Routine 2D inversion of magnetotelluric data using the determinant of the impedance tensor

Geophysics ◽  
2005 ◽  
Vol 70 (2) ◽  
pp. G33-G41 ◽  
Author(s):  
L. B. Pedersen ◽  
M. Engels
Keyword(s):  
Inverse Modeling ◽  
Sedimentary Cover ◽  
A Priori ◽  
Synthetic Data ◽  
Impedance Tensor ◽  
Quality Of Data ◽  
Magnetotelluric Data ◽  
Strike Direction ◽  
Recent Developments ◽  
3D Elements

Recent developments in the speed and quality of data acquisition using the radiomagnetotelluric (RMT) method, whereby large amounts of broadband RMT data can be collected along profiles, have prompted us to develop a strategy for routine inverse modeling using 2D models. We build a rather complicated numerical model containing both 2D and 3D elements believed to be representative for shallow conductors in crystalline basement overlain by a thin sedimentary cover. We then invert the corresponding synthetic data on selected profiles, using both traditional MT approaches, as well as the proposed approach, which is based on the determinant of the MT impedance tensor. We compare the estimated resistivity models with the true models along the selected profiles and find that the traditional approaches often lead to strongly biased models and bad data fit, in contrast to those using the determinant. In this case, much of the bias is removed and the data fit is improved. The determinant of the impedance tensor is independent of the chosen strike direction, and once the a priori model is set, the best fitting model is found to be practically independent of the starting model used. We conclude that the determinant of the impedance tensor is a useful tool for routine inverse modeling.

DIAGRAMS FOR MAGNETOTELLURIC DATA

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 766-770 ◽  
Author(s):  
F. E. M. Lilley
Keyword(s):  
Impedance Tensor ◽  
Two Dimensional ◽  
Magnetotelluric Data ◽  
One Dimensional ◽  
Magnetic Components ◽  
Strike Direction ◽  
Electric And Magnetic Fields ◽  
The Relationship ◽  
Special Case ◽  
Phase Differences

Observed magnetotelluric data are often transformed to the frequency domain and expressed as the relationship [Formula: see text]where [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] represent electric and magnetic components measured along two orthogonal axes (in this paper, for simplicity, to be north and east, respectively). The elements [Formula: see text] comprise the magnetotelluric impedance tensor, and they are generally complex due to phase differences between the electric and magnetic fields. All quantities in equation (1) are frequency dependent. For the special case of “two‐dimensional” geology (where structure can be described as having a certain strike direction along which it does not vary), [Formula: see text] with [Formula: see text]. For the special case of “one‐dimensional” geology (where structure varies with depth only, as if horizontally layered), [Formula: see text] and [Formula: see text].

Multisite, multifrequency tensor decomposition of magnetotelluric data

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 158-173 ◽  
Author(s):  
Gary W. McNeice ◽  
Alan G. Jones
Keyword(s):  
Computing Time ◽  
Regional Scale ◽  
Synthetic Data ◽  
Real Data ◽  
Impedance Tensor ◽  
Small Scale ◽  
Magnetotelluric Data ◽  
Data Set ◽  
Distortion Parameters ◽  
Galvanic Distortion

Accurate interpretation of magnetotelluric data requires an understanding of the directionality and dimensionality inherent in the data, and valid implementation of an appropriate method for removing the effects of shallow, small‐scale galvanic scatterers on the data to yield responses representative of regional‐scale structures. The galvanic distortion analysis approach advocated by Groom and Bailey has become the most adopted method, rightly so given that the approach decomposes the magnetotelluric impedance tensor into determinable and indeterminable parts, and tests statistically the validity of the galvanic distortion assumption. As proposed by Groom and Bailey, one must determine the appropriate frequency‐independent telluric distortion parameters and geoelectric strike by fitting the seven‐parameter model on a frequency‐by‐frequency and site‐by‐site basis independently. Although this approach has the attraction that one gains a more intimate understanding of the data set, it is rather time‐consuming and requires repetitive application. We propose an extension to Groom‐Bailey decomposition in which a global minimum is sought to determine the most appropriate strike direction and telluric distortion parameters for a range of frequencies and a set of sites. Also, we show how an analytically‐derived approximate Hessian of the objective function can reduce the required computing time. We illustrate application of the analysis to two synthetic data sets and to real data. Finally, we show how the analysis can be extended to cover the case of frequency‐dependent distortion caused by the magnetic effects of the galvanic charges.

