BibTeX
@ARTICLE{
         Sambridge2007Adi,
       author = "M. Sambridge and P. Rickwood and N. Rawlinson and S. Sommacal",
       title = "Automatic differentiation in geophysical inverse problems",
       journal = "Geophysical Journal International",
       pages = "1--8",
       year = "2007",
       volume = "170",
       number = "1",
       doi = "10.1111/j.1365-246X.2007.03400.x",
       abstract = "Automatic differentiation (AD) is the technique whereby output variables of a
         computer code evaluating any complicated function (e.g. the solution to a differential equation) can
         be differentiated with respect to the input variables. Often AD tools take the form of source to
         source translators and produce computer code without the need for deriving and hand coding of
         explicit mathematical formulae by the user. The power of AD lies in the fact that it combines the
         generality of finite difference techniques and the accuracy and efficiency of analytical
         derivatives, while at the same time eliminating human coding errors. It also provides the
         possibility of accurate, efficient derivative calculation from complex forward codes where no
         analytical derivatives are possible and finite difference techniques are too cumbersome. AD is
         already having a major impact in areas such as optimization, meteorology and oceanography. Similarly
         it has considerable potential for use in non-linear inverse problems in geophysics where
         linearization is desirable, or for sensitivity analysis of large numerical simulation codes, for
         example, wave propagation and geodynamic modelling. At present, however, AD tools appear to be
         little used in the geosciences. Here we report on experiments using a state of the art AD tool to
         perform source to source code translation in a range of geoscience problems. These include
         calculating derivatives for Gibbs free energy minimization, seismic receiver function inversion, and
         seismic ray tracing. Issues of accuracy and efficiency are discussed.",
       ad_area = "Geophysics",
       ad_tools = "TAF",
       ad_theotech = "Introduction"
}