Proper Generalized Decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems.

Author (s): Signorini, M., Zlotnik, S. and Díez, P.
Journal: International Journal for Numerical Methods in Engineering

Volume: 109, Issue 8
Pages: 1085 – 1102
Date: 2017

The identification of the geological structure form seismic data is formulated as an inverse problem. The properties and the shape of the rock formations in the subsoil are described by material and geometric parameters, which are taken as input data for a predictive model. Here, the model is based on the Helmholtz equation, describing the acoustic response of the system for a given wavelength. Thus, the inverse problem consists in identifying the values of these parameters such that the output of the model agrees the best with observations. this optimization algorithm requires multiple queries to the model with different values of the parameters. Reduced Order Models are especially well suited to significantly reduce the computational overhead of the multiple evaluations of the model.
In particular, the Proper Generalized Decomposition (PGD) produces a solution explicitly stating the parametric dependence, where the parameters play the same role as the physical coordinates. A PGD solver is devised to inexpensively explore the parametric space along the iterative process. This exploration of the parametric space is in fact seen as a post-process of the generalized solution. The approach adopted demonstrates its viability when tested in two illustrative examples.



@article {NME:NME5313,
author = {Signorini, Marianna and Zlotnik, Sergio and Díez, Pedro},
title = {Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems},
journal = {International Journal for Numerical Methods in Engineering},
volume = {109},
number = {8},
issn = {1097-0207},
url = {http://dx.doi.org/10.1002/nme.5313},
doi = {10.1002/nme.5313},
pages = {1085--1102},
keywords = {parameterized Helmholtz problem, proper generalized decomposition (PGD), parameter identification, inverse problems, seismic analysis},
year = {2017},
note = {nme.5313},