scholarly journals Efficient probabilistic inversion using the rejection sampler—exemplified on airborne EM data

2020 ◽  
Vol 224 (1) ◽  
pp. 543-557
Author(s):  
Thomas M Hansen
Keyword(s):  
Inverse Problems ◽  
Posterior Distribution ◽  
Prior Information ◽  
Local Minima ◽  
Electromagnetic Data ◽  
Novel Approach ◽  
Airborne Electromagnetic ◽  
Airborne Electromagnetic Data ◽  
Airborne Em ◽  
Probabilistic Inversion

SUMMARY Probabilistic inversion methods, typically based on Markov chain Monte Carlo, exist that allow exploring the full uncertainty of geophysical inverse problems. The use of such methods is though limited by significant computational demands, and non-trivial analysis of the obtained set of dependent models. Here, a novel approach, for sampling the posterior distribution is suggested based on using pre-calculated lookup tables with the extended rejection sampler. The method is (1) fast, (2) generates independent realizations of the posterior, and (3) does not get stuck in local minima. It can be applied to any inverse problem (and sample an approximate posterior distribution) but is most promising applied to problems with informed prior information and/or localized inverse problems. The method is tested on the inversion of airborne electromagnetic data and shows an increase in the computational efficiency of many orders of magnitude as compared to using the extended Metropolis algorithm.

Resistive limit modeling of airborne electromagnetic data

Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 492-500 ◽  
Author(s):  
James E. Reid ◽  
James C. Macnae
Keyword(s):  
Current Flow ◽  
Integral Equation Method ◽  
Near Surface ◽  
Electromagnetic Data ◽  
Airborne Electromagnetic ◽  
Source Current ◽  
Numerical Model Experiments ◽  
Airborne Electromagnetic Data ◽  
Airborne Em ◽  
Direct Induction

When a confined conductive target embedded in a conductive host is energized by an electromagnetic (EM) source, current flow in the target comes from both direct induction of vortex currents and current channeling. At the resistive limit, a modified magnetometric resistivity integral equation method can be used to rapidly model the current channeling component of the response of a thin-plate target energized by an airborne EM transmitter. For towed-bird transmitter–receiver geometries, the airborne EM anomalies of near-surface, weakly conductive features of large strike extent may be almost entirely attributable to current channeling. However, many targets in contact with a conductive host respond both inductively and galvanically to an airborne EM system. In such cases, the total resistive-limit response of the target is complicated and is not the superposition of the purely inductive and purely galvanic resistive-limit profiles. Numerical model experiments demonstrate that while current channeling increases the width of the resistive-limit airborne EM anomaly of a wide horizontal plate target, it does not necessarily increase the peak anomaly amplitude.

Automated interpretation of airborne electromagnetic data

Geophysics ◽  
1984 ◽  
Vol 49 (8) ◽  
pp. 1301-1312 ◽  
Author(s):  
G. T. DeMoully ◽  
A. Becker
Keyword(s):  
Data Interpretation ◽  
Earth Model ◽  
Computer Algorithms ◽  
Conductive Layer ◽  
Electromagnetic Data ◽  
Airborne Electromagnetic ◽  
Survey Results ◽  
Airborne Electromagnetic Data ◽  
Airborne Em ◽  
Interpretation Method

Recent improvements in equipment quality make it possible to increase the usefulness of airborne electromagnetic (EM) systems in areas of moderate electrical conductivity for the purpose of constructing simple electrical property maps which can be related to surficial geology. This application of airborne electromagnetics may be demonstrated and evaluated using Barringer/Questor Mark VI Input® survey results in places where independent verifications of the airborne data interpretation are available. For this purpose we have developed a set of computer algorithms which read digitally recorded Input data and interpret them automatically in terms of a simple electrical section that is defined by a single conductive layer whose thickness, conductivity, and subsurface depth are determined from the data. Because this technique is formally based on a one‐dimensional, three‐layer, three‐parameter, horizontally stratified earth model, it is only applicable in regions where the surficial formations are mildly dipping and the conductive layer is covered by, and rests on, highly resistive materials. The interpretation method is illustrated by three field examples. At the first field survey site, in Alberta, Canada, airborne EM survey data are used to map the depth of the interface between coarse and clayey sands. Data from a second survey site, this time in the Western USA, are interpreted to yield the section of a subsurface valley filled with conductive clay. The final example, taken from British Columbia, Canada, involves the mapping of all the three parameters for a weathered volcanic unit.

Probabilistic inversion of airborne electromagnetic data for basement conductors

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. E389-E400 ◽  
Author(s):  
Juerg Hauser ◽  
James Gunning ◽  
David Annetts
Keyword(s):  
Thin Plate ◽  
Parametric Bootstrap ◽  
Computationally Efficient ◽  
Prior Beliefs ◽  
Data Set ◽  
Layered Earth ◽  
Electromagnetic Data ◽  
Airborne Electromagnetic ◽  
Airborne Electromagnetic Data ◽  
Probabilistic Inversion

