Adjoint Method and Its Application in Mantle Convection

• 责任者：Liu Lijun (Seismological Laboratory ; California Institute of Technology ; Pasadena ; CA 91125 ; USA) ; Michael Gurnis
• 刊名：Earth Science Frontiers
• 出版年：2010
• 卷期：17(3)
• 关键词：地幔对流 ; mantle convection
• 页码：p.139-148
• 图表：4 illus., 21 refs.
• 分类号：0400
• issnNo：ISSN1005-2321
• isbnNo：CN11-3370/P

In this paper, the authors try to introduce the adjoint method in a systematic way, from the theoretical basis to its practical implementation in numerical models of mantle convection, with several examples to help the understanding. The adjoint operator of a temporally evolving system can be derived based on the perturbation theory, where a mismatch in the model output against observation is attributed to an error in the input, with their relation approximated as a first-order derivative (gradient) of the least-squared mismatch with respect to the input. For a nonlinear system, iterative processing is inevitable; the efficiency and convergence rate depend on the amount of a-priori information about the input (e. g. the initial condition). Seismic tomography, which describes the present-day mantle structures, has seen steady progress on both regional and global scales, and allows inverting mantle convection to the past.