CSAMT中的IP效应影响及应用研究
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摘要
在可控源音频大地电磁法(CSAMT)的正、反演计算中都把大地的电阻率看作一个与频率无关的实数,但由于IP效应的影响,大地电阻率实际上是一个随频率而变化的复数,在电磁场的响应中实际上包含了IP响应的成份。对基本Cole-Cole模型的频谱分析发现,复电阻率的实部一般远大于虚部,实部与幅值、虚部与相位变化规律一致；极化率和频率相关系数变化对模型电阻率幅值的影响要大于时间常数变化造成的影响,在提取IP参数时可以根据经验取为常数；复Cole-Cole模型的频谱变化规律与基本模型的规律基本一致,同类参数都发生变化对幅值的影响取决于总的变化量,而相位主要受参数小的基本模型的制约。IP效应对Ex、卡尼亚视电阻率的影响远大于对Hy的影响,这种影响主要发生在中低频段,在高频段IP效应基本消失,在分析IP效应和提取IP参数时要在中低频段进行,同时还要排除近场效应的影响；极化模型参数的变化对电磁场分量的影响规律与对自身频谱曲线的影响规律相似；IP效应对卡尼亚视电阻率幅值的影响大于对相位的影响,各参数的影响水平也不相同,极化率参数和频率相关系数的影响大,时间常数的影响小,在提取IP参数时,要优先考虑影响大的参数。建立了基于最小二乘方提取IP参数的目标函数,设计了算法程序,为加快函数的收敛速度,采用梯度法改变模型参数；利用给定的模型作为实测数据,对提取算法进行了测试。针对卡尼亚视电阻率中存在的IP效应的来源,提出了在CSAMT原始资料中去除IP效应的方法,它利用视电阻率替换的方法实现IP效应的去除；利用这种方法对在长白山地区寻找地热资源的资料进行了处理,反演结果能够合理地解释地热资源的形成原因。
Controlled source audio-frequency magnetotelluric(CSAMT) whics is developed on the basis of magnetotelluric method and the audiofrequency magnetotelluric method is an active source electromagnetic exploation method. In recent years it's theory research is continuous increasing, in the field of exploating concealed ore, oil, gas, geothermal resources and Hydrology has made good geological effect.
Induced polarization effect (IP) is caused by the effect of polarization in interface between the electronic conductor and the aqueous solution electrodes or the film polarization between clay surface and solution. IP phenomenon could be observed by DC or AC induced electronic field established artificially in mineralization rocks primarily consists of electronic conductor, graphitization rocks and ion conductor rocks. Because of the IP effect, the earth resistivity is a plural changing with frequency, but in the CSAMT the earth resistivity is regarded as a real number parametre in both forward and inversion, which is unrelated to frequency, ignoring the IP ingredients of electromagnetic response. These are a variety of plural models to describe polarization effect, this paper briefly summaries them.
In order to analysis the influence to electromagnetic field (Ex, Hy) produced by IP, firstly We derivate the calculation formula of the electromagnetic field in the homogeneous medium and layered medium, use the discrete method to calculate Ex and Hy in layered medium. To avoid attenuation of Hy in high frequency, we use a high precision filter coefficient to calculate it. According to scalar measurement of CSAMT, we summary it's working condition and parameters of observation so as to analysis the influence of IP.
We analysis the spectrum characteristics of basic Cole-Cole model, and find that the complex resistivity's real part generally far more than that of imaginary part, variation law between real part and amplitude or between imaginary part and phase follow the same variation law when Cole-Cole model parametres change. Real part is always positive and become smaller with the parameters of polarizability increasing, it tend to be a steady value at high frequeny band. Imaginary part changes according to concave curve, the high and low frequency band tend to be zero, and in the middle frequency band it gets negative value. The general varying trend's of real part and imaginary part when frequency correlation coefficient changes is similar to that of when polarization parametre changes. Real part increases in low frequency band with frequency correlation coefficient increasing, the absolute value of the imaginary part in lower and higher frequency band increases with the decrease of the C. Real part decrease with the increasing ofτ. But difference among real parts is very not obvious whenτis big enough, imaginary part changes as to concave curvee whenτis small, but it increases monotonously with frequency increase whenτis big enough, and finally it close to zero. And at higher frequency band, the absolute value of imaginary part decreased with the increasing ofτ, at low frequency band it changes more complexly. Then studies the influence level when model parameters changes, and find that the changing of polarization parametre and frequency correlation coefficient can produce greatly influences on amplitude and phase, but the time parameter changing has a little influence, so in extracting IP parameters can take it as an experience constant. By analysising the spectrum characteristics of compound Cole-Cole model, we find each parameters on the influence law of compound model is consistent with the influence law of basic model, if two models'similar parameters both change, the influence on amplitude depends on the total variation, and phase is mainly affected by the basic model with small parameters.