Probabilistic inversion of airborne electromagnetic data is often approximated by a layered earth using a computationally efficient 1D kernel. If the underlying framework accounts for prior beliefs on spatial correlation, the inversion will be able to recover spatially coherent interfaces and associated uncertainties. Greenfield exploration using airborne electromagnetic data, however, often seeks to identify discrete economical targets. In mature exploration provinces, such bodies are frequently obscured by thick, conductive regolith, and the response of such economic basement conductors presents a challenge to any layered earth inversion. A well-known computationally efficient way to approximate the response of a basement conductor is to use a thin plate. Here we have extended a Bayesian parametric bootstrap approach, so that the basement of a spatially varying layered earth can contain a thin plate. The resulting Bayesian framework allowed for the inversion of basement conductors and associated uncertainties, but more importantly, the use of model selection concepts to determine if the data supports a basement conductor model or not. Recovered maps of basement conductor probabilities show the expected patterns in uncertainty; for example, a decrease in target probability with increasing depth. Such maps of target probabilities generated using the thin plate approximation are a potentially valuable source of information for the planning of exploration activity, such as the targeting of drillholes to confirm the existence of a discrete conductor in a greenfield exploration scenario. We have used a field data set from northwest Queensland, Australia, to illustrate how the approach allowed inversion for a basement conductor and related uncertainties in a spatially variable layered earth, using the information from multiple survey lines and prior beliefs of geology.

Simulated annealing for airborne EM inversion

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. F189-F195 ◽  
Author(s):  
Changchun Yin ◽  
Greg Hodges
Keyword(s):  
Simulated Annealing ◽  
Random Walk ◽  
Boltzmann Distribution ◽  
Model Parameters ◽  
Local Minima ◽  
Model Configuration ◽  
Airborne Electromagnetic ◽  
Starting Model ◽  
Airborne Em ◽  
Cooling Schedule

The traditional algorithms for airborne electromagnetic (EM) inversion, e.g., the Marquardt-Levenberg method, generally run only a downhill search. Consequently, the model solutions are strongly dependent on the starting model and are easily trapped in local minima. Simulated annealing (SA) starts from the Boltzmann distribution and runs both downhill and uphill searches, rendering the searching process to easily jump out of local minima and converge to a global minimum. In the SA process, the calculation of Jacobian derivatives can be avoided because no preferred searching direction is required as in the case of the traditional algorithms. We apply SA technology for airborne EM inversion by comparing the inversion with a thermodynamic process, and we discuss specifically the SA procedure with respect to model configuration, random walk for model updates, objective function, and annealing schedule. We demonstrate the SA flexibility for starting models by allowing the model parameters to vary in a large range (far away from the true model). Further, we choose a temperature-dependent random walk for model updates and an exponential cooling schedule for the SA searching process. The initial temperature for the SA cooling scheme is chosen differently for different model parameters according to their resolvabilities. We examine the effectiveness of the algorithm for airborne EM by inverting both theoretical and survey data and by comparing the results with those from the traditional algorithms.

Projection methods and applications for seismic nonlinear inverse problems with multiple constraints

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R251-R269 ◽  
Author(s):  
Bas Peters ◽  
Brendan R. Smithyman ◽  
Felix J. Herrmann
Keyword(s):  
Inverse Problems ◽  
Prior Information ◽  
Waveform Inversion ◽  
Projection Methods ◽  
Multiple Constraints ◽  
Local Minima ◽  
Low Frequencies ◽  
Trade Off ◽  
Nonlinear Inverse Problems ◽  
Easy Integration

Nonlinear inverse problems are often hampered by local minima because of missing low frequencies and far offsets in the data, lack of access to good starting models, noise, and modeling errors. A well-known approach to counter these deficiencies is to include prior information on the unknown model, which regularizes the inverse problem. Although conventional regularization methods have resulted in enormous progress in ill-posed (geophysical) inverse problems, challenges remain when the prior information consists of multiple pieces. To handle this situation, we have developed an optimization framework that allows us to add multiple pieces of prior information in the form of constraints. The proposed framework is more suitable for full-waveform inversion (FWI) because it offers assurances that multiple constraints are imposed uniquely at each iteration, irrespective of the order in which they are invoked. To project onto the intersection of multiple sets uniquely, we use Dykstra’s algorithm that does not rely on trade-off parameters. In that sense, our approach differs substantially from approaches, such as Tikhonov/penalty regularization and gradient filtering. None of these offer assurances, which makes them less suitable to FWI, where unrealistic intermediate results effectively derail the inversion. By working with intersections of sets, we avoid trade-off parameters and keep objective calculations separate from projections that are often much faster to compute than objectives/gradients in 3D. These features allow for easy integration into existing code bases. Working with constraints also allows for heuristics, where we built up the complexity of the model by a gradual relaxation of the constraints. This strategy helps to avoid convergence to local minima that represent unrealistic models. Using multiple constraints, we obtain better FWI results compared with a quadratic penalty method, whereas all definitions of the constraints are in terms of physical units and follow from the prior knowledge directly.

3D parametric hybrid inversion of time-domain airborne electromagnetic data

Geophysics ◽  
2015 ◽  
Vol 80 (6) ◽  
pp. K25-K36 ◽  
Author(s):  
Michael S. McMillan ◽  
Christoph Schwarzbach ◽  
Eldad Haber ◽  
Douglas W. Oldenburg
Keyword(s):  
Time Domain ◽  
Electromagnetic Data ◽  
Airborne Electromagnetic ◽  
Airborne Electromagnetic Data

Upward and downward continuation of airborne electromagnetic data

1990 ◽  
Author(s):  
Clyde Bergeron ◽  
Terrence L. Morris ◽  
Juliette W. Ioup
Keyword(s):  
Downward Continuation ◽  
Electromagnetic Data ◽  
Airborne Electromagnetic ◽  
Airborne Electromagnetic Data
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