@article{fdi:010070971,
  title = {{J}oint use of singular value decomposition and {M}onte-{C}arlo simulation for estimating uncertainty in surface {NMR} inversion},
  author = {{L}egchenko, {A}natoli and {C}omte, {J}. {C}. and {O}fterdinger, {U}. and {V}ouillamoz, {J}ean-{M}ichel and {L}awson, {F}. {M}. {A}. and {W}alsh, {J}.},
  editor = {},
  language = {{ENG}},
  abstract = {{W}e propose a simple and robust approach for investigating uncertainty in the results of inversion in geophysics. {W}e apply this approach to inversion of {S}urface {N}uclear {M}agnetic {R}esonance ({SNMR}) data, which is also known as {M}agnetic {R}esonance {S}ounding ({MRS}). {S}olution of this inverse problem is known to be non-unique. {W}e inverse {MRS} data using the well-known {T}ikhonov regularization method, which provides an optimal solution as a trade-off between the stability and accuracy. {T}hen, we perturb this model by random values and compute the fitting error for the perturbed models. {T}he magnitude of these perturbations is limited by the uncertainty estimated with the singular value decomposition ({SVD}) and taking into account experimental errors. {W}e 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. {T}hus, 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. {F}or 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. {F}or demonstrating our approach, we use synthetic data sets and experimental data acquired in the framework of investigation of a hard rock aquifer in the {I}reland ({C}ounty {D}onegal).},
  keywords = {{H}ydrogeophysics ; {I}reland ; {H}ard rock aquifer ; {M}agnetic resonance sounding ; {MRS} ; {S}urface {NMR} ; {SNMR} ; {IRLANDE}},
  booktitle = {},
  journal = {{J}ournal of {A}pplied {G}eophysics},
  volume = {144},
  numero = {},
  pages = {28--36},
  ISSN = {0926-9851},
  year = {2017},
  DOI = {10.1016/j.jappgeo.2017.06.010},
  URL = {https://www.documentation.ird.fr/hor/fdi:010070971},
}