@article{fdi:010071953,
  title = {{L}inear geophysical inversion via the discrete cosine pseudo-inverse : application to potential fields},
  author = {{F}ernandez-{M}artinez, {J}. {L}. and {F}ernandez-{M}uniz, {Z}. and {P}allero, {J}. {L}. {G}. and {B}onvalot, {S}ylvain},
  editor = {},
  language = {{ENG}},
  abstract = {{I}n this paper, we present a methodology to perform geophysical inversion of large-scale linear systems via a covariance-free orthogonal transformation: the discrete cosine transform. {T}he methodology consists of compressing the matrix of the linear system as a digital image and using the interesting properties of orthogonal transformations to define an approximation of the {M}oore-{P}enrose pseudo-inverse. {T}his methodology is also highly scalable since the model reduction achieved by these techniques increases with the number of parameters of the linear system involved due to the high correlation needed for these parameters to accomplish very detailed forward predictions and allows for a very fast computation of the inverse problem solution. {W}e show the application of this methodology to a simple synthetic two-dimensional gravimetric problem for different dimensionalities and different levels of white {G}aussian noise and to a synthetic linear system whose system matrix has been generated via geostatistical simulation to produce a random field with a given spatial correlation. {T}he numerical results show that the discrete cosine transform pseudo-inverse outperforms the classical least-squares techniques, mainly in the presence of noise, since the solutions that are obtained are more stable and fit the observed data with the lowest root-mean-square error. {B}esides, we show that model reduction is a very effective way of parameter regularisation when the conditioning of the reduced discrete cosine transform matrix is taken into account. {W}e finally show its application to the inversion of a real gravity profile in the {A}tacama {D}esert (north {C}hile) obtaining very successful results in this non-linear inverse problem. {T}he methodology presented here has a general character and can be applied to solve any linear and non-linear inverse problems (through linearisation) arising in technology and, particularly, in geophysics, independently of the geophysical model discretisation and dimensionality. {N}evertheless, the results shown in this paper are better in the case of ill-conditioned inverse problems for which the matrix compression is more efficient. {I}n that sense, a natural extension of this methodology would be its application to the set of normal equations.},
  keywords = {{L}inear inversion ; {M}odel reduction ; {D}iscrete cosine transform ({DCT}) ; {P}seudo-inverse ; {CHILY} ; {ATACAMA} {DESERT}},
  booktitle = {},
  journal = {{G}eophysical {P}rospecting},
  volume = {65},
  numero = {1},
  pages = {94--111},
  ISSN = {0016-8025},
  year = {2017},
  DOI = {10.1111/1365-2478.12548},
  URL = {https://www.documentation.ird.fr/hor/fdi:010071953},
}