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@ARTICLE{Bobe:904444,
      author       = {Bobe, Christin and Keller, Johannes and Vijver, Ellen Van
                      De},
      title        = {{S}ensitivity and depth of investigation from {M}onte
                      {C}arlo ensemble statistics},
      journal      = {Geophysical prospecting},
      volume       = {69},
      number       = {4},
      issn         = {0016-8025},
      address      = {Oxford [u.a.]},
      publisher    = {Wiley-Blackwell},
      reportid     = {FZJ-2021-06014},
      pages        = {761 - 778},
      year         = {2021},
      abstract     = {For many geophysical measurements, such as direct current
                      or electromagnetic induction methods, information fades away
                      with depth. This has to be taken into account when
                      interpreting models estimated from such measurements. For
                      that reason, a measurement sensitivity analysis and
                      determining the depth of investigation are standard steps
                      during geophysical data processing. In deterministic
                      gradient-based inversion, the most used sensitivity measure,
                      the differential sensitivity, is readily available since
                      these inversions require the computation of Jacobian
                      matrices. In contrast, differential sensitivity may not be
                      readily available in Monte Carlo inversion methods, since
                      these methods do not necessarily include a linearization of
                      the forward problem. Instead, a prior ensemble is used to
                      simulate an ensemble of forward responses. Then, the prior
                      ensemble is updated according to Bayesian inference. We
                      propose to use the covariance between the prior ensemble and
                      the forward response ensemble for constructing sensitivity
                      measures. In Monte Carlo approaches, the estimation of this
                      covariance does not require additional computations of the
                      forward model. Normalizing this covariance by the variance
                      of the prior ensemble, one obtains a simplified regression
                      coefficient. We investigate differences between this
                      simplified regression coefficient and differential
                      sensitivity using simple forward models. For linear forward
                      models, the simplified regression coefficient is equal to
                      differential sensitivity, except for the influences of the
                      sampling error and of the correlation structure of the prior
                      distribution. In the non-linear case, the behaviour of the
                      simplified regression coefficient as sensitivity measure is
                      analysed for a simple non-linear forward model and a
                      frequency-domain electromagnetic forward model. Differential
                      sensitivity and the simplified regression coefficient are
                      similar for prior intervals on which the forward model
                      response is approximately linear. Differences between the
                      two sensitivity measures increase with the degree of
                      non-linearity in the prior range. Additionally, we
                      investigate the correlation between prior ensemble and
                      forward response ensemble as sensitivity measure.
                      Correlation yields a normalized version of the simplified
                      regression coefficient. We propose to use this correlation
                      and the simplified regression coefficient for determining
                      depth of investigation in Monte Carlo inversions.},
      cin          = {IBG-3},
      ddc          = {550},
      cid          = {I:(DE-Juel1)IBG-3-20101118},
      pnm          = {2173 - Agro-biogeosystems: controls, feedbacks and impact
                      (POF4-217)},
      pid          = {G:(DE-HGF)POF4-2173},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000611909000001},
      doi          = {10.1111/1365-2478.13068},
      url          = {https://juser.fz-juelich.de/record/904444},
}