The paper analyzes the IP effect in homogeneous half-space and various types of cross-section layer earth by using the model of Cole-Cole, find that the influence to Ex and to Cagniard resistivity is far more than to Hy, this kind of influence mainly takes place in low-middle frequency band, at high frequencies IP effect disappeares off basically, so to analyzes the IP effect of CSAMT mainly considers the low-middle frequency band. Also, there exists the effect of near field at low frequency band, this is must be excluded. The influence law to electromagnetic field components is similar with the influence law of their own spectrum curve when the model parameters changing. The analysis showes that IP influence has a greatly effection on resistivity amplitude than that on phase, the influence level of various parameters is not the same:polarizability parameters and frequency correlation coefficient have greater influence than that caused by the time constant, to extract IP parameters should priority consider the parametres which can produce great influence.
Give the method of how to established polarization model of CSAMT measurement on polarization level layer, establish target function of least squares sense to extract the IP parameters. And the objective function and parameter expression is optimized. We give detailes of calculation, and in order to accelerate the convergence speed, using gradient method to modify model parameters. Run the procedures by setting initial model portfolio and using given model as the experimental data to extraction algorithm as to verify its validity.
According to the source of IP effect existing in the Cagniard resistivity, puts forward mean to remove IP effect from original data. This method firstly use the original data to design layered polarization model and establish objective function to extract IP parameters, then use extracted parameters to calculate model apparent resistivity of relevant frequency, and use it to replace the apparent resistivity of the original data with corresponding frequency, so to update the original CSAMT data. We apply this treatment to the CSAMT data of Changbai mountain area exploring for geothermal resources, the inversion result can reasonably explain the reasons for the formation of the geothermal resources.
The main innovation of this paper is:
(1) Through the study of Cole-Cole model's spectrum, we find that the influence level on the amplitude and phase of complex resistivity by the polarizability parameter and the correlation coefficent of frequency when they are changing is larger than the influence level by parameter of time, at the same time we find that it is more superior to extract IP parameters through real part or amplitude than imaginary part. Through the study of compound Cole-Cole model's spectrum when its parametre is changes, we find that the compound model can be equal to a basic Cole-Cole model. In addition, we prove the amplitude of complex resistivity is lower than that of zero-frequency, it provides a thereunder for choosing initial parameter when doing inversion.
(2) Through the analyzing the result of cagniard apparent resistivity caused by the parameters changing of Cole-Cole model, concluding that the influence caused by the polarizability parameter or the frequency correlation coefficient is larger than that caused by time constant. This provides an evidence for regarding it as an empirical value when extracting IP parameters.
(3) We design an object function based on least squares sense to extract IP parameters, which modifing model parameters by gradient direction in order to speed up the convergence of the objective function.
(4) For the source of the IP effect consisting in cagniard apparent resistivity, we propose a method that can remove IP effect in the original data of CSAMT. The core of this method is to use IP parameters extracted, to calculate the theoretical value of relative frequency of apparent resistivity, and replace the value of corresponding frequency of original data, at the same time providing approach to select initial model and relative parameter.
This paper's endeavor will further promote the research of IP effect in the fields of Controlled Source Audio-frequency Magnetotelluric(CSATM), Magnetotelluric method(MT) and Transient electromagnetic method(TEM), and has an important theoretical and realistic significance on how to remove the IP effect, use IP effect in these fields.
Controlled source audio-frequency magnetotelluric(CSAMT) whics is developed on the basis of magnetotelluric method and the audiofrequency magnetotelluric method is an active source electromagnetic exploation method. In recent years it's theory research is continuous increasing, in the field of exploating concealed ore, oil, gas, geothermal resources and Hydrology has made good geological effect.
Induced polarization effect (IP) is caused by the effect of polarization in interface between the electronic conductor and the aqueous solution electrodes or the film polarization between clay surface and solution. IP phenomenon could be observed by DC or AC induced electronic field established artificially in mineralization rocks primarily consists of electronic conductor, graphitization rocks and ion conductor rocks. Because of the IP effect, the earth resistivity is a plural changing with frequency, but in the CSAMT the earth resistivity is regarded as a real number parametre in both forward and inversion, which is unrelated to frequency, ignoring the IP ingredients of electromagnetic response. These are a variety of plural models to describe polarization effect, this paper briefly summaries them.
In order to analysis the influence to electromagnetic field (Ex, Hy) produced by IP, firstly We derivate the calculation formula of the electromagnetic field in the homogeneous medium and layered medium, use the discrete method to calculate Ex and Hy in layered medium. To avoid attenuation of Hy in high frequency, we use a high precision filter coefficient to calculate it. According to scalar measurement of CSAMT, we summary it's working condition and parameters of observation so as to analysis the influence of IP.
