Bayesian subsampling of time-domain electromagnetic data using kernel density product

Geophysics ◽  
2021 ◽  
pp. 1-45
Author(s):  
Hai Li ◽  
Guoqiang Xue ◽  
Wen Chen
Keyword(s):  
Time Domain ◽  
Kernel Density ◽  
Model Space ◽  
Drill Hole ◽  
Divide And Conquer ◽  
Bayesian Inversion ◽  
Model Parameters ◽  
Model Spaces ◽  
Time Domain Electromagnetic ◽  
Speed Up

The Bayesian method is a powerful tool to estimate the resistivity distribution and associate uncertainty from time-domain electromagnetic (TDEM) data. As the forward simulation of the TDEM method is computationally expensive and a large number of samples are needed to globally explore the model space, the full Bayesian inversion of TDEM data is limited to layered models. To make high-dimensional Bayesian inversion tractable, we propose a divide-and-conquer strategy to speed up the Bayesian inversion of TDEM data. First, the full datasets and model spaces are divided into disjoint batches based on the coverage of the sources so that independent and highly efficient Bayesian subsampling can be conducted. Then, the samples from each subsampling procedure are combined to get the full posterior. To obtain an asymptotically unbiased approximation to the full posterior, a kernel density product method is used to reintegrate samples from each subposterior. The model parameters and their uncertainty are estimated from the full posterior. The proposed method is tested on synthetic examples and applied to a field dataset acquired with a large fixed-loop configuration. The 2D section from the Bayesian inversion revealed several mineralized zones, one of which matches well with the information from a nearby drill hole. The field example shows the ability of Bayesian inversion to infer reliable resistivity and uncertainty.

3D inversion of time domain electromagnetic data using finite elements and a triple mesh formulation

Geophysics ◽  
2021 ◽  
pp. 1-43
Author(s):  
Zhang Bo ◽  
Engebretsen Wann Kim ◽  
Fiandaca Gianluca ◽  
Hongzhu Cai ◽  
Esben Auken
Keyword(s):  
Electromagnetic Fields ◽  
Time Domain ◽  
Unstructured Mesh ◽  
Model Parameters ◽  
Coarse Mesh ◽  
The Finite Element Method ◽  
Electromagnetic Data ◽  
Tetrahedral Elements ◽  
Time Domain Electromagnetic ◽  
Speed Up

During several decades, much research has been done to develop 3D electromagnetic inversion algorithms. Due to the computational complexity and the memory requirements for 3D time domain electromagnetic (TEM) inversion algorithms, many real world surveys are inverted with in 1D. To speed up calculations and manage memory for 3D inversions of TEM data, we propose an approach using three uncoupled meshes: an inversion mesh, a forward-model mesh, and a mesh for Jacobian calculations. The inversion mesh is a coarse regular and structured mesh, such that constraints are easily enforced between model parameters. Forward responses are calculated on a dense unstructured mesh to obtain accurate electromagnetic fields, while the Jacobian is calculated on a coarse unstructured mesh. We show that using a coarse mesh for the Jacobian is sufficient for the inversion to converge and, equally important, it provides a significant speed boost in the overall inversion process, compared to calculating it on the forward modeling mesh. The unstructured meshes are made of tetrahedral elements and the electromagnetic fields are calculated using the finite-element method. The inversion optimization uses a standard Gauss-Newton formulation. For further speed up and memory optimizing of the inversion we use domain decomposition for calculating the responses for each transmitter separately and parallelize the problem over domains using OpenMP. Compared to a 1D solution, the accuracy for the Jacobian is 1 – 5% for the dense mesh and 2 – 7 % for the coarse mesh but the calculation time is about 5.0× faster for the coarse mesh. We also demonstrate the algorithm on a small ground-based TEM dataset acquired in an area where a 3D earth distorts the electromagnetic fields to such a degree that a 1D inversion is not feasible.

