3-D inversion of transient EM data with topography using unstructured tetrahedral grids

Airborne electromagnetic (AEM) data processing and inversion has progressed from the early conductivity-depth imaging, to 1D inversion for a layered earth model, and most recently to 2D/3D inversions. The new processes have used methods for searching for solutions, applying constraints, and focusing images, such as Occam’s, laterally constrained, and holistic inversions. For airborne data imaging and 1D inversion, some algorithms are fast, whereas others have control over data misfit and the vertical or lateral smoothness. Beyond 1D algorithms, 2D/3D inversions are based on currently used methods such as isolated conductor models (which are good for highly conductive orebodies in resistive background) and techniques that discretized regions that are used for more complex structures and backgrounds. In the latter case, the computations are slow, so research is focusing on time-efficient computer algorithms for solving the equations such as Gauss-Newton, quasi-Newton, and nonlinear conjugate gradient algorithms. For the electromagnetic (EM) problem, the solution can be obtained in a more practical time frame if material that has minimal impact is ignored. Two approaches can be used to speedup the EM inversion process — the moving footprint and direct solver methods. We hope our work will to some extent help stimulate and focus the research in AEM inversion.

Review on airborne electromagnetic inverse theory and applications

3D time-domain airborne EM modeling for an arbitrarily anisotropic earth

We investigate an algorithm for 3D time-domain airborne electromagnetic (AEM) inversion based on the finite-volume (FV) method and direct Gauss-Newton optimization, where we obtain high efficiency by constraining the modeling volume to the AEM volume of influence (VOI) of a 3D source within the earth, rather than using the larger VOI of the AEM system. A half-space or layered earth is used to model the background field in the time domain, taking into account the transmitter waveform through convolution. Assuming that the 3D source of any secondary field detected at a survey point lies within the moving VOI of the airborne system, we conduct time-domain forward modeling and Jacobian calculation using an FV method within the 3D source VOI that requires a small number of cells for discretization. A local mesh and direct solver are shown to further speed up the computation. A synthetic isolated synclinal conductor inversion shows good agreement with the model geometry and provides a good fit to the data contaminated with noise. A synthetic multiple-body model inversion was also quite successful, showing that our algorithm is effective and about four times faster than inversion using the total-field method. Finally, we inverted GEOTEM data over the Lisheen deposit, where our inversion result was consistent with the published geology.

3D time-domain airborne electromagnetic inversion based on secondary field finite-volume method

3D time-domain airborne EM forward modeling with topography

We have developed a goal-oriented adaptive unstructured finite-element method based on the scattered field for 3D frequency-domain airborne electromagnetic (AEM) modeling. To guarantee the EM field divergence free within each element and the continuity conditions at electrical material interfaces, we have used the edge-based shape functions to approximate the electrical field. The posterior error for finite-element adaptive meshing procedure is estimated from the continuity of the normal component of the current density, whereas the influence functions are estimated by solving a dual forward problem. Because the imaginary part of the scattered current is discontinuous and the real part is continuous, we use the latter to estimate the posterior error. For the multisources and multifrequencies problem in AEM, we calculate the weighted posterior error for each element by considering only those transmitter-receiver pairs that do not adhere to our convergence criteria. Finally, we add a minimum volume ...

A goal-oriented adaptive finite-element method for 3D scattered airborne electromagnetic method modeling

An airborne electromagnetic (AEM) survey often covers hundreds of square kilometers. Huge amounts of survey data make 2D/3D data inversion very difficult. However, due to the compact configurations of AEM systems, the sensitive area for each single survey station is much smaller than the whole survey area, which makes it possible to only invert partial survey data. The sensitive area is called the footprint. Based on “moving-footprint” technology, the entire survey can be divided into subareas and the data are first inverted individually and then combined to form the inversions of the entire survey area, so that the cost for forward and inverse modeling can be vastly reduced. Contrary to previous electromagnetic (EM) footprints defined only for an EM transmitter or for a perfectly conductive earth, we defined the frequency-domain AEM footprint by considering a complete AEM transmitter-receiver system over an earth with limited conductivity. We used the tensor Green’s function to calculate the seco...

Footprint for frequency-domain airborne electromagnetic systems

We present an efficient three-dimensional (3D) time-domain airborne electromagnetic (EM) modeling based on finite-volume method, in combination with the merits of solving the secondary field, local mesh, and the direct solver. Taking the strategy of separating primary from secondary field for the calculation of time-domain EM field, we greatly reduce the number of grids in comparison to direct solution of the total field. The primary field is obtained by Hankel transform from the frequency-domain for a half-space or layered earth model. The techniques of local mesh and direct solver are adopted to further improve the modeling efficiency. We compare and discuss the characteristics of the method developed in this paper from time consumption and grid sizes. The EM responses for different transmitting waveforms are calculated via a convolution between step-wave responses and the transmitting current or its derivatives. All numerical experiments on models with multiple geological bodies and fracture z...

Efficient Modeling of Time-domain AEM using Finite-volume Method

The 3-D spectral-element method (SE) based on Gauss–Lobatto–Legendre (GLL) polynomials is a very efficient and accurate solver for high-frequency computational electromagnetic (EM) modeling. Although the SE method is based on a weighted residual technique similar to the finite-element method (FE), it utilizes polynomial interpolation functions rather than linear interpolation functions. The GLL polynomials have the characteristic of exponential convergence with the order of polynomial that helps improve the modeling accuracy. We apply the SE method in the frequency range (900 Hz to 56 kHz) to airborne EM modeling. Starting from the vector Maxwell's equations, we use the SE method to establish spatial-discrete forms of 3-D vector Helmholtz equations and adopt GLL integration to calculate the matrix elements. The magnetic field is calculated using Faraday's law. To check the accuracy of the SE algorithm, we compare our results with semi-analytical solutions for a homogeneous half-space and a layere...

Jing Cai

Papers

A goal-oriented adaptive finite-element method for 3D scattered airborne electromagnetic method modeling

Footprint for frequency-domain airborne electromagnetic systems

3D time-domain airborne EM forward modeling with topography

Efficient Modeling of Time-domain AEM using Finite-volume Method

3-D Modeling for Airborne EM using the Spectral-element Method