伪随机编码源电磁响应的精细辨识

Accurate identification for the electromagnetic impulse response of the earth with pseudo random coded waveforms

与传统阶跃源激励方式相比,采用m序列伪随机编码对发射源波形进行编码,提高了电磁探测的深度和分辨能力.然而受这种编码源发射波形自相关旁瓣效应的影响,使得对大地冲激响应的精细辨识效果受到一定限制.为了解决这一问题,在以往相关辨识方法研究的基础上,进一步考虑发射自相关旁瓣的影响,首先提出一种由收发互相关中高精度提取大地冲激响应的数学方法;然后通过数值模拟给出了m序列编码源大地冲激响应的精细辨识结果;同时对以m序列为发射波形的勘探系统相关参数选择进行了分析;最后利用本文提出的方法对野外实测数据进行辨识处理,通过与其他EM方法结果进行对比,证明了本文提出方法的可靠性.

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.