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T.W. Alexander Drive P.O.Box 14006 Research Triangle Park, NC 27709-4006 Tel: 919.685.9350 Fax: 919.685.9360 [email protected] |
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19
T.W. Alexander Drive P.O.Box 14006 Research Triangle Park, NC 27709-4006 Tel: 919.685.9350 Fax: 919.685.9360 [email protected] |
Waves and Imaging
A
Working Group in Random Media
Group
Leader: Laurent Demanet
Webmaster: Qiu Wu
Password Protected Site
(future)
Announcements
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Meeting
Time: Tuesday, 1:00-3:00 Remote access for the meeting is available: WebEx Go to https://samsi.webex.com Click on the meeting you want to join. Enter Your Name, Your Email Address and the meeting password from the email.
Now you are in the meeting and can use all the features of WebEx. Make sure you are seeing the screen of the presenters, if not send a message or tell via phone. You can learn more about WebEx and take tutorials at university.webex.com
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Meeting Activities
| Date | Topics & Readings | Presentation Slides |
| Oct. 2 | Short introductory presentations by all participants | 1. Demanet 2. Ou 3. Garnier |
| Oct. 9 | Josselin Garnier's presentation on cross-correlations Campillo-paul paper(PDF) | Garnier slides(PDF) |
| Oct. 16 | Yu Chen's presentation on FM imaging | Chen slides(PDF) |
| Oct. 23 | Presentation by Laurent Demanet on seismic imaging; Slides by Bill Symes: 1 and 2 | |
| Oct. 30 | Presentation by Laurent Demanet on multiscale methods for wave computation - Wave atoms paper. | |
| Nov. 06 | Semyon Tsynkov's presentation on nonlinear waves in optics, including numerical method | Tsynkov slides(PDF) |
| Nov. 13 | Laurent Demanet's presentation on optimal transport and model velocity estimation | |
| Nov. 20 | Mauro Maggioni's presentation on superposition of exponentials and imaging | |
| Nov. 27 | Mauro Maggioni's presentation on compressed sensing | Maggioni slides(PDF) |
| Dec. 4 | Yvonne Ou and Jean-Pierre Fouque's presentation on time-reversal for elastic waves | |
| Dec. 11 | Mike (Pengchong) Yan's presentation on "Multi-frequency imaging of multiple targets in Rician fading media" | Yan slides(PDF) |
Group Members and Photo
| Name | Affiliation |
| Daniel Alfaro-Vigo | Inst. of Pure and Applied Mathematics (Brazil) |
| J. Thomas Beale | Duke University |
| Yu Chen | New York University |
| Sava Dediu | N.C. State University |
| Maarten de Hoop | Purdue University |
| Laurent Demanet | Stanford University |
| Albert Fannjiang | Univ. of California-Davis |
| Jean-Pierre Fouque | Univ. of California-Santa Barbara |
| Josselin Garnier | Institute of Mathematics - Jussieu |
| Kazufumi Ito | N.C. State University |
| Jian-Guo Liu | Duke University |
| Mauro Maggioni | Duke University |
| Vahagn Manukian | N.C. State University |
| Yvonne Ou | University of Central Florida |
| Gabriel Peyre | Ceremade, Universite Paris-Dauphine |
| Knut Solna | Univ. of California-Irvine |
| John Strain | Univ. of California-Berkeley |
| Semyon V. Tsynkov | North Carolina State University |
| Qiu Wu | University of Texas |
| Jack Xin | Univ. of California-Irvine |
| Pengchong Yan | Univ. of California-Davis |
| Lexing Ying | University of Texas |
| Hongkai Zhao | Univ. of California-Irvine |
Open Problems
| Problem | Detailed Descriptions | Readings |
| 1. Optimal transport and 1D wave equations | The problem is to investigate the form in which optimal transport ideas can complement migration for the resolution of the seismic imaging inverse problem. We propose to start looking at the case of the 1D wave equation, where the data is a NtD map at the origin. General reference about seismic imaging and migration: these lecture notes by Bill Symes. Reference on optimal transport: Kazufumi Ito's paper. | 1. Demanet 2. Symes 3.Ito |
| 2. A model for waves in granular materials | The problem is to formulate a model for waves in granular materials that would explain (1) why waves travel along force chains, and (2) why they attenuate. The answer is probably a wave equation with stres-dependent friction at interfaces, that may homogenize into memory terms in some limit. Reference: L. Demanet's presentation Reference on granular materials: Karen Daniels's webpage . For a state of current research on modeling waves in granular media, see this ppt presentation. | |
| 3. Time reversal for elastic waves | The problem is to provide a mathematical treatment of time reversal in the elastic wave equation, which generalizes the acoustic case. References provided by JP Fouque: 1. Localization and Mode Conversion for Elastic Waves in Randomly Layered Media, W. Kohler, G. Papanicolaou and B. White . 2. Reflection and transmission of acoustic waves by a locally-layered slab, W. Kohler, G. Papanicolaou and B. White (163K). In: Diffuse Waves in Complex Media, edited by Jean-Pierre | |
| 4. Surfaces waves and cross-correlations | See the last page of the presentation (PDF) by J. Garnier on Oct 9. Also see Larose's Geophysics paper(PDF) | |
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