Integrated application of heliborne and ground electromagnetic surveys for mapping EM conductor for uranium exploration and its subsurface validation, North Delhi Fold Belt, Rajasthan, India: A case study

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. B13-B24 ◽  
Author(s):  
A. K. Chaturvedi ◽  
Cas Lotter ◽  
Shailesh Tripathi ◽  
A. K. Maurya ◽  
Indrajit Patra ◽  
...  
Keyword(s):  
Time Domain ◽  
Uranium Mineralization ◽  
Model Parameters ◽  
Fold Belt ◽  
The North ◽  
Geophysical Surveys ◽  
Uranium Exploration ◽  
Time Domain Electromagnetic ◽  
Conducting Bodies ◽  
Electromagnetic Surveys

A fracture-controlled uranium deposit was identified in Proterozoic Ajabgarh metasediments of the North Delhi Fold Belt within the Khetri subbasin at Rohil, Sikar district, Rajasthan, India. Uranium mineralization in the area is associated with geologic structures, albitization, and pyroxenization of metasediments and conductors such as metallic sulfides and carbonaceous phyllites/graphitic schists. To locate uranium mineralization akin to Rohil in nearby thick soil covered areas, this association was targeted through heliborne geophysical surveys. High-resolution heliborne magnetic and time domain electromagnetic (TEM) surveys were conducted around Rohil. The survey delineated several targets with favorable geologic structures and conductors such as graphitic schist for further uranium exploration. One favorable target near Chappar village was taken up for follow-up exploration work. The EM conductor mapped from heliborne survey was subsequently validated through ground time-domain electromagnetic surveys and subsurface exploration. Modeling of heliborne and ground-based electromagnetic data revealed the presence of subsurface conducting bodies with comparable model parameters. Drilling established the presence of a subsurface conductor up to a depth of 300 m, which was attributed to the presence of graphite and sulfides (pyrrhotite) along foliation plane of carbon phyllite/graphitic schist/quartz-biotite schist and calc-silicate rock. Further detailed laboratory investigations (petrology/X-ray diffraction) of selected core samples from the conductive zones confirmed the presence of pyrrhotite and graphite responsible for EM signature. This study, carried out by using multiparameter data sets, proved the efficacy of heliborne surveys in locating favorable targets for uranium exploration in Ajabgarh group of rocks.

scholarly journals Three-Dimensional Anisotropic Inversions for Time-Domain Airborne Electromagnetic Data

Minerals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 218
Author(s):  
Yang Su ◽  
Changchun Yin ◽  
Yunhe Liu ◽  
Xiuyan Ren ◽  
Bo Zhang ◽  
...  
Keyword(s):  
Time Domain ◽  
Three Dimensional ◽  
Model Parameters ◽  
Anisotropic Model ◽  
Regularized Inversion ◽  
Earth Structures ◽  
Airborne Electromagnetic ◽  
Speed Up ◽  
The Time Domain ◽  
Airborne Electromagnetic Data

Rocks and ores in nature usually appear macro-anisotropic, especially in sedimentary areas with strong layering. This anisotropy will lead to false interpretation of electromagnetic (EM) data when inverted under the assumption of an isotropic earth. However, the time-domain (TD) airborne EM (AEM) inversion for an anisotropic model has not attracted much attention. To get reasonable inversion results from TD AEM data, we present in this paper the forward modeling and inversion methods based on a triaxial anisotropic model. We apply three-dimensional (3D) finite-difference on the secondary scattered electric field equation to calculate the frequency-domain (FD) EM responses, then we use the inverse Fourier transform and waveform convolution to obtain TD responses. For the regularized inversion, we calculate directly the sensitivities with respect to three diagonal conductivities and then use the Gauss–Newton (GN) optimization scheme to recover model parameters. To speed up the computation and to reduce the memory requirement, we adopt the moving footprint concept and separate the whole model into a series of small sub-models for the inversion. Finally, we compare our anisotropic inversion scheme with the isotropic one using both synthetic and field data. Numerical experiments show that the anisotropic inversion has inherent advantages over the isotropic ones, we can get more reasonable results for the anisotropic earth structures.

