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Due to the high detection efficiency of the airborne time-domain electromagnetic method, it can quickly collect electromagnetic response data for large area-wide regions, but it also brings great challenges to the inversion interpretation of the data because there are numerous survey data that need to be inverted. Conventional optimal inversion and fast imaging methods still take a long time to obtain conductivity and depth information, which affect the efficiency of real-time data interpretation. In this paper, we present a deep learning inversion method that can be used to solve the fast inversion problem of airborne time-domain electromagnetic data; the method uses a one-dimensional convolutional neural network. The network structure consists of two parts containing different numbers of convolutional and pooling layers. The training sample dataset was generated via two ways of constructing geoelectric models through forward modelling. To check the effectiveness of our deep learning inversion strategy, we tested it on synthetic data and two types of survey data. The experimental results show that this inversion method is effective and that it can be applied to airborne time-domain electromagnetic data collected using different observation systems. The proposed inversion method can obtain better inversion results for both simple and complex stratigraphic structures and requires significantly less computation time compared to conventional optimal inversion methods. [ABSTRACT FROM AUTHOR]

In mineral exploration, the ores with different magnetic susceptibility can be well delineated by physical property inversion of magnetic data. However, further wide applications of the magnetic inversion method have been seriously restricted by the existence of strong remanence and the computation of large-scale datasets. To solve these two problems, this study innovatively presents an efficient magnetic inversion algorithm in the presence of strong remanence. The weighted data misfit term and regularization term were used to establish the objective function. The detailed related formulas were derived and presented. For numerical computation, the Taylor series approximation was introduced in the objective function to linearize the relationship between the transformed magnetic data and magnetic susceptibility. The objective function was converted to a general Tikhonov form by several matrix transformations. To realize computational efficiency, a fast randomized algorithm was utilized to efficiently solve the Tikhonov problem and to efficiently determine the suitable regularization parameter along with the generalized cross-validation (GCV) method. Comparative tests on synthetic example show the effectiveness and efficiency of the proposed algorithm. The proposed efficient algorithm is successfully applied to two sets of real magnetic data, and the inversion results are verified. [ABSTRACT FROM AUTHOR]

Due to the high detection efficiency of the airborne time-domain electromagnetic method, it can quickly collect electromagnetic response data for large area-wide regions, but it also brings great challenges to the inversion interpretation of the data because there are numerous survey data that need to be inverted. Conventional optimal inversion and fast imaging methods still take a long time to obtain conductivity and depth information, which affect the efficiency of real-time data interpretation. In this paper, we present a deep learning inversion method that can be used to solve the fast inversion problem of airborne time-domain electromagnetic data; the method uses a one-dimensional convolutional neural network. The network structure consists of two parts containing different numbers of convolutional and pooling layers. The training sample dataset was generated via two ways of constructing geoelectric models through forward modelling. To check the effectiveness of our deep learning inversion strategy, we tested it on synthetic data and two types of survey data. The experimental results show that this inversion method is effective and that it can be applied to airborne time-domain electromagnetic data collected using different observation systems. The proposed inversion method can obtain better inversion results for both simple and complex stratigraphic structures and requires significantly less computation time compared to conventional optimal inversion methods.

Residual Bouguer gravity anomaly inversion can be used to imaging for local density structures or to interpret near-surface anomalous mass distribution. The reasonable prior information is the crucial recipe for obtaining a realistic geological inversion result, especially for the ill-posed geophysical inversion problem. The conventional strategies introduce the prior constraints or joint multidisciplinary information in object function as regularization, and then use some optimization algorithm to minimize the object function. This process is called model-driven approach and is usually time-consuming. In recent years, the rapid development of machine learning technology has provided new solutions for solving geophysical inversion problems. Machine learning methods can reduce the dependence on prior information in the inversion process through setting special training datasets, and the time consumption of an inversion process executed by the trained model can be shortened by several orders of magnitude, which is conducive to fast inversion for the same type of application scenarios. In this study, we were inspired by the U-net model and develops the GV-Net (Gravity voxels inversion network) model using the convolutional neural network for the inversion of residual gravity anomalies. We first discussed the effects of different loss functions on the convergence speed of model training and prediction accuracy. Then, we analyzed the robustness of our model by changing noise levels of the datasets. At last, we employed this model in a real scenario. The results have demonstrated that the GV-Net model has the ability to deal with specific inverse problems by predefined training datasets.

