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摘要
Traditional airborne EM full-wave forward modeling may be problematic when simulating complex transmitting waveforms and underground structures. The convolution algorithm requires high-precision of second order of derivative of transmitting current, which brings big challenges to AEM modeling, while the FDTD method is restrained by the mesh size and time step. To solve these problems, we adopt the edge finite-element method based on unstructured grids in combination with backward Euler scheme to perform 3D time-domain airborne EM (ATEM) modeling. This research will lay a foundation for the processing and interpretation of 3D full-wave time-domain airborne EM data.We start from time-domain electric field diffusion equation and discretize it with edge finite element method based on unstructured grids. The vector basis functions can automatically satisfy the divergence-free property of electrical fields. The tetrahedral grids have big advantages in simulating complex geological structures. We further adopt Galerkin's method to obtain the finite-element governing equation. The backward Euler scheme is then used to discretize the governing equation to establish an unconditionally stable implicit equations system. We simulate the full-wave responses of arbitrary transmitting waveform by directly changing the instantaneous current for each time channel. @@@ To check the accuracy of our algorithm, we first construct a homogeneous half-space model for a center-loop AEM system. We calculate the responses for a half-sine and trapezoid transmitting wave that shows a good agreement with 1D solutions. Secondly, we simulate the EM responses for the transmitting wave used by HELITEM MULTIPULSE system over a 3D geological model with both convolution algorithm and FETD method. The modeling results of dB(z)/dt from the convolutional algorithm shows drastic oscillations for both on- and off-time. That's due to the low precision of second derivative of transmitting current. However, the results obtained from FETD are stable and smooth. Thirdly, to further prove the capability of FETD to model complex-waveforms, we simulate the responses of VTEM-system. It shows that the results obtained by FETD method is more stable. Fourthly, we model the full-wave responses for half sine, trapezoidal-, and triangular transmitting waves with the same energy over a vertical plate model. The comparison of the responses for the three waveforms shows that trapezoidal wave has the biggest investigation depth. Finally, we simulate the full-wave responses for a dipping plates model, which verifies the capability of FETD method to handle complex geological structures. @@@ We have successfully implemented the 3D ATEM forward modeling with edge finite-element method based on tetrahedral grids. Different from the convolution algorithm, the full-wave responses of arbitrary transmitting waveform is simulated by directly changing the instantaneous current of every time channel. The use of vector basis functions and unstructured grids avoid the false solutions for complex structures. As a stiff integration, backward Euler scheme is unconditional stable that relaxes the condition on the time steps, resulting high-precision AEM responses.
- 出版日期2017-1
- 单位吉林大学
