摘要
目前Cole-Cole模型主要用在激电和生物制药等方面。瞬变电磁场的建立过程及其附加效应—集流效应、激发极化效应、磁张弛效应等都具有张弛特征,而Cole-Cole模型是表征张弛效应最经典的数学物理模型,因此研究基于Cole-Cole模型的瞬变电磁响应具有重要意义。
论文简单介绍了Cole-Cole模型的由来,并举实例说明了各个参数的变化对Cole-Cole模型的影响。然后详细推导了水平层状介质条件下,基于Cole-Cole模型中心回线瞬变电磁法阶跃响应的求解及计算方法,并得出了圆回线中心磁场垂直分量的表达式。针对积分的核函数,通过整体趋势和具体频率两个方面的比较,得出了Cole-Cole模型同实电阻率模型的核函数变化趋势相近,从而在实电阻率模型中应用的数值算法同样可以应用到Cole-Cole电阻率模型中。又通过计算时间和计算精度两个方面的比较,选择了更适合本论文的改进的数值滤波法,并编写了基于Cole-Cole模型的一维正演程序。在所编正演程序的基础上,分别计算了两层和三层两种地质模型中Cole-Cole模型电阻率中各个参数的变化对瞬变电磁衰减曲线的影响。通过改变Cole-Cole电阻率模型中同一个参数,比较同一参数不同情况下瞬变电磁的衰减曲线,分析其特征和规律,得出了以下结论：充电率m在0.1～0.9之间变化时,基于Cole-Cole模型的瞬变电磁衰减曲线的衰减趋势随着m的增大而减小,但是变化不大；频率相关系数c在0.1～0.9之间变化时,衰减曲线的衰减趋势随着c值的增大而增大,但是这种衰减趋势变化也不是很明显；τ值对Cole-Cole模型的瞬变电磁衰减曲线趋势影响大,同时瞬变电磁衰减曲线的衰减趋势与时间常数τ的变化并不是简单的正反比关系。
论文最后采用Cole-Cole电阻率模型和实电阻率模型对广西大厂矿区,某测点实测瞬变电磁响应曲线进行了正演拟合,实电阻率模型的拟合曲线自始自终都是正值衰减,而Cole-Cole电阻率模型不但能够拟合的瞬变电磁衰减曲线而且能拟合负值现象,从而为实现定量解释极化介质奠定基础。
Cole-Cole model currently used primarily in IP and biopharmaceutical aspects. The process of building transient electromagnetic and its additional effect such as galvanic induced polarization, magnetic relaxation effects and so on, are all of relaxation characteristics. Cole-Cole model is the most classical mathematical and physical model to explain the relaxation effects, therefore, based on Cole-Cole model of transient electromagnetic response is important.
Paper briefly describes the origin of Cole-Cole model, citing examples of various parameters on the Cole-Cole models. Then the level of layered media is derived in detail under the conditions, based on Cole-Cole model of central loop transient electromagnetic method to solve the step response and calculation methods, and obtained a circular loop center of the magnetic field vertical component of the expression. For the integral kernel function, the overall trends and specific frequencies through the two areas, and obtains the Cole-Cole model with the actual trend of the kernel function is similar to the resistivity model in the real application, so numerical algorithms can also be applied to Cole-Cole model. Also the improved linear filter was chosen by two comparisons of computation time and accuracy, and prepared one-dimensional forward program of the Cole-Cole model. In the compilation process is performed based on two and three are calculated geological model of two Cole-Cole model in the resistivity of the various parameters on the transient electromagnetic decay curves. By changing Cole-Cole model in the same parameters to compare the same parameters under different conditions of transient electromagnetic attenuation curve of the characteristics and laws, reached the following conclusions:the chargeability m varied between 0.1 and 0.9, based on Cole-Cole model of transient electromagnetic decay curve of the attenuation trend of decrease with the increase of m, but little change; the frequency dependence c between 0.1～0.9 changes, the decay curve of the attenuation trend with the c value increases, but this attenuation is not very clear trend of change; the time constantτvalue of the Cole-Cole model of transient electromagnetic trends affecting the decay curve, but the time constantτand electromagnetic decay curve of the change is not a simple relationship between positive and negative ratio.
Finally using Cole-Cole model and the real resistivity model in Dachang area, measured in a measuring point of the transient electromagnetic response of the forward curve fitting, real resistivity model curve fitting from beginning to end positive attenuation, and Cole-Cole model can fit the transient electromagnetic decay curve and can fit a negative phenomenon, so as to achieve quantitative interpretation of polarized media basis.
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