带地形的三维复电阻率电磁场正反演研究

1、带地形的三维复电阻率电磁场正反演研究        本文就目前复电阻率法中的一些问题,开展了同时考虑激电效应、电磁效应和地形影响的三维复电阻率电磁场正反演理论研究。首先根据电磁散射积分方程理论,将地形看作空气中的不均匀体,并与均匀大地中的不均匀体同等看待,然后将大地中不均匀体的电导率表示成为?Cole-Cole?模型,通过剖分离散,变成代数方程组,再通过解方程组实现了考虑地形影响下电偶源和长导线源地面一次激发、一次接收和多次激发、多次接收的三维复电阻率电磁场正演模拟,并分析了异常体复电阻率参数对正演结果的影响特征。

2、随后本文推导了观测点处电磁场对于地下三维异常体复电阻率参数的灵敏度矩阵,利用灵敏度矩阵并结合复电阻率三维电磁场正演算法及阻尼最小二乘最优化拟合技术,实现了电偶源和长导线源地面一次激发、一次接收;多次激发、多次接收情况下三维复电阻率电磁场反演。理论算例的结果表明,本文中所提出的带地形的三维复电阻率电磁场正反演方法在理论上是完全可行的the characteristics of complex resistivity. Some scholars have expressed thecomplex resistivity by some mathematical models, for examp

3、le the ColeColemodel. It has been proved that the electrical anomaly of geologic body can bequantitative estimated by ColeColemodel parameters (direct resistivity 0 r ,chargeability m , time constant t and frequency dependence c ). It is veryimportant to study the methods to obtain the complex param

4、eters of geologicbody. Our country has lots of mountains, mountainous area take part in twoover three, and many metals are in them. In order to enhance the veracity andreasonably of the complex resistivity data, we must consider the effect oftopography. Therefore, we studied the research on electrom

5、agnetic forwardand inversion of complex resistivity by volume integral equation.Firstly, on the basis of analysis about the complex resistivity mathematicalmodels, the abnormal body with ColeColemodel and the topography areintroduced into the 3D electromagnetic modeling, and then the electric andmag

6、netic field of the 3D electromagnetic modeling are computed by volumeintegral equation .The complex resistivity 3D electromagnetic forwardcalculation with topography included electric dipole and line source. By modelcalculating, this article analyses the effect of source frequency and ColeColemodel

7、parameters ( 0 m r、t、c ) on electric and magnetic field at survey site.It concludes that: 1. The min values of secondary electric field real componentappear at the middle of abnormal body and topography body. The amplitude of min value at the middle of abnormal body decreases with source frequency、r

8、esistivity of topography and direct resistivity ( 0 r )? it increases withchargeability ( m )?but it almost dont change with time constant (t ) andfrequency dependence( c ).The amplitude of min value at the middle oftopography body almost dont change with direct resistivity ( 0 r )、chargeability ( m

9、 )、ti me constant (t )、frequency dependence( c ).2. The maxvalues of secondary electric field imaginary component appear at the middleof abnormal body and topography body. The amplitude of max value at themiddle of abnormal body decreases with direct resistivity ( 0 r )? it increaseswith source freq

10、uency ,chargeability ( m )?time constant (t ) and frequencydependence( c ).The amplitude of max value at the middle of topography bodyalmost dont change with direct resistivity ( 0 r )、chargeability ( m )、timeconstant (t )、frequency dependence( c ).3. The max and min values ofsecondary magnetic fiel

11、d real component appear near the middle of abnormalbody. The amplitude of max and min values near the middle of abnormal bodydecrease with source frequency and direct resistivity ( 0 r )? they increase withchargeability ( m )?but almost dont change with time constant (t ) andfrequency dependence( c

12、). There is not abnormal value at the middle oftopography. 4. The max and min values of secondary magnetic field imaginarycomponent appear near the middle of abnormal body. The amplitude of maxand min values near the middle of abnormal body decrease with directresistivity ( 0 r )? they increase with

13、 source frequency、chargeability ( m )、time constant (t ) and frequency dependence( c ).There is not abnormal valueat the middle of topography.Secondly, the paper develops the partial derivative matrix that reflects therate of real measurement field to the ColeColemodel parameters. It isachieved that

14、 the complex resistivity 3D electromagnetic with topographyinversion base on electric dipole and line source, and the inversion data can beacquired either one or several survey times. In the inversion, the convergence rate of dc resistivity ( 0 r ) is fastest , the convergence rate of dependence( c

15、) isthe second, and the convergence rate of time constant (t ) is slowest. On theother side, due to strong correlativity between time constant (t ) andchargeability ( m ), the time constant (t ) cant be accurate inversed when allthe complex resistivity parameters take part in the inversion. For this

16、 problem,considering the chargeability ( m ) can be measured or estimated before theinversion calculation. So we fixed the values of the chargeability ( m ) in theinversion, and then inversed other resistivity parameters ( 0 r、t、c ). Throughthe method we can obtain accurate result of inversion. The results oftheoretical calculation example indicate that the method about inversingresistivity parameters of 3D geologic body from el