Research On Electromagnetic Modeling Of 3D Complex Resistivity With Topography

the characteristics of complex resistivity. Some scholars have expressed thecomplex resistivity by some mathematical models, for example 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 parameters 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 electromagnetic 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 andmagnetic 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 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,resistivity of topography and direct resistivity ( 0 r )? it increases withchargeability ( m )?but it almost don't change with time constant (t ) andfrequency dependence( c ).The amplitude of min value at the middle oftopography body almost don't change with direct resistivity ( 0 r ),chargeability ( m ),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 frequency ,chargeability ( m )?time constant (t ) and frequencydependence( c ).The amplitude of max value at the middle of topography bodyalmost don't change with direct resistivity ( 0 r ),chargeability ( m ),timeconstant (t ),frequency dependence( c ).3. The max and min values ofsecondary magnetic field 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 don't change with time constant (t ) andfrequency dependence( c ). 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 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 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 ) 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 ) can't be accurate inversed when allthe complex resistivity parameters take part in the inversion. For this 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 electromagnetic informationis feasible.The production of research further developed the theory of forward andinversion for complex resistivity method. It has important theoretical andpractical significance.