Reduced Order Model Based Nonlinear Waveform Inversion for the 1D Helmholtz Equation

Andreas Tataris; Tristan van Leeuwen

doi:10.1007/s10440-024-00700-y

Reduced Order Model Based Nonlinear Waveform Inversion for the 1D Helmholtz Equation

Andreas Tataris^*
, Tristan van Leeuwen

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We study a reduced order model (ROM) based waveform inversion method applied to a Helmholtz problem with impedance boundary conditions and variable refractive index. The first goal of this paper is to obtain relations that allow the reconstruction of the Galerkin projection of the continuous problem onto the space spanned by solutions of the Helmholtz equation. The second goal is to study the introduced nonlinear optimization method based on the ROM aimed to estimate the refractive index from reflection and transmission data. Finally we compare numerically our method to the conventional least squares inversion based on minimizing the distance between modelled to measured data.

Original language	English
Article number	11
Journal	Acta Applicandae Mathematicae
Volume	194
Issue number	1
DOIs	https://doi.org/10.1007/s10440-024-00700-y
Publication status	Published - 13 Nov 2024

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature B.V. 2024.

Funding

Authors would like to thank Sjoerd Verduyn Lunel, Carolin Kreisbeck and Ivan Vasconcelos for their suggestions and the fruitful discussions. We would also like to thank the reviewers for their insightful suggestions and comments that helped us improve our manuscript.

Funders
Utrecht Consortium for Subsurface Imaging (UCSI)

Keywords

Full waveform inversion
Helmholtz equation
Nonlinear inversion
Reduced order models

Access to Document

10.1007/s10440-024-00700-y

s10440-024-00700-yFinal published version, 1.3 MBLicence: Taverne

Cite this

@article{6180cd723f1b426bad0e98fa09abdd99,

title = "Reduced Order Model Based Nonlinear Waveform Inversion for the 1D Helmholtz Equation",

abstract = "We study a reduced order model (ROM) based waveform inversion method applied to a Helmholtz problem with impedance boundary conditions and variable refractive index. The first goal of this paper is to obtain relations that allow the reconstruction of the Galerkin projection of the continuous problem onto the space spanned by solutions of the Helmholtz equation. The second goal is to study the introduced nonlinear optimization method based on the ROM aimed to estimate the refractive index from reflection and transmission data. Finally we compare numerically our method to the conventional least squares inversion based on minimizing the distance between modelled to measured data.",

keywords = "Full waveform inversion, Helmholtz equation, Nonlinear inversion, Reduced order models",

author = "Andreas Tataris and \{van Leeuwen\}, Tristan",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Nature B.V. 2024.",

year = "2024",

month = nov,

day = "13",

doi = "10.1007/s10440-024-00700-y",

language = "English",

volume = "194",

journal = "Acta Applicandae Mathematicae",

issn = "0167-8019",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Reduced Order Model Based Nonlinear Waveform Inversion for the 1D Helmholtz Equation

AU - Tataris, Andreas

AU - van Leeuwen, Tristan

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature B.V. 2024.

PY - 2024/11/13

Y1 - 2024/11/13

N2 - We study a reduced order model (ROM) based waveform inversion method applied to a Helmholtz problem with impedance boundary conditions and variable refractive index. The first goal of this paper is to obtain relations that allow the reconstruction of the Galerkin projection of the continuous problem onto the space spanned by solutions of the Helmholtz equation. The second goal is to study the introduced nonlinear optimization method based on the ROM aimed to estimate the refractive index from reflection and transmission data. Finally we compare numerically our method to the conventional least squares inversion based on minimizing the distance between modelled to measured data.

AB - We study a reduced order model (ROM) based waveform inversion method applied to a Helmholtz problem with impedance boundary conditions and variable refractive index. The first goal of this paper is to obtain relations that allow the reconstruction of the Galerkin projection of the continuous problem onto the space spanned by solutions of the Helmholtz equation. The second goal is to study the introduced nonlinear optimization method based on the ROM aimed to estimate the refractive index from reflection and transmission data. Finally we compare numerically our method to the conventional least squares inversion based on minimizing the distance between modelled to measured data.

KW - Full waveform inversion

KW - Helmholtz equation

KW - Nonlinear inversion

KW - Reduced order models

UR - https://www.scopus.com/pages/publications/85209207693

U2 - 10.1007/s10440-024-00700-y

DO - 10.1007/s10440-024-00700-y

M3 - Article

AN - SCOPUS:85209207693

SN - 0167-8019

VL - 194

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

IS - 1

M1 - 11

ER -

Reduced Order Model Based Nonlinear Waveform Inversion for the 1D Helmholtz Equation

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this