Towards using direct methods in seismic tomography: computation of the full resolution matrix using high-performance computing and sparse QR factorization

For more than two decades, the number of data and model parameters in seismic tomography problems has exceeded the available computational resources required for application of direct computational methods, leaving iterative solvers the only option. One disadvantage of the iterative techniques is th...

Full description

Saved in:
Bibliographic Details
Published in:Geophysical journal international 2016-05, Vol.205 (2), p.830-836
Main Authors: Bogiatzis, Petros, Ishii, Miaki, Davis, Timothy A.
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-a320t-c170056a5a1b2d8e530cb0d546e59266e5327f1c45459349a63d0718e39c95f23
cites cdi_FETCH-LOGICAL-a320t-c170056a5a1b2d8e530cb0d546e59266e5327f1c45459349a63d0718e39c95f23
container_end_page 836
container_issue 2
container_start_page 830
container_title Geophysical journal international
container_volume 205
creator Bogiatzis, Petros
Ishii, Miaki
Davis, Timothy A.
description For more than two decades, the number of data and model parameters in seismic tomography problems has exceeded the available computational resources required for application of direct computational methods, leaving iterative solvers the only option. One disadvantage of the iterative techniques is that the inverse of the matrix that defines the system is not explicitly formed, and as a consequence, the model resolution and covariance matrices cannot be computed. Despite the significant effort in finding computationally affordable approximations of these matrices, challenges remain, and methods such as the checkerboard resolution tests continue to be used. Based upon recent developments in sparse algorithms and high-performance computing resources, we show that direct methods are becoming feasible for large seismic tomography problems. We demonstrate the application of QR factorization in solving the regional P-wave structure and computing the full resolution matrix with 267 520 model parameters.
doi_str_mv 10.1093/gji/ggw052
format article
fullrecord <record><control><sourceid>oup_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1093_gji_ggw052</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><oup_id>10.1093/gji/ggw052</oup_id><sourcerecordid>10.1093/gji/ggw052</sourcerecordid><originalsourceid>FETCH-LOGICAL-a320t-c170056a5a1b2d8e530cb0d546e59266e5327f1c45459349a63d0718e39c95f23</originalsourceid><addsrcrecordid>eNp9kMtKAzEYhYMoWKsbnyAbN8LY3NtxJ8UbFESp0N2QZpKZlMlkSDJofRSf1ull7eb_4ZzDt_gAuMboDqOcTqqNnVTVF-LkBIwwFTwjTKxOwQjlXGScodU5uIhxgxBmmM1G4Hfpv2QoI-yjbStY2qBVgk6n2g-hbWHUNjqrYPLOV0F29fYeKu-6PslkfQu9ganW0PRNA4OOvun3sZMp2O8jtbZVnXU6GB-cbJU-AnaVbEsYOxmihu8f0EiVfLA_e_QlODOyifrq-Mfg8-lxOX_JFm_Pr_OHRSYpQSlTeIoQF5JLvCblTHOK1BqVnAnNcyKGS8nUYMU44zlluRS0RFM80zRXOTeEjsHtgauCjzFoU3TBOhm2BUbFzmoxWC0OVofxzWHs--6_3R_QvXyJ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Towards using direct methods in seismic tomography: computation of the full resolution matrix using high-performance computing and sparse QR factorization</title><source>Open Access: Oxford University Press Open Journals</source><creator>Bogiatzis, Petros ; Ishii, Miaki ; Davis, Timothy A.</creator><creatorcontrib>Bogiatzis, Petros ; Ishii, Miaki ; Davis, Timothy A.</creatorcontrib><description>For more than two decades, the number of data and model parameters in seismic tomography problems has exceeded the available computational resources required for application of direct computational methods, leaving iterative solvers the only option. One disadvantage of the iterative techniques is that the inverse of the matrix that defines the system is not explicitly formed, and as a consequence, the model resolution and covariance matrices cannot be computed. Despite the significant effort in finding computationally affordable approximations of these matrices, challenges remain, and methods such as the checkerboard resolution tests continue to be used. Based upon recent developments in sparse algorithms and high-performance computing resources, we show that direct methods are becoming feasible for large seismic tomography problems. We demonstrate the application of QR factorization in solving the regional P-wave structure and computing the full resolution matrix with 267 520 model parameters.</description><identifier>ISSN: 0956-540X</identifier><identifier>EISSN: 1365-246X</identifier><identifier>DOI: 10.1093/gji/ggw052</identifier><language>eng</language><publisher>Oxford University Press</publisher><ispartof>Geophysical journal international, 2016-05, Vol.205 (2), p.830-836</ispartof><rights>The Authors 2016. Published by Oxford University Press on behalf of The Royal Astronomical Society. 2016</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a320t-c170056a5a1b2d8e530cb0d546e59266e5327f1c45459349a63d0718e39c95f23</citedby><cites>FETCH-LOGICAL-a320t-c170056a5a1b2d8e530cb0d546e59266e5327f1c45459349a63d0718e39c95f23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Bogiatzis, Petros</creatorcontrib><creatorcontrib>Ishii, Miaki</creatorcontrib><creatorcontrib>Davis, Timothy A.