scholarly journals Modeling induced polarization effects in helicopter time domain electromagnetic data: Synthetic case studies

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. E31-E50 ◽  
Author(s):  
Andrea Viezzoli ◽  
Vladislav Kaminski ◽  
Gianluca Fiandaca
Keyword(s):  
Time Domain ◽  
A Priori ◽  
Induced Polarization ◽  
Earth Model ◽  
Model Parameters ◽  
Model Approximation ◽  
Generic Models ◽  
Time Domain Electromagnetic ◽  
Airborne Electromagnetic ◽  
Priori Information

We have developed a synthetic multiparametric modeling and inversion exercise undertaken to study the robustness of inverting airborne time-domain electromagnetic (TDEM) data to extract Cole-Cole parameters. The following issues were addressed: nonuniqueness, ill posedness, dependency on manual processing and the effect of constraints, and a priori information. We have used a 1D layered earth model approximation and lateral constraints. Synthetic simulations were performed for several models and the corresponding Cole-Cole parameters. The possibility to recover these models by means of laterally constrained multiparametric inversion was evaluated, including recovery of chargeability distributions from shallow and deep targets based on analysis of induced polarization (IP) effects, simulated in airborne TDEM data. Different scenarios were studied, including chargeable targets associated with the conductive and resistive environments. In particular, four generic models were considered for the exercise: a sulfide model, a kimberlite model, and two generic models focusing on the depth of investigation. Our study indicated that, in cases when relaxation time ([Formula: see text]) values are in the range to which the airborne electromagnetic is most sensitive (e.g., approximately 1 ms), it is possible to recover deep chargeable targets (to depths more than 130 m) in association with high electrical conductivity and in resistive environments. Furthermore, it was found that the recovery of a deep conductor, masked by a shallower chargeable target, became possible only when full Cole-Cole modeling was used in the inversion. Lateral constraints improved the recoverability of model parameters. Finally, modeling IP effects increased the accuracy of recovered electrical resistivity models.

Decoupling induced polarization effect from time domain electromagnetic data in a Bayesian framework

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. A59-A63 ◽  
Author(s):  
Hai Li ◽  
Guoqiang Xue ◽  
Yiming He
Keyword(s):  
Time Domain ◽  
Computational Cost ◽  
Bayesian Framework ◽  
Induced Polarization ◽  
Linear Perturbation ◽  
Model Parameters ◽  
Bayesian Sampling ◽  
3D Space ◽  
Time Domain Electromagnetic ◽  
Induced Polarization Effect

We have developed a scheme for decoupling the induced polarization (IP) effect from time-domain electromagnetic (TDEM) data. This scheme is achieved by simultaneously sampling the resistivity and pseudochargeability in a Bayesian framework. The TDEM and IP responses are simulated separately with the sampled model parameters and then are stacked to fit the IP-affected TDEM data. Thus, the influence of the IP phenomenon is eliminated in the process of recovering the resistivity. To reduce the computational cost brought by the Bayesian sampling, we use a 2D parametrization instead of sampling the full 3D space and we use a linear perturbation approximation for calculating the IP response. The linearized inversion results are used as the initial model, and a multiple proposed points algorithm is used to accelerate the sampling. We validate the proposed method with synthetic and field examples showing that it restores accurate estimates of electrical structures from the TDEM data that are significantly affected by the IP phenomenon. Our method could advance the application of the TDEM method to the scenario in which the IP may affect the TDEM data and mask the underlying geologic targets.