We analysis the spectrum characteristics of basic Cole-Cole model, and find that the complex resistivity's real part generally far more than that of imaginary part, variation law between real part and amplitude or between imaginary part and phase follow the same variation law when Cole-Cole model parametres change. Real part is always positive and become smaller with the parameters of polarizability increasing, it tend to be a steady value at high frequeny band. Imaginary part changes according to concave curve, the high and low frequency band tend to be zero, and in the middle frequency band it gets negative value. The general varying trend's of real part and imaginary part when frequency correlation coefficient changes is similar to that of when polarization parametre changes. Real part increases in low frequency band with frequency correlation coefficient increasing, the absolute value of the imaginary part in lower and higher frequency band increases with the decrease of the C. Real part decrease with the increasing ofτ. But difference among real parts is very not obvious whenτis big enough, imaginary part changes as to concave curvee whenτis small, but it increases monotonously with frequency increase whenτis big enough, and finally it close to zero. And at higher frequency band, the absolute value of imaginary part decreased with the increasing ofτ, at low frequency band it changes more complexly. Then studies the influence level when model parameters changes, and find that the changing of polarization parametre and frequency correlation coefficient can produce greatly influences on amplitude and phase, but the time parameter changing has a little influence, so in extracting IP parameters can take it as an experience constant. By analysising the spectrum characteristics of compound Cole-Cole model, we find each parameters on the influence law of compound model is consistent with the influence law of basic model, if two models'similar parameters both change, the influence on amplitude depends on the total variation, and phase is mainly affected by the basic model with small parameters.
The paper analyzes the IP effect in homogeneous half-space and various types of cross-section layer earth by using the model of Cole-Cole, find that the influence to Ex and to Cagniard resistivity is far more than to Hy, this kind of influence mainly takes place in low-middle frequency band, at high frequencies IP effect disappeares off basically, so to analyzes the IP effect of CSAMT mainly considers the low-middle frequency band. Also, there exists the effect of near field at low frequency band, this is must be excluded. The influence law to electromagnetic field components is similar with the influence law of their own spectrum curve when the model parameters changing. The analysis showes that IP influence has a greatly effection on resistivity amplitude than that on phase, the influence level of various parameters is not the same:polarizability parameters and frequency correlation coefficient have greater influence than that caused by the time constant, to extract IP parameters should priority consider the parametres which can produce great influence.
Give the method of how to established polarization model of CSAMT measurement on polarization level layer, establish target function of least squares sense to extract the IP parameters. And the objective function and parameter expression is optimized. We give detailes of calculation, and in order to accelerate the convergence speed, using gradient method to modify model parameters. Run the procedures by setting initial model portfolio and using given model as the experimental data to extraction algorithm as to verify its validity.
According to the source of IP effect existing in the Cagniard resistivity, puts forward mean to remove IP effect from original data. This method firstly use the original data to design layered polarization model and establish objective function to extract IP parameters, then use extracted parameters to calculate model apparent resistivity of relevant frequency, and use it to replace the apparent resistivity of the original data with corresponding frequency, so to update the original CSAMT data. We apply this treatment to the CSAMT data of Changbai mountain area exploring for geothermal resources, the inversion result can reasonably explain the reasons for the formation of the geothermal resources.
The main innovation of this paper is:
(1) Through the study of Cole-Cole model's spectrum, we find that the influence level on the amplitude and phase of complex resistivity by the polarizability parameter and the correlation coefficent of frequency when they are changing is larger than the influence level by parameter of time, at the same time we find that it is more superior to extract IP parameters through real part or amplitude than imaginary part. Through the study of compound Cole-Cole model's spectrum when its parametre is changes, we find that the compound model can be equal to a basic Cole-Cole model. In addition, we prove the amplitude of complex resistivity is lower than that of zero-frequency, it provides a thereunder for choosing initial parameter when doing inversion.
(2) Through the analyzing the result of cagniard apparent resistivity caused by the parameters changing of Cole-Cole model, concluding that the influence caused by the polarizability parameter or the frequency correlation coefficient is larger than that caused by time constant. This provides an evidence for regarding it as an empirical value when extracting IP parameters.
(3) We design an object function based on least squares sense to extract IP parameters, which modifing model parameters by gradient direction in order to speed up the convergence of the objective function.
(4) For the source of the IP effect consisting in cagniard apparent resistivity, we propose a method that can remove IP effect in the original data of CSAMT. The core of this method is to use IP parameters extracted, to calculate the theoretical value of relative frequency of apparent resistivity, and replace the value of corresponding frequency of original data, at the same time providing approach to select initial model and relative parameter.
This paper's endeavor will further promote the research of IP effect in the fields of Controlled Source Audio-frequency Magnetotelluric(CSATM), Magnetotelluric method(MT) and Transient electromagnetic method(TEM), and has an important theoretical and realistic significance on how to remove the IP effect, use IP effect in these fields.
引文
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