</creatorcontrib><title>Towards using direct methods in seismic tomography: computation of the full resolution matrix using high-performance computing and sparse QR factorization</title><title>Geophysical journal international</title><description>For more than two decades, the number of data and model parameters in seismic tomography problems has exceeded the available computational resources required for application of direct computational methods, leaving iterative solvers the only option. One disadvantage of the iterative techniques is that the inverse of the matrix that defines the system is not explicitly formed, and as a consequence, the model resolution and covariance matrices cannot be computed. Despite the significant effort in finding computationally affordable approximations of these matrices, challenges remain, and methods such as the checkerboard resolution tests continue to be used. Based upon recent developments in sparse algorithms and high-performance computing resources, we show that direct methods are becoming feasible for large seismic tomography problems. We demonstrate the application of QR factorization in solving the regional P-wave structure and computing the full resolution matrix with 267 520 model parameters.</description><issn>0956-540X</issn><issn>1365-246X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKAzEYhYMoWKsbnyAbN8LY3NtxJ8UbFESp0N2QZpKZlMlkSDJofRSf1ull7eb_4ZzDt_gAuMboDqOcTqqNnVTVF-LkBIwwFTwjTKxOwQjlXGScodU5uIhxgxBmmM1G4Hfpv2QoI-yjbStY2qBVgk6n2g-hbWHUNjqrYPLOV0F29fYeKu-6PslkfQu9ganW0PRNA4OOvun3sZMp2O8jtbZVnXU6GB-cbJU-AnaVbEsYOxmihu8f0EiVfLA_e_QlODOyifrq-Mfg8-lxOX_JFm_Pr_OHRSYpQSlTeIoQF5JLvCblTHOK1BqVnAnNcyKGS8nUYMU44zlluRS0RFM80zRXOTeEjsHtgauCjzFoU3TBOhm2BUbFzmoxWC0OVofxzWHs--6_3R_QvXyJ</recordid><startdate>20160501</startdate><enddate>20160501</enddate><creator>Bogiatzis, Petros</creator><creator>Ishii, Miaki</creator><creator>Davis, Timothy A.</creator><general>Oxford University Press</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20160501</creationdate><title>Towards using direct methods in seismic tomography: computation of the full resolution matrix using high-performance computing and sparse QR factorization</title><author>Bogiatzis, Petros ; Ishii, Miaki ; Davis, Timothy A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a320t-c170056a5a1b2d8e530cb0d546e59266e5327f1c45459349a63d0718e39c95f23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bogiatzis, Petros</creatorcontrib><creatorcontrib>Ishii, Miaki</creatorcontrib><creatorcontrib>Davis, Timothy A.</creatorcontrib><collection>CrossRef</collection><jtitle>Geophysical journal international</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bogiatzis, Petros</au><au>Ishii, Miaki</au><au>Davis, Timothy A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Towards using direct methods in seismic tomography: computation of the full resolution matrix using high-performance computing and sparse QR factorization</atitle><jtitle>Geophysical journal international</jtitle><date>2016-05-01</date><risdate>2016</risdate><volume>205</volume><issue>2</issue><spage>830</spage><epage>836</epage><pages>830-836</pages><issn>0956-540X</issn><eissn>1365-246X</eissn><abstract>For more than two decades, the number of data and model parameters in seismic tomography problems has exceeded the available computational resources required for application of direct computational methods, leaving iterative solvers the only option. One disadvantage of the iterative techniques is that the inverse of the matrix that defines the system is not explicitly formed, and as a consequence, the model resolution and covariance matrices cannot be computed. Despite the significant effort in finding computationally affordable approximations of these matrices, challenges remain, and methods such as the checkerboard resolution tests continue to be used. Based upon recent developments in sparse algorithms and high-performance computing resources, we show that direct methods are becoming feasible for large seismic tomography problems. We demonstrate the application of QR factorization in solving the regional P-wave structure and computing the full resolution matrix with 267 520 model parameters.</abstract><pub>Oxford University Press</pub><doi>10.1093/gji/ggw052</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0956-540X
ispartof Geophysical journal international, 2016-05, Vol.205 (2), p.830-836
issn 0956-540X
1365-246X
language eng
recordid cdi_crossref_primary_10_1093_gji_ggw052
source Open Access: Oxford University Press Open Journals
title Towards using direct methods in seismic tomography: computation of the full resolution matrix using high-performance computing and sparse QR factorization
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-02T17%3A17%3A35IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-oup_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Towards%20using%20direct%20methods%20in%20seismic%20tomography:%20computation%20of%20the%20full%20resolution%20matrix%20using%20high-performance%20computing%20and%20sparse%20QR%20factorization&rft.jtitle=Geophysical%20journal%20international&rft.au=Bogiatzis,%20Petros&rft.date=2016-05-01&rft.volume=205&rft.issue=2&rft.spage=830&rft.epage=836&rft.pages=830-836&rft.issn=0956-540X&rft.eissn=1365-246X&rft_id=info:doi/10.1093/gji/ggw052&rft_dat=%3Coup_cross%3E10.1093/gji/ggw052%3C/oup_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a320t-c170056a5a1b2d8e530cb0d546e59266e5327f1c45459349a63d0718e39c95f23%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_oup_id=10.1093/gji/ggw052&rfr_iscdi=true