Joint use of singular value decomposition and Monte-Carlo simulation for estimating uncertainty in surface NMR inversion

Anatoly Legchenko, Jean-Christophe Comte, Ulrich Ofterdinger, Jean-Michel Vouillamoz, Fabrice Messan Amen Lawson, John Walsh

Research output: Contribution to journalArticle

6 Citations (Scopus)
4 Downloads (Pure)

Abstract

We propose a simple and robust approach for investigating uncertainty in the results of inversion in geophysics. We apply this approach to inversion of Surface Nuclear Magnetic Resonance (SNMR) data, which is also known as Magnetic Resonance Sounding (MRS). Solution of this inverse problem is known to be non-unique. We inverse MRS data using the well-known Tikhonov regularization method, which provides an optimal solution as a trade-off between the stability and accuracy. Then, we perturb this model by random values and compute the fitting error for the perturbed models. The magnitude of these perturbations is limited by the uncertainty estimated with the singular value decomposition (SVD) and taking into account experimental errors. We use 106 perturbed models and show that the large majority of these models, which have all the water content within the variations given by the SVD estimate, do not fit data with an acceptable accuracy. Thus, we may limit the solution space by only the equivalent inverse models that fit data with the accuracy close to that of the initial inverse model. For representing inversion results, we use three equivalent solutions instead of the only one: the “best” solution given by the regularization or other inversion technic and the extreme variations of this solution corresponding to the equivalent models with the minimum and the maximum volume of water. For demonstrating our approach, we use synthetic data sets and experimental data acquired in the framework of investigation of a hard rock aquifer in the Ireland (County Donegal).
Original languageEnglish
Pages (from-to)28-36
Number of pages9
JournalJournal of Applied Geophysics
Volume144
Early online date30 Jun 2017
DOIs
Publication statusPublished - 1 Sep 2017

Fingerprint

nuclear magnetic resonance
estimating
decomposition
inversions
simulation
sounding
magnetic resonance
Ireland
aquifers
geophysics
hard rock
inverse problem
inversion
trade-off
moisture content
water content
perturbation
aquifer
rocks
estimates

Keywords

  • hydrogeophysics
  • Ireland
  • hard rock aquifer
  • magnetic resonance sounding
  • MRS
  • surface NMR
  • SNMR

Cite this

Joint use of singular value decomposition and Monte-Carlo simulation for estimating uncertainty in surface NMR inversion. / Legchenko, Anatoly; Comte, Jean-Christophe; Ofterdinger, Ulrich; Vouillamoz, Jean-Michel; Lawson, Fabrice Messan Amen; Walsh, John.

In: Journal of Applied Geophysics, Vol. 144, 01.09.2017, p. 28-36.

Research output: Contribution to journalArticle

Legchenko, Anatoly ; Comte, Jean-Christophe ; Ofterdinger, Ulrich ; Vouillamoz, Jean-Michel ; Lawson, Fabrice Messan Amen ; Walsh, John. / Joint use of singular value decomposition and Monte-Carlo simulation for estimating uncertainty in surface NMR inversion. In: Journal of Applied Geophysics. 2017 ; Vol. 144. pp. 28-36.
@article{18808db86ce74d29abdb9f1819fe2200,
title = "Joint use of singular value decomposition and Monte-Carlo simulation for estimating uncertainty in surface NMR inversion",
abstract = "We propose a simple and robust approach for investigating uncertainty in the results of inversion in geophysics. We apply this approach to inversion of Surface Nuclear Magnetic Resonance (SNMR) data, which is also known as Magnetic Resonance Sounding (MRS). Solution of this inverse problem is known to be non-unique. We inverse MRS data using the well-known Tikhonov regularization method, which provides an optimal solution as a trade-off between the stability and accuracy. Then, we perturb this model by random values and compute the fitting error for the perturbed models. The magnitude of these perturbations is limited by the uncertainty estimated with the singular value decomposition (SVD) and taking into account experimental errors. We use 106 perturbed models and show that the large majority of these models, which have all the water content within the variations given by the SVD estimate, do not fit data with an acceptable accuracy. Thus, we may limit the solution space by only the equivalent inverse models that fit data with the accuracy close to that of the initial inverse model. For representing inversion results, we use three equivalent solutions instead of the only one: the “best” solution given by the regularization or other inversion technic and the extreme variations of this solution corresponding to the equivalent models with the minimum and the maximum volume of water. For demonstrating our approach, we use synthetic data sets and experimental data acquired in the framework of investigation of a hard rock aquifer in the Ireland (County Donegal).",
keywords = "hydrogeophysics, Ireland, hard rock aquifer, magnetic resonance sounding, MRS, surface NMR, SNMR",
author = "Anatoly Legchenko and Jean-Christophe Comte and Ulrich Ofterdinger and Jean-Michel Vouillamoz and Lawson, {Fabrice Messan Amen} and John Walsh",
note = "This work was supported by a grant from Labex OSUG@2020 (Investissements d'avenir – ANR10 LABX56). We also thank the French National Program (ANR)” Investment for Future - Excellency Equipment” project EQUIPEX CRITEX (grant # ANR-11-EQPX-0011) for providing MRS equipment. The Geological Survey of Ireland (GSI) provided financial support for the fieldwork in the framework of the Geoscience Research Program (2016).",
year = "2017",
month = "9",
day = "1",
doi = "10.1016/j.jappgeo.2017.06.010",
language = "English",
volume = "144",
pages = "28--36",
journal = "Journal of Applied Geophysics",
issn = "0926-9851",
publisher = "Elsevier Science B. V.",