Accurate measurements of the emitted radiation are crucial for controlling a fusion reactor. In addition to affecting the global power balances, high levels of local radiation emission can indicate that the plasma is losing stability and can disrupt. Several radiation events can occur in a tokamak differing in localization, shape, and dimension. Each of these can be originated by various causes and degrade the plasma confinement in different ways. On current tokamaks, radiation is measured by bolometers, but these provide only line integrated values. For this reason, quite sophisticated tomography inversion algorithms are required to obtain local information, but this approach is slow and cannot be used in real time yet. A fast inversion method, which provides local information with high temporal resolution, has been developed. This allows to reconstruct the emissivity in all the relevant regions of the plasma and so to recognize different anomalous radiation events. In this work, an analysis of the fast inversion method and of its performances is presented using synthetic data. The reliability of the method is tested by simulating different patterns of radiation. Then the accuracy is evaluated by analysing the impact of different features, such as shape and position, on the reconstruction. [ABSTRACT FROM AUTHOR]

Objectives: Based on the gravity focusing inversion, we propose the multi‑scale source grid focusing inversion. This method aims to reduce the computation time and improve the spatial resolution of the focusing inversion. Methods: Firstly, the source grid is divided into the coarse grid, which contains less cells than the regular grid. Then we perform the focusing inversion in the coarse grid using conjugate gradient method. In the coarse grid phase it consumes short computation time for each iteration. Secondly, as the relative residual decreases to a low threshold value, the iteration is suspended and the coarse grid density is mapped into the fine grid. We compared 3 density mapping methods. Those methods use the average value of coarse cells, the value of the maximum area coarse cell and the maximum value of coarse cells. Then we adopt the average value method for the optimum density mapping. Finally, the iteration is resumed in the fine grid and converges to the final solution. Results: The model testing result shows: (1) More than 50% computation time is cut down by using the multi‑scale source grid. (2)Compare to the single scale focusing inversion, the multi‑scale source grid focusing inversion of gravity and gravity gradient data considerably improve the revelation of the single hexahedron model, the double hexahedrons model placed horizontally and the double hexahedrons model with different sizes and depths. (3)In particular the revelation of the body bottom or the deeper bodies is improved from the regular gravity inversions. The measured data testing result shows: (1)The inversion result of gravity and gravity gradient data of Kauring testing ground is generally consistent with the known results. The revelation of the top and bottom of the center anomaly body is close to the previous results. (2)The result indicates the larger depth of the south side anomaly body than the previous results. That supports the wide and gentle slope form of the gravity gz data at the south side. Conclusions: The multi‑scale grid focusing inversion can process the gravity or/and gravity gradient simulated or measured data. This method significantly reduces the computation time and improves the resolution ability from the regular focusing inversion with the single scale source grid. [ABSTRACT FROM AUTHOR]

Information about anisotropic resistivity is essential in real-time correlation, updating of formation model and making more confident geosteering decisions in logging-while-drilling (LWD) application. However, abnormal responses such as curve separations and apparent resistivity "horns" often exist in the LWD resistivity measurements due to the influences of complex downhole environments. Thus, accurate formation resistivity is not readily available. In this paper, we present an efficient inversion scheme for the rapid estimation of anisotropic resistivity from LWD resistivity measurements acquired in high-angle and horizontal wells. Several strategies are adopted in the inversion: (1) a one-dimensional (1D) simulator with a simplified three-layered model guarantees the forward speed and keeps the number of inverted parameters as few as possible; (2) combined with geological and petrophysical bounds, the tool constraints derived from a detection capability analysis of LWD resistivity measurements are applied to scale down the inverted parameters' searching scope, which avoids meaningless solutions and accelerates the inversion significantly; (3) multiple-initial guesses are used in the inversion to ensure a global solution. Inversion results over synthetic examples demonstrate that the proposed 1D inversion algorithm is well suited for complex formation structures. It is also robust and fast in extracting anisotropic resistivities from LWD resistivity measurements. [ABSTRACT FROM AUTHOR]