3D inversion of magnetotelluric data by using a hybrid forward-modeling approach and mesh decoupling

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. E191-E205
Author(s):  
Deniz Varılsüha
Keyword(s):  
Graphics Processing Units ◽  
Hybrid Approach ◽  
Synthetic Data ◽  
Forward Modeling ◽  
Impedance Tensor ◽  
Inversion Algorithm ◽  
Data Types ◽  
Fe Method ◽  
Magnetotelluric Data ◽  
Modeling Approach

We have developed a new algorithm for the inversion of magnetotelluric (MT) data. The developed algorithm is built to be fast, versatile, and accurate. A fast inversion algorithm has to include a fast forward-modeling routine. To achieve that, a hybrid approach consisting of finite-difference (FD) and finite-element (FE) methods is used to benefit from the speed of the FD method and the flexibility to add topographic features of the FE method. To reduce the number of cells, and thus reducing the size of the system to be solved in the forward and pseudoforward solutions, different meshes for various groups of frequencies are used. Then, these are mapped onto the inversion mesh by a mesh-decoupling technique to further accelerate the inversion. To build a versatile inversion algorithm, the capability of using different data types is implemented. In addition to the impedance tensor and the magnetic transfer function, the algorithm also computes the phase tensor and phase vector, which are distortion-free forms of MT data. It is also possible to invert intersite data and their respective phase tensors using the developed code. Furthermore, the distortion matrix can also be estimated as a parameter. The new code is tested with different noisy and distorted synthetic data measured on a surface with topography to evaluate the inversion accuracy and computational efficiency. The results indicate that the code is accurate and that the runtimes are reasonable for the large 3D models considered. Using four graphics processing units, the hybrid forward-modeling approach and the mesh-decoupling technique together result in a 12 times speedup for the examples presented in this study.

Magnetotelluric data analysis: removal of bias

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1157-1166 ◽  
Author(s):  
Wolfgang M. Goubau ◽  
Thomas D. Gamble ◽  
John Clarke
Keyword(s):  
Magnetic Fields ◽  
Reference Signal ◽  
Impedance Tensor ◽  
Magnetotelluric Data ◽  
New Techniques ◽  
One Dimensional ◽  
Strike Direction ◽  
Electric And Magnetic Fields ◽  
A Site ◽  
Correlated Noises

Two new techniques for analyzing 4‐channel magnetotelluric (MT) data are described. These techniques produce estimates of the elements [Formula: see text] of the impedance tensor that are unbiased by noise in the autopowers of the electric and magnetic fields. Effectively, each technique uses one field channel as a reference signal that can be correlated with the other three channels. Method 1 obtains estimates for the [Formula: see text] in terms of crosspowers of the Fourier components of the electric and magnetic fields [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. Method 2 is a generalization of method 1, and obtains estimates for [Formula: see text] in terms of weighted crosspowers. Both methods fail when the geology is one‐dimensional, or two‐dimensional with one electrode oriented along the strike direction. To obtain results that are stable for any geology and that are unbiased by autopower noise, at least five channels of data are required. To also minimize bias by correlated noises, one needs six channels of data, two channels of which are for fields measured at a site that is remote from the base MT station. The analysis of MT data using a remote magnetometer as a reference is discussed.

scholarly journals Benchmarking Unsupervised Outlier Detection with Realistic Synthetic Data

2021 ◽  
Vol 15 (4) ◽  
pp. 1-20
Author(s):  
Georg Steinbuss ◽  
Klemens Böhm
Keyword(s):  
Outlier Detection ◽  
Synthetic Data ◽  
Real Data ◽  
Detection Methods ◽  
Quality Of Data ◽  
Benchmark Data ◽  
Core Idea ◽  
Generic Process ◽  
Unsupervised Outlier Detection

