;Institute of Geology and Geophysics,Chinese Academy of Sciences;Beijing University of Technology;  
The electromagnetic method with m sequence,one kind of pseudo random binary sequences,that codes transmitting waveforms has several advantages over the traditional electromagnetic method with square-form transmitting waveforms.However,because of the existing sidelobes of auto-correlation of transmitting waveforms and its influence in a complicated way,the precision of identification would be limited if the identification process is only based on a basic cross-correlation algorithm.A new algorithm is proposed to overcome this difficulty.The fundamental of system identification using the m sequence is the Wiener-Hopf function,which reveals the relation between auto-correlation of input signal AR,identified system g and cross-correlation between input and output signal CR that is the convolution of AR and g.Because of the complicated effect of the sidelobes of AR,even if the main lobe of AR could be regarded as a delta function,g cannot yet be read out directly from CR with high precision.From the Wiener-Hopf function,it can be recognized that the effect of the sidelobes comes into the CR through the convolution process.This means that the AR could be regarded as a filter,and therefore,a deconvolution could be performed to extract g from CR by inverting the effect of theconvolution with AR.For this purpose,CR,AR and g are primarily discretized and reformed individually into vectors and matrixes,and the convolution process is consequently reformed into vector=matrix×vector,where the left vector is CR,matrix is AR and right vector is g.The AR matrix could be regarded as a linear operator.Therefore the least square procedure could be introduced for the g vector estimation.Through several iterations and smoothing,g could be extracted with high precision.To check the effectiveness of this method,a numerical simulation is performed.A grounded line source on a homogeneous half-space is computed as the model,and the transmitting waveforms are coded by the m sequence.The result shows that the relative identification error is smaller than 2%in the time interval from 0to 10 tpeak,where tpeakis the arrival time of the peak of the earth impulse response.On contrary the relative identification error with the traditional method in the same interval is much worse,and the biggest relative error is more than 538%.In another numerical simulation,it is proved that this method can provide identification result with high quality even if the choice of m sequence parameters is considered not fully enough from the perspective of some existing theories.Furthermore,we organized a field test in 2014 and compared the identified earth impulse response with that of other EM methods.The comparison shows that the identified result is matched well with other EM methods.The sidelobes can be regarded as a disturbing factor in identification,and its effect comes into cross-correlation through the convolution process.The new algorithm proposed in this paper realized the high precision identification of earth impulse response by deconvolution.Numerical simulation shows that the relative identification error using this method is smaller than 2%in the main section of the earth impulse response.This method is also applied to field data processing already,and the identified earth impulse response is in good agreement with that of other EM methods.All these tests prove that this method is an applicable method in the future EM surveys.
【Fund】: 国家重大科研装备研制项目(ZDYZ2012-1-05-01)资助
【CateGory Index】: P631.325
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