Least-squares reverse time migration (LSRTM) is a powerful tool in seeking broadband-wavenumber reflectivity images. It produces better images over reverse-time migration (RTM) at the expense of computational cost. The Hessian effect can be measured in the image domain with the point-spread function (PSF). Here, we try to measure the Hessian effect in the data domain with the so-called trace-spread function (TSF). The difference between PSF and TSF is that the former originates from ${{\mathbf{L}}^{T}}{\mathbf{L}}$ in the image domain while the latter from ${\mathbf{L}}{{\mathbf{L}}^{T}}$ in the data domain. By comparing the TSFs with their original corresponding traces (or beams), we can design adaptive matching filters for preconditioning to alleviate the Hessian effect. However, the full TSF matrix is expensive. In this article, we propose a multiscale solution, which first has a diagonal approximation to ${\mathbf{L}}{{\mathbf{L}}^{T}}$ in beams, and then handle the full submatrix composed of the one-beam traces using the Sherman–Morrison formula. The preconditioned beams are superimposed into a “deblurred” data for remigration. Through synthetic and real data examples, we see that: 1) single-step data-domain LSRTM can yield deblurred RTM images via adaptive matching filters and 2) the beam-by-beam consideration outperforms the trace-by-trace one. [ABSTRACT FROM AUTHOR]

Self-potential (SP) method has many applications, where the interpretation of SP data can be used for qualitative and quantitative interpretation. However, inversion of SP data in this paper is of quantitative interpretation and consists of highly non-linear, multimodal data and deploys global optimum method (GOM). Micro-differential evolution (MDE) is a GOM with small or micro-population size (5–8 populations) for each iteration. Consequently, this approach involves small numbers of forward computation in the inversion process. Two MDE variants, including adaptive MDE (μ JADE) and vectorized random mutation factor (MVDE) were tested first for different level of noises containing synthetic SP data with single anomaly and applied to synthetic SP data of multiple anomalies. The MDE variants are reliable and effective for inverting noisy SP data. Furthermore, in order to check the rationality of MDE variants, the algorithm is applied to seven field data from different applications, including groundwater exploration, shear zone tracing, water accumulation in landslides and embankment stability assessment. The model parameters revealed by MDE variants are accurate and show good agreement with the previous results estimated using other approaches. In addition, MDE variants also require fewer forward modelling calculations than other optimization approaches. [ABSTRACT FROM AUTHOR]

With the rapid development of science and technology, the operation and calculation in synthetic aperture radar (SAR) imaging systems require high throughput, and the system has high requirement for real-time performance. At the same time, in the SAR imaging technology, many Vandermonde matrix inversion operations are used in places where the weight coefficients are calculated. Especially when multi-channel inverse filtering is performed, the use of the Vandermonde matrix inversion operation is a crucial step. In this study, the authors worked hard to find a high speed and accurate Vandermonde matrix inversion algorithm for complex SAR imaging systems. Considering the field-programmable gate array (FPGA) can be parallel computing and its computing speed is high, the authors chose FPGA to achieve a large number of Vandermonde matrix inversion calculation, and it can meet the requirements of high speed and real time. So, first the realisation method of the fast inversion of the Vandermonde matrix based on Lagrange interpolation polynomial is discussed in this study, which includes pre-processing module, u matrix calculation module, v matrix calculation module, [inline-formula] vector calculation module and post-processing module. Then, the simulation results of the design are compared and analysed, which proved the correctness and feasibility of the rapid inversion method of Vandermonde matrix.

With the rapid development of science and technology, the operation and calculation in synthetic aperture radar (SAR) imaging systems require high throughput, and the system has high requirement for real-time performance. At the same time, in the SAR imaging technology, many Vandermonde matrix inversion operations are used in places where the weight coefficients are calculated. Especially when multi-channel inverse filtering is performed, the use of the Vandermonde matrix inversion operation is a crucial step. In this study, the authors worked hard to find a high speed and accurate Vandermonde matrix inversion algorithm for complex SAR imaging systems. Considering the field-programmable gate array (FPGA) can be parallel computing and its computing speed is high, the authors chose FPGA to achieve a large number of Vandermonde matrix inversion calculation, and it can meet the requirements of high speed and real time. So, first the realisation method of the fast inversion of the Vandermonde matrix based on Lagrange interpolation polynomial is discussed in this study, which includes pre-processing module, u matrix calculation module, v matrix calculation module, $\pi ^{\prime}$π′ vector calculation module and post-processing module. Then, the simulation results of the design are compared and analysed, which proved the correctness and feasibility of the rapid inversion method of Vandermonde matrix. [ABSTRACT FROM AUTHOR]