Astronomy and Astrophysics – Astronomy
Scientific paper
Nov 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006geoji.167..495p&link_type=abstract
Geophysical Journal International, Volume 167, Issue 3, pp. 495-503.
Astronomy and Astrophysics
Astronomy
37
Adjoint State, Gradient, Migration, Tomography
Scientific paper
Estimating the model parameters from measured data generally consists of minimizing an error functional. A classic technique to solve a minimization problem is to successively determine the minimum of a series of linearized problems. This formulation requires the Fréchet derivatives (the Jacobian matrix), which can be expensive to compute. If the minimization is viewed as a non-linear optimization problem, only the gradient of the error functional is needed. This gradient can be computed without the Fréchet derivatives. In the 1970s, the adjoint-state method was developed to efficiently compute the gradient. It is now a well-known method in the numerical community for computing the gradient of a functional with respect to the model parameters when this functional depends on those model parameters through state variables, which are solutions of the forward problem. However, this method is less well understood in the geophysical community. The goal of this paper is to review the adjoint-state method. The idea is to define some adjoint-state variables that are solutions of a linear system. The adjoint-state variables are independent of the model parameter perturbations and in a way gather the perturbations with respect to the state variables. The adjoint-state method is efficient because only one extra linear system needs to be solved.
Several applications are presented. When applied to the computation of the derivatives of the ray trajectories, the link with the propagator of the perturbed ray equation is established.
No associations
LandOfFree
A review of the adjoint-state method for computing the gradient of a functional with geophysical applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A review of the adjoint-state method for computing the gradient of a functional with geophysical applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A review of the adjoint-state method for computing the gradient of a functional with geophysical applications will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1314800