Regularization parameter selection in the 3D gravity inversion of the basement relief using GCV: A parallel approach

Mojica, Oscar F.; Bassrei, Amin

doi:10.1016/j.cageo.2015.06.013

Cited by 19 publications

(4 citation statements)

References 14 publications

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“…It is a standard choice in the geo-electromagnetic induction community to minimise the above l 2 -norm variant of the cost function Q (Menke 2012;Aster et al 2012;Farquharson and Oldenburg 2004;Krakauer et al 2004;Schwarzbach and Haber 2013;Usui 2015;Mojica and Bassrei 2015;Jahandari and Farquharson 2017;Wang et al 2018a). However, it may be desirable to use general l p norms instead.…”

Section: Methods Of Model Analysismentioning

confidence: 99%

“…Then, an optimal value of is obtained by minimising this newly created function. Both the L-curve and the GCV techniques can effectively determine optimal values of the weighting factor (Farquharson and Oldenburg 2004;Krakauer et al 2004;Mojica and Bassrei 2015). However, the GCV technique has a tendency of biasing the final value of to its initial value.…”

Section: • Variations △mentioning

confidence: 99%

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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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Section: Methods Of Model Analysismentioning

confidence: 99%

Section: • Variations △mentioning

confidence: 99%

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

Ren

Kalscheuer

2019

Surv Geophys

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“…These methods require additional constraints to get sharp discontinuity limits for anomalous bodies 26 . For other approaches, the parameters to be adjusted are geometric (non-linear approach): depth of a discontinuity surface 27 – 29 , polyhedral structures 30 , 31 , aggregation of small cells 32 . Binary or multinary approaches 33 could be considered as intermediate.…”

Section: Introductionmentioning

confidence: 99%

A free-geometry geodynamic modelling of surface gravity changes using Growth-dg software

Camacho

Vajda

Miller

et al. 2021

Sci Rep

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Globally there is abundant terrestrial surface gravity data used to study the time variation of gravity related to subsurface mass and density changes in different geological, geodynamical and geotechnical environments. We present here a tool for analysing existing and newly acquired, 4D gravity data, which creates new findings from its reuse. Our method calculates in an almost automatic way the possible sources of density change responsible for the observed gravity variations. The specifics of the new methodology are: use of a low number of observation points, relatively small source structures, low signal/noise ratio in the data, and a free 3D source geometry without initial hypothesis. The process is based on the non-linear adjustment of structures defined by aggregation of small cells corresponding to a 3D section of the sub-floor volume. This methodology is implemented in a software tool, named GROWTH-dg, which can be freely downloaded for immediate use, together with a user manual and application examples.

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“…GCV has been used in several papers related to geophysical applications. Mojica & Bassrei (2015) used GCV to select the optimum 𝜆 in the inversion of 3-D gravity data with parallel processing. Oliveira & Bassrei (2015) used GCV to select the optimum 𝜆 in electromagnetic tomography.…”

Section: Introductionmentioning

confidence: 99%

The Generalized Cross Validation Method for the Selection of Regularization Parameter in Geophysical Diffraction Tomography

2021

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Inverse problems are usually ill-posed in such a way that it is necessary to use some method to reduce their deficiencies. For this purpose, we use the regularization by derivative matrices, known as Tikhonov regularization. There is a crucial problem in regularization, which is the selection of the regularization parameter 𝜆. In this work, we use generalized cross validation (GCV) as a tool for the selection of 𝜆. GCV is used here for an application in geophysical diffraction tomography, where the objective is to obtain the 2-D velocity distribution from the measured values of the scattered acoustic field. The results are compared to those obtained using L-curve, and also Θ-curve, which is an extension of L-curve. We present several simulation results with synthetic data, and in general the results using GCV are equal or eventually better than the other two approaches.

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Regularization parameter selection in the 3D gravity inversion of the basement relief using GCV: A parallel approach

Cited by 19 publications

References 14 publications

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

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

A free-geometry geodynamic modelling of surface gravity changes using Growth-dg software

The Generalized Cross Validation Method for the Selection of Regularization Parameter in Geophysical Diffraction Tomography

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