Publication: Automatic differentiation in geophysical inverse problems
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Automatic differentiation in geophysical inverse problems

- Article in a journal -
 

Area
Geophysics

Author(s)
M. Sambridge , P. Rickwood , N. Rawlinson , S. Sommacal

Published in
Geophysical Journal International

Year
2007

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 Tools
TAF

AD Theory and Techniques
Introduction

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"
}


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