Two-dimensional Bayesian inversion of magnetotelluric data using trans-dimensional Gaussian processes

2021 ◽  
Author(s):  
Daniel Blatter ◽  
Anandaroop Ray ◽  
Kerry Key
Keyword(s):  
Gaussian Process ◽  
Process Model ◽  
Field Data ◽  
Probability Distributions ◽  
Bulk Composition ◽  
Computational Cost ◽  
Model Space ◽  
Bayesian Inversion ◽  
Adaptive Finite Element ◽  
Magnetotelluric Data

Summary Bayesian inversion of electromagnetic data produces crucial uncertainty information on inferred subsurface resistivity. Due to their high computational cost, however, Bayesian inverse methods have largely been restricted to computationally expedient 1D resistivity models. In this study, we successfully demonstrate, for the first time, a fully 2D, trans-dimensional Bayesian inversion of magnetotelluric data. We render this problem tractable from a computational standpoint by using a stochastic interpolation algorithm known as a Gaussian process to achieve a parsimonious parametrization of the model vis-a-vis the dense parameter grids used in numerical forward modeling codes. The Gaussian process links a trans-dimensional, parallel tempered Markov chain Monte Carlo sampler, which explores the parsimonious model space, to MARE2DEM, an adaptive finite element forward solver. MARE2DEM computes the model response using a dense parameter mesh with resistivity assigned via the Gaussian process model. We demonstrate the new trans-dimensional Gaussian process sampler by inverting both synthetic and field magnetotelluric data for 2D models of electrical resistivity, with the field data example converging within 10 days on 148 cores, a non-negligible but tractable computational cost. For a field data inversion, our algorithm achieves a parameter reduction of over 32x compared to the fixed parameter grid used for the MARE2DEM regularized inversion. Resistivity probability distributions computed from the ensemble of models produced by the inversion yield credible intervals and interquartile plots that quantitatively show the non-linear 2D uncertainty in model structure. This uncertainty could then be propagated to other physical properties that impact resistivity including bulk composition, porosity and pore-fluid content.

scholarly journals Lightweight Unmanned Aerial System for Time-Domain Electromagnetic Prospecting—The Next Stage in Applied UAV-Geophysics

2021 ◽  
Vol 11 (5) ◽  
pp. 2060 ◽  
Author(s):  
Alexander Parshin ◽  
Ayur Bashkeev ◽  
Yuriy Davidenko ◽  
Marina Persova ◽  
Sergey Iakovlev ◽  
...  
Keyword(s):  
Time Domain ◽  
Gamma Ray ◽  
Pulse Generator ◽  
Measuring System ◽  
Electromagnetic Sounding ◽  
Mountainous Regions ◽  
Time Domain Electromagnetic ◽  
Unmanned System ◽  
Classical Triad ◽  
The Time Domain

Nowadays in solving geological problems, the technologies of UAV-geophysics, primarily magnetic and gamma surveys, are being increasingly used. However, for the formation of the classical triad of airborne geophysics methods in the UAV version, there was not enough technology for UAV-electromagnetic sounding, which would allow studying the geological environment at depths of tens and hundreds of meters with high detail. This article describes apparently the first technology of UAV-electromagnetic sounding in the time domain (TDEM, TEM), implemented as an unmanned system based on a light multi-rotor UAV. A measuring system with an inductive sensor—an analogue of a 20 × 20 or 50 × 50 m receiving loop is towed by a UAV, and a galvanically grounded power transmitter is on the ground and connected to a pulse generator. The survey is carried out along a network of parallel lines at low altitude with a terrain draping at a speed of 7–8 m/s, the maximum distance of the UAV’s departure from the transmitter line can reach several kilometers, thus the created technology is optimal for performing detailed areal electromagnetic soundings in areas of several square kilometers. The results of the use of the unmanned system (UAS) in real conditions of the mountainous regions of Eastern Siberia are presented. Based on the obtained data, the sensitivity of the system was simulated and it was shown that the developed technology allows one to collect informative data and create geophysical sections and maps of electrical resistivity in various geological situations. According to the authors, the emergence of UAV-TEM systems in the near future will significantly affect the practice of geophysical work, as it was earlier with UAV-magnetic prospecting and gamma-ray survey.

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