Benchmarking unsupervised outlier detection is difficult. Outliers are rare, and existing benchmark data contains outliers with various and unknown characteristics. Fully synthetic data usually consists of outliers and regular instances with clear characteristics and thus allows for a more meaningful evaluation of detection methods in principle. Nonetheless, there have only been few attempts to include synthetic data in benchmarks for outlier detection. This might be due to the imprecise notion of outliers or to the difficulty to arrive at a good coverage of different domains with synthetic data. In this work, we propose a generic process for the generation of datasets for such benchmarking. The core idea is to reconstruct regular instances from existing real-world benchmark data while generating outliers so that they exhibit insightful characteristics. We propose and describe a generic process for the benchmarking of unsupervised outlier detection, as sketched so far. We then describe three instantiations of this generic process that generate outliers with specific characteristics, like local outliers. To validate our process, we perform a benchmark with state-of-the-art detection methods and carry out experiments to study the quality of data reconstructed in this way. Next to showcasing the workflow, this confirms the usefulness of our proposed process. In particular, our process yields regular instances close to the ones from real data. Summing up, we propose and validate a new and practical process for the benchmarking of unsupervised outlier detection.

On the reconstruction of the shape of a seismic streamer

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. H1-H6
Author(s):  
Bruno Goutorbe ◽  
Violaine Combier
Keyword(s):  
A Priori ◽  
Synthetic Data ◽  
Seismic Survey ◽  
Random Errors ◽  
Generalized Inversion ◽  
Reconstruction Methods ◽  
Seismic Acquisition ◽  
Marine Seismic ◽  
Gps Devices ◽  
Vessel Reconstruction

In the frame of 3D seismic acquisition, reconstructing the shape of the streamer(s) for each shot is an essential step prior to data processing. Depending on the survey, several kinds of constraints help achieve this purpose: local azimuths given by compasses, absolute positions recorded by global positioning system (GPS) devices, and distances calculated between pairs of acoustic ranging devices. Most reconstruction methods are restricted to work on a particular type of constraint and do not estimate the final uncertainties. The generalized inversion formalism using the least-squares criterion can provide a robust framework to solve such a problem — handling several kinds of constraints together, not requiring an a priori parameterization of the streamer shape, naturally extending to any configuration of streamer(s), and giving rigorous uncertainties. We explicitly derive the equations governing the algorithm corresponding to a marine seismic survey using a single streamer with compasses distributed all along it and GPS devices located on the tail buoy and on the vessel. Reconstruction tests conducted on several synthetic examples show that the algorithm performs well, with a mean error of a few meters in realistic cases. The accuracy logically degrades if higher random errors are added to the synthetic data or if deformations of the streamer occur at a short length scale.

Explaining monotonic ranking functions

2020 ◽  
Vol 14 (4) ◽  
pp. 640-652
Author(s):  
Abraham Gale ◽  
Amélie Marian
Keyword(s):  
Decision Making ◽  
Selection Process ◽  
A Priori ◽  
Data Distribution ◽  
Synthetic Data ◽  
Decision Processes ◽  
Decision Makers ◽  
Ranking Functions ◽  
High School Admissions ◽  
Parameter Values

Ranking functions are commonly used to assist in decision-making in a wide variety of applications. As the general public realizes the significant societal impacts of the widespread use of algorithms in decision-making, there has been a push towards explainability and transparency in decision processes and results, as well as demands to justify the fairness of the processes. In this paper, we focus on providing metrics towards explainability and transparency of ranking functions, with a focus towards making the ranking process understandable, a priori , so that decision-makers can make informed choices when designing their ranking selection process. We propose transparent participation metrics to clarify the ranking process, by assessing the contribution of each parameter used in the ranking function in the creation of the final ranked outcome, using information about the ranking functions themselves, as well as observations of the underlying distributions of the parameter values involved in the ranking. To evaluate the outcome of the ranking process, we propose diversity and disparity metrics to measure how similar the selected objects are to each other, and to the underlying data distribution. We evaluate the behavior of our metrics on synthetic data, as well as on data and ranking functions on two real-world scenarios: high school admissions and decathlon scoring.

