电磁探测“盲区”中偶极子源的位移电流效应分析

发布时间：2018-02-11 11:46

本文关键词： 位移电流偶极子源汉克尔变换 G-S变换　出处：《重庆大学》2015年硕士论文　论文类型：学位论文

【摘要】：利用地质体的电性,结合不同的场源形式、工作方式、观察要素等可形成不同的电磁探测方法。电磁法按照响应的性质可分为频率域和时间域方法两类,目前常用的频率域电磁法所采用的频率都较低,穿透深度大,地下2m~20m左右的深度成了它的探测“盲区”,而瞬变电磁法(时间域电磁法)的早期信号携带地下浅部结构信息,而现有的仪器记录或处理的数据几乎全是晚期信号,使瞬变电磁法损失了浅部探测能力,从地表到地下20m左右也是它的探测“盲区”。地下浅层范围(包含探测“盲区”)的勘查对农业、地下水、废物处理、考古和土壤工程都是非常重要的,也有利于对深部电磁法勘探资料进行解释。要实现“盲区”探测,必须提高发射频率或使用早期瞬变信号,此时就必须考虑位移电流的影响,而现有的电磁法理论和应用研究几乎都未考虑位移电流。针对以上这些问题,本文首先系统推导了偶极子源(磁偶极子、电偶极子)在典型结构(全空间、均匀半空间、分层媒质)下计及位移电流的频域电磁响应,将其转换到复频域后再转换到时域,结合供电电流便得到不同时域响应的逆拉氏变换形式。针对频域响应中涉及到的汉克尔变换,在Pravin指数函数展开的基础上新增基函数,提出计算汉克尔变换的改进方法,该方法具有简单易行、可逼近凸函数、插值精度高和计算效果稳定的优点,为汉克尔变换的计算提供另一种可选方案。而在时域响应的数值计算中,采用了具有纯实数运算、计算精度高、所需频点少和可用于计算复杂地电模型等优点的Gaver-Stehfest逆拉氏变换法。最后分析了位移电流对频域和时域电磁响应的影响,并总结了以下规律:1)频域内:高频下计算更能表示有效研究深度的博斯蒂克深度时,必须考虑位移电流的影响,且可根据频率、电阻率和相对介电常数大致确定博斯蒂克深度;频率和介电常数的增大、电导率的减小,都将加深位移电流效应的影响;与电偶极子相比较,磁偶极子可忽略位移电流影响的低频范围更大,且在高频时更易受位移电流的影响;在分层媒质下,若顶层地电参数确定的博斯蒂克深度小于顶层厚度,那么顶层的电导率和介电常数就决定了幅度响应比随频率变化的规律,且电导率的减小和相对介电常数的增大,将使比值出现波动所对应的频率和幅度减小,电偶极子的比值在高频时变化更剧烈。2)时域内:计及位移电流时两种偶极子源的时域响应到达测点的时间都晚于忽略位移电流时的到达时间;受0ike-ρ这一衰减因子的影响,G-S变换得到的时域响应在小范围内出现了正负值交替现象;位移电流对斜阶跃响应的影响比阶跃响应大,对z1h斜阶跃的影响在几微秒范围内,而对z1?h?t的范围可扩展到几十甚至几百微秒;在非零关断时,若仍按阶跃响应理论分析将产生较大误差,且关断时间越长,误差越大;现有瞬变仪器只有关断时间达10ns时,能部分测量计及位移电流对z1h和z1?h?t斜阶跃响应产生影响的信号;若关断时间为T1s和采样时间范围为T2s~T3s(关断后)的仪器要测量位移电流效应对斜阶跃响应的影响信号,那么应使(T1+T2)s小于t1s(t1指关断时间T1对应的计及位移电流时斜阶跃响应到达测点的时间),且(T1+T3)s的值应尽可能的大,至少应大于t2s(t2指计及和忽略位移电流时斜阶跃响应的相对误差小于2%的时间)。
[Abstract]:Using electrical geological bodies, combined with the field source form, different ways of working, observation elements can form different electromagnetic detection method. According to the nature of the electromagnetic response can be divided into the frequency domain and time domain method of class two, the frequency domain electromagnetic method commonly used in the low frequency, large penetration depth underground, the depth of about 2m~20m to its detection "blind spots", and the transient electromagnetic method (time domain electromagnetic method) of the early signal carrying information of underground shallow structure, while the existing instrument records or data processing almost all advanced signal, the transient electromagnetic method loss detection ability shallow, from the earth's surface to about 20m and its detection "blind spot". The shallow groundwater range (including the detection of "blind spots") for exploration of agriculture, groundwater, waste disposal, archaeological and soil engineering is very important, but also conducive to the deep electromagnetic prospecting information The material was explained. The realization of "blind spot" detection, must improve the emission frequency or early transient signal, we should consider the effect of displacement current, and electromagnetic theory and Application Research of almost all of the existing without considering the displacement current. To solve these problems, this paper firstly deduces the system (magnetic dipole, dipole source the electric dipole in a typical structure (space), homogeneous half space, layered medium frequency electromagnetic) considering the displacement current response, convert it to a complex frequency domain and then converted to time domain, combined with the power supply current is not at the same time domain response of the inverse Laplace transform. For Hankel transform frequency response involved in based on the foundation, the new function of Pravin index function, put forward the improvement method of calculating Hankel transform, this method is simple, approximate convex function, interpolation accuracy and calculation stability The advantages, provide another alternative for computing Hankel transform. And in the numerical calculation of time domain response, with a pure real operation, high accuracy, less required frequency and can be used for the calculation of complex geoelectric model and other advantages of Gaver-Stehfest inverse Laplace transform method. Finally analyzes the influence of displacement current the frequency and time domain electromagnetic response, and summarizes the following rules: 1) in frequency domain: high frequency calculation more Bostic said the depth of effective depth research, must consider the effect of displacement current, and according to the frequency, resistivity and relative dielectric constant of approximately determined Bostic depth; increasing the frequency and the dielectric constant of the conductivity. The effect will be reduced, deepen the displacement current effect; compared with the electric dipole and magnetic dipole frequency range of displacement current may be omitted more affected, and at high frequency is more susceptible to the displacement current Effect; in layered media, if Bostick depth determine the top-level geoelectric parameters is less than the top thickness, so the top of the conductivity and dielectric constant determines the amplitude response of the ratio varies with frequency, and the decrease of conductivity and relative dielectric constant increases, will make the ratio of value of frequency and amplitude corresponding to the decrease of volatility the change of.2 ratio, more intense electric dipole in high frequency domain and time domain): two kinds of displacement current dipole source in response to the arrival point time is later than the arrival time ignore the displacement current; 0ike- P this attenuation factor influence, time domain by G-S transform in response to positive and negative value alternation in a small range; the displacement current step response effect on the oblique order response than the step of z1h, ramp effect in a few microseconds range of Z1? H? T range can be extended to dozens or even hundreds of micro In non zero seconds; turn off, if according to the step response theory will have a greater error, and the turn off time is longer, the greater the error; the existing transient instrument only the off time of 10ns, part of gauge and displacement current of z1h and Z1? H? T oblique step response the influence of the signal; if the shutdown time is T1s and the sampling time range is T2s~T3s (turned off) of the instrument to affect the signal measurement of displacement current effect in response to the ramp, so should be less than t1s (T1+T2) s (T1 refers to the total displacement and current off time T1 corresponding to the ramp response arrive at the measuring point in time), and (T1+T3) the value of s should be as large as possible, at least should be greater than T2S (T2 means considering or neglecting displacement currents when the oblique step response of the relative error is less than 2% of the time).

【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.325

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