Summary Based on the regular triangular dissection for finite element method, we implemented the forward modeling of 2.5-D airborne transient electromagnetic method. The 3-D EM field was firstly transformed into Laplace domain and after that we will apply Fourier transform to reduce the dimension from 3-D to 2.5-D. We can obtain the EM field solution in Laplace domain by applying finite element method. The inverse Laplace transform is applied to our solution which finally leads to the airborne EM response in time domain. In compared to the traditional method, we apply our finite element method to the anomalous field which can avoid the singularity problem caused by the source which can excite the anomalous EM field. The EM source can be imposed to our process by incorporate the background EM field. The computation error can be accumulated due to the large variation of EM field and it can also be amplified in the process of Laplace transform and Fourier transform. In order to get accurate result, the error should be well controlled in every procedure. The induced electromagnetic force can be computed accurately from vertical magnetic component by applying Lagrange interpolation. The synthetic model study shows that our numerical solution fits well with the analytical solution for homogeneous and layered earth model. The study also demonstrated the effectiveness of our numerical method.
We have investigated the 3D topographic effects on controlled-source audio-frequency magnetotelluric data. Two 3D topographic models are considered: a trapezoidal-hill model and a trapezoidal-valley model. Different responses are generated, including the amplitude of the electric field, the amplitude of the magnetic field, the apparent resistivity, and phase data. The responses distorted by the 3D topography are simulated for the source located next to and on the hill/valley. Our study indicates that all electric field, magnetic field, apparent resistivity, and phase data are influenced by 3D topography, but to different extents. These topographic effects depend on the transmission-receiver-topography geometry, the transmission frequency, earth resistivity, and the roughness of the surface. The effects in the near-field generated by topography in the survey area are quite different from those in the far-field because of the existence of the source. Compared with those in the far-field zone, the magnetic field and phase data in the near-field zone are less distorted, but more distortions can be found on the electric field and apparent resistivity data over the hill and valley models. Our results also indicate that not only can the 3D topography in the receiver area lead to strong distortions, but also that at the source position can lead to strong distortions. We concluded our study by quantifying the roughness with which the topographic distortion can be ignored, setting the accepted data distortion to a maximum of 10%.
We introduce a new method of modeling and inversion of potential field data generated by a density contrast surface. Our method is based on 3D Cauchy-type integral representation of the potential fields. Traditionally, potential fields are calculated using volume integrals of the domains occupied by anomalous masses subdivided into prismatic cells. This discretization is computationally expensive, especially in a 3D case. The Cauchy-type integral technique makes it possible to represent the gravity field and its gradients as surface integrals. This is especially significant in the solution of problems of modeling and inversion of gravity data for determining the depth to the basement. We demonstate our inversion method based on the Cauchy-type integral for several synthetic models. The results show that the new method is capable of providing high-resolution depth estimation for the sediment-to-basement interface.
Abstract The total magnetization of an underground magnetic source is the vector sum of the induced magnetization and the natural remanent magnetization. The direction of the total magnetization serves as important a priori information in the inversion and processing of magnetic data. We demonstrated that the total gradient of the magnetic potential with vertical magnetization constitutes the envelope of the vertical component of the magnetic field for all directions of the Earth's field and source magnetization. The total gradient of the magnetic potential with vertical magnetization and the reduction‐to‐the‐pole field simultaneously tend to achieve maximum symmetry near the correct total magnetization direction. As a result, the total magnetization direction can be estimated by computing the correlations between the reduction‐to‐the‐pole and the total gradient of the magnetic potential with vertical magnetization. The proposed method yields accurate magnetization directions in synthetic model examples. The total gradient of the magnetic potential with vertical magnetization is less susceptible to data noise than transforms which are derived from the high‐order magnetic field derivatives or tensors. The estimation results are slightly affected by changes in the source magnetization direction. In a field example in the Weilasito region (North China), the reduction‐to‐the‐pole fields calculated using the estimated magnetization directions are well centred over the source. The proposed method obtained a more focused magnetization direction than that of a three‐dimensional magnetization vector inversion. The total gradient of the magnetic potential with vertical magnetization therefore provides a novel and accurate approach to determine the total magnetization direction from the total field anomaly in a variety of situations.
Inverting potential field data presents a significant challenge due to its ill-posed nature, often leading to nonunique model solutions. Addressing this, our work focuses on developing a robust joint inversion method for potential field data, aiming to achieve more accurate density and magnetic susceptibility distributions. Unlike most previous work that used regular meshes, our approach adopts an adaptive, unstructured tetrahedral mesh, offering enhanced capabilities in handling the inverse problem of potential field methods. During inversion, the tetrahedral mesh is refined in response to the model update rate. We integrate a Gramian constraint into the objective function, allowing the enforcement of model similarity in terms of either the model parameters or their spatial gradients on an unstructured mesh. In addition, we use the moving least-squares method for gradient operator computation, which is essential for model regularization. Our model studies indicate that this method effectively inverts potential field data, yielding reliable subsurface density and magnetic susceptibility distributions. The joint inversion approach, compared with individual data set inversion, produces coherent geophysical models with enhanced correlations. Notably, it significantly mitigates the nonuniqueness problem, with the recovered anomaly locations aligning more closely with actual ground truths. Applying our methodology and algorithm to field data from the Ring of Fire area in Canada, the joint inversion process has generated comprehensive geophysical models with robust correlations, offering potential benefits for mineral exploration in the region.
Following recent advances in SQUID technology, full tensor magnetic gradiometry (FTMG) is emerging as a practical exploration method. We introduce 3D regularized focusing inversion for FTMG data. Our model studies show that inversion of magnetic tensor data can significantly improve resolution compared to inversion of magnetic vector data for the same model. We present a case study for the 3D inversion of GETMAG® FTMG data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from our 3D inversion agree very well with the known geology of the area.
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