}

TY - JOUR

T1 - Joint use of singular value decomposition and Monte-Carlo simulation for estimating uncertainty in surface NMR inversion

AU - Legchenko, Anatoly

AU - Comte, Jean-Christophe

AU - Ofterdinger, Ulrich

AU - Vouillamoz, Jean-Michel

AU - Lawson, Fabrice Messan Amen

AU - Walsh, John

N1 - This work was supported by a grant from Labex OSUG@2020 (Investissements d'avenir – ANR10 LABX56). We also thank the French National Program (ANR)” Investment for Future - Excellency Equipment” project EQUIPEX CRITEX (grant # ANR-11-EQPX-0011) for providing MRS equipment. The Geological Survey of Ireland (GSI) provided financial support for the fieldwork in the framework of the Geoscience Research Program (2016).

PY - 2017/9/1

Y1 - 2017/9/1

N2 - We propose a simple and robust approach for investigating uncertainty in the results of inversion in geophysics. We apply this approach to inversion of Surface Nuclear Magnetic Resonance (SNMR) data, which is also known as Magnetic Resonance Sounding (MRS). Solution of this inverse problem is known to be non-unique. We inverse MRS data using the well-known Tikhonov regularization method, which provides an optimal solution as a trade-off between the stability and accuracy. Then, we perturb this model by random values and compute the fitting error for the perturbed models. The magnitude of these perturbations is limited by the uncertainty estimated with the singular value decomposition (SVD) and taking into account experimental errors. We use 106 perturbed models and show that the large majority of these models, which have all the water content within the variations given by the SVD estimate, do not fit data with an acceptable accuracy. Thus, we may limit the solution space by only the equivalent inverse models that fit data with the accuracy close to that of the initial inverse model. For representing inversion results, we use three equivalent solutions instead of the only one: the “best” solution given by the regularization or other inversion technic and the extreme variations of this solution corresponding to the equivalent models with the minimum and the maximum volume of water. For demonstrating our approach, we use synthetic data sets and experimental data acquired in the framework of investigation of a hard rock aquifer in the Ireland (County Donegal).

AB - We propose a simple and robust approach for investigating uncertainty in the results of inversion in geophysics. We apply this approach to inversion of Surface Nuclear Magnetic Resonance (SNMR) data, which is also known as Magnetic Resonance Sounding (MRS). Solution of this inverse problem is known to be non-unique. We inverse MRS data using the well-known Tikhonov regularization method, which provides an optimal solution as a trade-off between the stability and accuracy. Then, we perturb this model by random values and compute the fitting error for the perturbed models. The magnitude of these perturbations is limited by the uncertainty estimated with the singular value decomposition (SVD) and taking into account experimental errors. We use 106 perturbed models and show that the large majority of these models, which have all the water content within the variations given by the SVD estimate, do not fit data with an acceptable accuracy. Thus, we may limit the solution space by only the equivalent inverse models that fit data with the accuracy close to that of the initial inverse model. For representing inversion results, we use three equivalent solutions instead of the only one: the “best” solution given by the regularization or other inversion technic and the extreme variations of this solution corresponding to the equivalent models with the minimum and the maximum volume of water. For demonstrating our approach, we use synthetic data sets and experimental data acquired in the framework of investigation of a hard rock aquifer in the Ireland (County Donegal).

KW - hydrogeophysics

KW - Ireland

KW - hard rock aquifer

KW - magnetic resonance sounding

KW - MRS

KW - surface NMR

KW - SNMR

U2 - 10.1016/j.jappgeo.2017.06.010

DO - 10.1016/j.jappgeo.2017.06.010

M3 - Article

VL - 144

SP - 28

EP - 36

JO - Journal of Applied Geophysics

JF - Journal of Applied Geophysics

SN - 0926-9851

ER -