Recent developments in fast and scalable inverse modeling and data assimilation methods in hydrology

2020 ◽  
Vol 591 ◽  
pp. 125266 ◽  
Author(s):  
Hojat Ghorbanidehno ◽  
Amalia Kokkinaki ◽  
Jonghyun Lee ◽  
Eric Darve
Keyword(s):  
Data Assimilation ◽  
Inverse Modeling ◽  
Recent Developments

Marlim R3D: A realistic model for controlled-source electromagnetic simulations — Phase 2: The controlled-source electromagnetic data set

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. E293-E299
Author(s):  
Jorlivan L. Correa ◽  
Paulo T. L. Menezes
Keyword(s):  
A Priori ◽  
Synthetic Data ◽  
Realistic Model ◽  
Earth Model ◽  
Data Sets ◽  
Data Set ◽  
Geoelectric Model ◽  
Controlled Source ◽  
The North ◽  
Electromagnetic Simulations

Synthetic data provided by geoelectric earth models are a powerful tool to evaluate a priori a controlled-source electromagnetic (CSEM) workflow effectiveness. Marlim R3D (MR3D) is an open-source complex and realistic geoelectric model for CSEM simulations of the postsalt turbiditic reservoirs at the Brazilian offshore margin. We have developed a 3D CSEM finite-difference time-domain forward study to generate the full-azimuth CSEM data set for the MR3D earth model. To that end, we fabricated a full-azimuth survey with 45 towlines striking the north–south and east–west directions over a total of 500 receivers evenly spaced at 1 km intervals along the rugged seafloor of the MR3D model. To correctly represent the thin, disconnected, and complex geometries of the studied reservoirs, we have built a finely discretized mesh of [Formula: see text] cells leading to a large mesh with a total of approximately 90 million cells. We computed the six electromagnetic field components (Ex, Ey, Ez, Hx, Hy, and Hz) at six frequencies in the range of 0.125–1.25 Hz. In our efforts to mimic noise in real CSEM data, we summed to the data a multiplicative noise with a 1% standard deviation. Both CSEM data sets (noise free and noise added), with inline and broadside geometries, are distributed for research or commercial use, under the Creative Common License, at the Zenodo platform.

scholarly journals Bayesian inversion of magnetotelluric data considering dimensionality discrepancies

2020 ◽  
Vol 223 (3) ◽  
pp. 1565-1583
Author(s):  
Hoël Seillé ◽  
Gerhard Visser
Keyword(s):  
Learning Algorithm ◽  
Synthetic Data ◽  
Real Data ◽  
Error Model ◽  
Bayesian Inversion ◽  
Magnetotelluric Data ◽  
Data Set ◽  
Likelihood Functions ◽  
Training Images ◽  
Phase Tensor

SUMMARY Bayesian inversion of magnetotelluric (MT) data is a powerful but computationally expensive approach to estimate the subsurface electrical conductivity distribution and associated uncertainty. Approximating the Earth subsurface with 1-D physics considerably speeds-up calculation of the forward problem, making the Bayesian approach tractable, but can lead to biased results when the assumption is violated. We propose a methodology to quantitatively compensate for the bias caused by the 1-D Earth assumption within a 1-D trans-dimensional Markov chain Monte Carlo sampler. Our approach determines site-specific likelihood functions which are calculated using a dimensionality discrepancy error model derived by a machine learning algorithm trained on a set of synthetic 3-D conductivity training images. This is achieved by exploiting known geometrical dimensional properties of the MT phase tensor. A complex synthetic model which mimics a sedimentary basin environment is used to illustrate the ability of our workflow to reliably estimate uncertainty in the inversion results, even in presence of strong 2-D and 3-D effects. Using this dimensionality discrepancy error model we demonstrate that on this synthetic data set the use of our workflow performs better in 80 per cent of the cases compared to the existing practice of using constant errors. Finally, our workflow is benchmarked against real data acquired in Queensland, Australia, and shows its ability to detect the depth to basement accurately.

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