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

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 the Galerkin 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 2D TM-mode, TE-mode data, which measured with the RMT method at frequencies between 10 and 300 kHz. 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 1/4 wavelength, 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.