Inversion of magnetotelluric data in a sparse model domain

Nittinger, C.; Becken, Michael

doi:10.1093/gji/ggw222

Cited by 14 publications

(11 citation statements)

References 38 publications

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“…We need to minimise the objective function formulated in the wavelet domain in terms of wavelet coefficients c . We use the algorithm presented by Nittinger and Becken (), which solves the following optimisation problem:

Φ false(boldc false) = false| false| W_{e} (G false(boldRc false) - d^{obs}) {false| false|}_{2}^{2} + λ {| | c | |}_{1}^{1} .

…”

Section: Methodsmentioning

confidence: 99%

“…In the end, the inverse model is a representation of the coefficients that yield the sparsest solution. For more details regarding the algorithm, we refer the reader to the work of Nittinger and Becken ().…”

Section: Methodsmentioning

confidence: 99%

“…The spatial support of wavelet functions on finer scales

j = 0, 1, \dots, J

decreases by a factor of 2 j compared with the coarsest scale

j = 0

. In the work of Nittinger and Becken (), the different scales were truncated to estimate inversion models described by wavelet functions of different sizes. Here, we do not change the scales and choose the maximum possible scale, which was shown to yield the sparsest model (cf Nittinger and Becken ).…”

Section: Synthetic Datamentioning

confidence: 99%

“…Here, we parameterise the MT resistivity model in a wavelet domain and conceive the wavelet coefficients as the model parameters (Daubechies ). This allows us to apply sparsity constraints to estimate a solution to the inverse problem (cf Nittinger and Becken ). This alternative inversion scheme has emerged from signal processing, where it has found wide applications in the field of compressed sensing (Donoho ), aiming at efficient signal reconstruction when the signal at hand is sparse in some domain.…”

Section: Introductionmentioning

confidence: 99%

“…Nittinger and Becken () showed that the compressive sensing scheme is feasible for MT inversion, but the study was confined to a smooth wavelet representation of only one family and was more focused on the exploitation of different model scales. Here, we use the same approach but with two different wavelet representations.…”

Section: Introductionmentioning

confidence: 99%

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Compressive sensing approach for two‐dimensional magnetotelluric inversion using wavelet dictionaries

Nittinger

Becken

2018

Geophysical Prospecting

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We present a 2D inversion scheme for magnetotelluric data, where the conductivity structure is parameterised with different wavelet functions that are collected in a wavelet‐based dictionary. The inversion model estimate is regularised in terms of wavelet coefficient sparsity following the compressive sensing approach. However, when the model is expressed on the basis of a single wavelet family only, the geometrical appearance of model features reflects the shape of the wavelet functions. Combining two or more wavelet families in a dictionary provides greater flexibility to represent the model structure, permitting, for example, the simultaneous occurrence of smooth and sharp anomalies within the same model. We show that the application of the sparsity regularisation scheme with wavelet dictionaries provides the user with a number of different model classes that may explain the data to the same extent. For a real data example from the Dead Sea Transform, we show that the use of such a scheme can be beneficial to evaluate the geometries of conductivity anomalies and to understand the effect of regularisation on the model estimate.

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Φ false(boldc false) = false| false| W_{e} (G false(boldRc false) - d^{obs}) {false| false|}_{2}^{2} + λ {| | c | |}_{1}^{1} .

…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…The spatial support of wavelet functions on finer scales

j = 0, 1, \dots, J

decreases by a factor of 2 j compared with the coarsest scale

j = 0

Section: Synthetic Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Compressive sensing approach for two‐dimensional magnetotelluric inversion using wavelet dictionaries

Nittinger

Becken

2018

Geophysical Prospecting

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Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Ren

Kalscheuer

2019

Surv Geophys

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A meaningful solution to an inversion problem should be composed of the preferred inversion model and its uncertainty and resolution estimates. The model uncertainty estimate describes an equivalent model domain in which each model generates responses which fit the observed data to within a threshold value. The model resolution matrix measures to what extent the unknown true solution maps into the preferred solution. However, most current geophysical electromagnetic (also gravity, magnetic and seismic) inversion studies only offer the preferred inversion model and ignore model uncertainty and resolution estimates, which makes the reliability of the preferred inversion model questionable. This may be caused by the fact that the computation and analysis of an inversion model depend on multiple factors, such as the misfit or objective function, the accuracy of the forward solvers, data coverage and noise, values of trade-off parameters, the initial model, the reference model and the model constraints. Depending on the particular method selected, large computational costs ensue. In this review, we first try to cover linearised model analysis tools such as the sensitivity matrix, the model resolution matrix and the model covariance matrix also providing a partially nonlinear description of the equivalent model domain based on pseudo-hyperellipsoids. Linearised model analysis tools can offer quantitative measures. In particular, the model resolution and covariance matrices measure how far the preferred inversion model is from the true model and how uncertainty in the measurements maps into model uncertainty. We also cover nonlinear model analysis tools including changes to the preferred inversion model (nonlinear sensitivity tests), modifications of the data set (using bootstrap re-sampling and generalised cross-validation), modifications of data uncertainty, variations of model constraints (including changes to the trade-off parameter, reference model and matrix regularisation operator), the edgehog method, mostsquares inversion and global searching algorithms. These nonlinear model analysis tools try to explore larger parts of the model domain than linearised model analysis and, hence, may assemble a more comprehensive equivalent model domain. Then, to overcome the bottleneck of computational cost in model analysis, we present several practical algorithms to accelerate the computation. Here, we emphasise linearised model analysis, as efficient computation of nonlinear model uncertainty and resolution estimates is mainly determined by fast forward and inversion solvers. In the last part of our review, we present applications of model analysis to models computed from individual and joint inversions of electromagnetic data; we also describe optimal survey design and inversion grid design as important Extended author information available on the last page of the article applications of model analysis. The currently available model uncertainty and resolution analyses are mainly for 1D and 2D problems due to the limitation...

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Groundwater exploration by magnetotelluric method within the birimian rocks of mankessim, Ghana

Agyemang

2022

Appl Water Sci

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The Magnetotelluric (MT) geophysical method has successfully been applied in groundwater exploration within the Birimian rocks of Mankessim. The technique has provided information on the rocks and structural relationships within the investigative depth of up to 300 m for hydrogeological purposes. The method provides information on the aquiferous zone and the general depth of burial. The study revealed that the resistivity of the subsurface materials within the study area ranges from 0.1 Ωm to 4.0 Ωm. The study shows that the groundwater occurrence in the area is mainly controlled by fractured and weathered zones. It is highly possible to encounter groundwater at the saprock zone. This zone is fractured and weathered zones sandwiched by the overburden and the bedrock. The static water level of the study area is about 25 m. This shallow depth makes the groundwater resource prone to contamination through anthropogenic activities such as the application of agrochemicals and the use of pit latrine which are common practices in the study area. The MT method is effective in the exploration of groundwater within the sedimentary environment.

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Inversion of magnetotelluric data in a sparse model domain

Cited by 14 publications

References 38 publications

Compressive sensing approach for two‐dimensional magnetotelluric inversion using wavelet dictionaries

Compressive sensing approach for two‐dimensional magnetotelluric inversion using wavelet dictionaries

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Groundwater exploration by magnetotelluric method within the birimian rocks of mankessim, Ghana

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