基于非结构化网格的任意复杂2D RMT有限元模拟

Two-dimensional complicated radio-magnetotelluric finite-element modeling using unstructured grids

射频大地电磁法(RMT)是以潜艇天线发射的射线源等作为场源的一种地球物理勘探方法,目前被广泛应用于近地表工程和环境地球物理勘探.RMT数据解释常采用基于静态假设的大地电磁法(MT)程序,往往会反演出不真实的浅层目标体.为解决这一长期困扰RMT资料解释的问题,本文实现了考虑位移电流的RMT有限元数值模拟.为了处理任意复杂模型,如起伏地形,非结构的三角形网格被用于离散RMT模型.首先通过算例对比,验证了程序的正确性和可靠性.通过Dike模型讨论了空气层厚度对RMT数值解的影响,结果表明当空气层厚度大于1/4波长即可满足精度要求.以山脊模型为例计算了位移电流对RMT响应的影响,表明位移电流的影响会随着山脊高程的增加而增大.最后通过舒家店实际模型进一步验证了位移电流在RMT中的重要性.

As a newly developed geophysical exploration method,the radio-magnetotelluric（RMT） method is widely used in near-surface engineering and environment geophysical investigation.Since the interpretation of RMT data usually adopts the magnetotelluric（MT）forward modeling routine,in which displacement currents are generally neglected,the inverted conductivity model may not correctly reflect the true conductivity structure in the shallow subsurface.To solve this issue,we developed a finite-element forward modeling code for RMT data,in which displacement currents are considered.With this code,we analyze the dielectric effect of displacement currents on RMT responses over resistive subsurface models.First,we derived the boundary value problem（BVP）about the EM field components by theGalerkin method,in which the displacement currents were considered.Then we used the finite element method and PARDISO solver to calculate the electric and magnetic field components.To deal with complicated structure and surface topography,unstructured triangle grids were adopted for mesh generation.To improve the computation accuracy,the local refinement was used.At last,we developed a forward modeling code for RMT data with the consideration of displacement currents and analyzed the effect of displacement currents on 2DTM-mode,TE-mode data,which measured with the RMT method at frequencies between 10 and 300kHz.First,a synthetic model was used to verify the correction of our new code.The result shows that the response calculated by our code agrees well with other results.Utilizing the Dike model,the effect of the thickness of the air layer on accuracy of numerical solutions was investigated.The result shows that when the thickness of the air layer is greater than 1/4wavelength,highly accurate solutions can be guaranteed.Then the impact of displacement currents on RMT data with ridge terrain was studied on a hill model with complicated topography.From this model,the following results can be demonstrated：（1）The effect of displacement currents would increase with increasing height of the hill and the corner of hill was more easier to be affected.（2）The phase curves are more likely to be affected than apparent resistivity curves at high frequency.（3）The effect of displacement currents on apparent resistivity cannot be neglected when the frequency is larger than 100 kHz and the effect on phase must be considered when the frequency is larger than 20 kHz.Finally,a field model was studied to further demonstrate the importance of displacement currents in the RMT method.The results show that：（1）The error caused by displacement currents increases with frequency.（2）The apparent resistivity of TM-mode is more easily to be affected by displacement currents than TE-mode apparent resistivity.（3）For the area of quartz diorite with high resistivity,the percentage of displacement current density in all current density can be 10%.It is clear that displacement currents must be considered in RMT forward modeling.With numerical calculations,we demonstrated the effect of displacement currents on 2D RMT data.Forward modeling confirms that responses computed in the quasi-static approximation become increasingly inaccurate with rising frequency and strongly affected by terrain.However,RMT data processing and interpretation are mostly based on the MT program in recent years,which may result in incorrect structure.Based on the work in this paper,the author will develop RMT inversion code with consideration of displacement current.