帶地形的三維復電阻率電磁場正反演研究

1、帶地形的三維復電阻率電磁場正反演研究        本文就目前復電阻率法中的一些問題,開展了同時考慮激電效應、電磁效應和地形影響的三維復電阻率電磁場正反演理論研究。首先根據電磁散射積分方程理論,將地形看作空氣中的不均勻體,并與均勻大地中的不均勻體同等看待,然后將大地中不均勻體的電導率表示成為?Cole-Cole?模型,通過剖分離散,變成代數方程組,再通過解方程組實現了考慮地形影響下電偶源和長導線源地面一次激發(fā)、一次接收和多次激發(fā)、多次接收的三維復電阻率電磁場正演模擬,并分析了異常體復電阻率參數對正演結果的影響特征。

2、隨后本文推導了觀測點處電磁場對于地下三維異常體復電阻率參數的靈敏度矩陣,利用靈敏度矩陣并結合復電阻率三維電磁場正演算法及阻尼最小二乘最優(yōu)化擬合技術,實現了電偶源和長導線源地面一次激發(fā)、一次接收;多次激發(fā)、多次接收情況下三維復電阻率電磁場反演。理論算例的結果表明,本文中所提出的帶地形的三維復電阻率電磁場正反演方法在理論上是完全可行的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