@article{PAR00012150,
  title = {{M}onte {C}arlo inversion of 3-{D} magnetic resonance measurements},
  author = {{C}hevalier, {A}. and {L}egchenko, {A}natoli and {G}irard, {J}. {F}. and {D}escloitres, {M}arc},
  editor = {},
  language = {{ENG}},
  abstract = {{T}he surface nuclear magnetic resonance ({SNMR}) method is a geophysical method designed for non-invasive groundwater investigations. {I}nversion of experimental data provides the spatial distribution of the water content in the subsurface. {H}owever, {SNMR} inversion is ill-posed and admits many solutions because of the imaging equation properties that are compounded by experimental error. {SNMR} data sets are conveniently presented as complex numbers, thus possessing phase and amplitude components. {S}ubsurface electroconductive formations and fluctuations of the {E}arth's magnetic field cause non-negligible phase shifts. {C}onsequently, the forward modelling of the {SNMR} signal generated by 3-{D} water saturated formations is achieved in the complex domain. {N}evertheless, in many cases, phase measurements are less reliable than amplitude measurements and water content rendering cannot be carried out using the complex {SNMR} signal. {T}his problem is resolved by performing inversion using complex forward modelling whose resulting signal amplitude is used for comparison with the data. {A}long with water content boundaries ranging from 0 to 1, this property turns the linear initial value inversion problem into a non-linear one. {I}n such a situation, the comprehensive analysis of inversion uncertainties is achieved by performing a solution space exploration based on a {M}onte {C}arlo approach. {A}n adapted {M}etropolis-{H}astings algorithm has been used on {SNMR} 3-{D} data sets to perform such an exploration. {C}omputing time depends on the problem dimensions. {W}ith a standard laptop computer about 10 hr were necessary for the inversion of our field data set. {T}he resulting model collection is used to calculate the probability density functions of the water content. {F}rom there, it is possible to estimate the uncertainty of the water content imagery. {U}sing both synthetic and experimental data, we show that our routine provides robust estimates of the spatial distribution of the water content for the {SNMR} 3-{D} initial amplitude inversion.},
  keywords = {{N}umerical solutions ; {I}nverse theory ; {H}ydrogeophysics},
  booktitle = {},
  journal = {{G}eophysical {J}ournal {I}nternational},
  volume = {198},
  numero = {1},
  pages = {216--228},
  ISSN = {0956-540{X}},
  year = {2014},
  DOI = {10.1093/gji/ggu091},
  URL = {https://www.documentation.ird.fr/hor/{PAR}00012150},
}