Analysis and algorithms for a regularized Cauchy problem arising from a non-linear elliptic PDE for seismic velocity estimation

PDF Version Also Available for Download.

Description

In the present work we derive and study a nonlinear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite difference time-marching numerical scheme inspired by the Lax-Friedrichs method. The key features of this scheme is the Lax-Friedrichs averaging and the wide stencil in space. The second approach ... continued below

Creation Information

Cameron, M.K.; Fomel, S.B. & Sethian, J.A. January 1, 2009.

Context

This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this article can be viewed below.

Who

People and organizations associated with either the creation of this article or its content.

Publisher

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this article. Follow the links below to find similar items on the Digital Library.

Description

In the present work we derive and study a nonlinear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite difference time-marching numerical scheme inspired by the Lax-Friedrichs method. The key features of this scheme is the Lax-Friedrichs averaging and the wide stencil in space. The second approach is a spectral Chebyshev method with truncated series. We show that our schemes work because of (1) the special input corresponding to a positive finite seismic velocity, (2) special initial conditions corresponding to the image rays, (3) the fact that our finite-difference scheme contains small error terms which damp the high harmonics; truncation of the Chebyshev series, and (4) the need to compute the solution only for a short interval of time. We test our numerical scheme on a collection of analytic examples and demonstrate a dramatic improvement in accuracy in the estimation of the sound speed inside the Earth in comparison with the conventional Dix inversion. Our test on the Marmousi example confirms the effectiveness of the proposed approach.

Subjects

Keywords

STI Subject Categories

Source

  • Journal Name: Journal of Computational Physics

Language

Item Type

Identifier

Unique identifying numbers for this article in the Digital Library or other systems.

  • Report No.: LBNL-1447E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 946809
  • Archival Resource Key: ark:/67531/metadc901633

Collections

This article is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

What responsibilities do I have when using this article?

When

Dates and time periods associated with this article.

Creation Date

  • January 1, 2009

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

Description Last Updated

  • Nov. 8, 2016, 12:12 p.m.

Usage Statistics

When was this article last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 1

Interact With This Article

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

Cameron, M.K.; Fomel, S.B. & Sethian, J.A. Analysis and algorithms for a regularized Cauchy problem arising from a non-linear elliptic PDE for seismic velocity estimation, article, January 1, 2009; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc901633/: accessed June 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.