publication . Article . 2016

Graph theory for analyzing pair-wise data: application to geophysical model parameters estimated from interferometric synthetic aperture radar data at Okmok volcano, Alaska

Reinisch, Elena C.; Cardiff, Michael; Feigl, Kurt L.;
Open Access English
  • Published: 01 Jul 2016 Journal: Journal of Geodesy, volume 91, issue 1, pages 9-24 (issn: 0949-7714, Copyright policy)
  • Publisher: Springer Nature
Abstract
Graph theory is useful for analyzing time-dependent model parameters estimated from interferometric synthetic aperture radar (InSAR) data in the temporal domain. Plotting acquisition dates (epochs) as vertices and pair-wise interferometric combinations as edges defines an incidence graph. The edge-vertex incidence matrix and the normalized edge Laplacian matrix are factors in the covariance matrix for the pair-wise data. Using empirical measures of residual scatter in the pair-wise observations, we estimate the relative variance at each epoch by inverting the covariance of the pair-wise data. We evaluate the rank deficiency of the corresponding least-squares pro...
Subjects
free text keywords: Computers in Earth Sciences, Geochemistry and Petrology, Geophysics, Original Article, Remote sensing of volcanoes, Numerical solutions, Transient deformation, Inverse theory, Covariance matrix, Vertex (geometry), Graph theory, Statistics, Covariance, Geodesy, Mathematics, Laplacian matrix, Incidence matrix, Residual, Interferometric synthetic aperture radar
Related Organizations
Funded by
NSF| Collaborative Research: Improving the Generic Mapping Tools for Seismology, Geodesy, Geodynamics and Geology
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1347190
  • Funding stream: Directorate for Geosciences | Division of Earth Sciences
,
NSF| Graduate Reserach Fellowship Program (GRFP)
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1256259
  • Funding stream: Directorate for Education & Human Resources | Division of Graduate Education
,
NSF| COLLABORATIVE RESEARCH: Geodetic measurements and mechanical models of the volcano deformation cycle
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 0943965
  • Funding stream: Directorate for Geosciences | Division of Earth Sciences
49 references, page 1 of 4

Agram PS, Simons M (2015) A noise model for InSAR time series. J Geophys Res Solid Earth. doi:10.1002/2014JB011271

Aster, RC, Borchers, B, Thurber, CH. Parameter estimation and inverse problems. 2013: 360

Beauducel, F, Briole, P, Froger, J-L. Volcano-wide fringes in ERS synthetic aperture radar interferograms of Etna (1992–1998): deformation or tropospheric effect?. J Geophys Res Solid Earth. 2000; 105 (B7): 16391-16402 [OpenAIRE] [DOI]

Berardino, P, Fornaro, G, Lanari, R, Sansosti, E. A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms. IEEE Trans Geosci Remote Sens. 2002; 40 (11): 2375-2383 [OpenAIRE] [DOI]

Biggs, J, Wright, T, Lu, Z, Parsons, B. Multi-interferogram method for measuring interseismic deformation: Denali Fault, Alaska. Geophys J Int. 2007; 170 (3): 1165-1179 [DOI]

Biggs J, Lu Z, Fournier T, Freymueller JT (2010) Magma flux at Okmok volcano, Alaska, from a joint inversion of continuous GPS, campaign GPS, and interferometric synthetic aperture radar. J Geophys Res Solid Earth 115(B12). doi:10.1029/2010JB007577

Byrd, HR, Gilbert, CJ, Nocedal, J. A trust region method based on interior point techniques for nonlinear programming. Math Program. 2000; 89 (1): 149-185 [DOI]

Casu, F, Manzo, M, Pepe, A, Lanari, R. SBAS-DInSAR analysis of very extended areas: first results on a 60,000-km\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^2$$\end{document}2 test site. Geosci Remote Sens Lett IEEE. 2008; 5 (3): 438-442 [OpenAIRE] [DOI]

Deo, N. Graph theory with applications to engineering and computer science. 2004: 478

Emardson TR, Simons M, Webb FH (2003) Neutral atmospheric delay in interferometric synthetic aperture radar applications: statistical description and mitigation. J Geophys Res Solid Earth 108(B5). doi:10.1029/2002JB001781

Feigl, KL, Lee, WHK, Kanamoori, H, Jennings, PC. Measurement of coseismic deformation by satellite geodesy. International handbook of earthquake and engineering seismology. 2002: 607-620

Feigl, KL, Thurber, CH. A method for modelling radar interferograms without phase unwrapping: application to the M 5 Fawnskin, California earthquake of 1992 December 4. Geophys J Int. 2009; 176 (2): 491-504 [OpenAIRE] [DOI]

Feigl, KL, Sergent, A, Jacq, D. Estimation of an earthquake focal mechanism from a satellite radar interferogram: application to the December 4, 1992 Landers aftershock. Geophys Res Lett. 1995; 22 (9): 1037-1040 [OpenAIRE] [DOI]

Feigl, KL, Le Mével, H, Ali, ST, Córdova, L, Andersen, NL, DeMets, C, Singer, BS. Rapid uplift in Laguna del Maule volcanic field of the Andean Southern Volcanic zone (Chile) 2007–2012. Geophys J Int. 2014; 196 (2): 885-901 [OpenAIRE] [DOI]

Fialko, Y, Sandwell, D, Agnew, D, Simons, M, Shearer, P, Minster, B. Deformation on nearby faults induced by the 1999 Hector Mine earthquake. Science. 2002; 297 (5588): 1858-1862 [OpenAIRE] [PubMed] [DOI]

49 references, page 1 of 4
Related research
Abstract
Graph theory is useful for analyzing time-dependent model parameters estimated from interferometric synthetic aperture radar (InSAR) data in the temporal domain. Plotting acquisition dates (epochs) as vertices and pair-wise interferometric combinations as edges defines an incidence graph. The edge-vertex incidence matrix and the normalized edge Laplacian matrix are factors in the covariance matrix for the pair-wise data. Using empirical measures of residual scatter in the pair-wise observations, we estimate the relative variance at each epoch by inverting the covariance of the pair-wise data. We evaluate the rank deficiency of the corresponding least-squares pro...
Subjects
free text keywords: Computers in Earth Sciences, Geochemistry and Petrology, Geophysics, Original Article, Remote sensing of volcanoes, Numerical solutions, Transient deformation, Inverse theory, Covariance matrix, Vertex (geometry), Graph theory, Statistics, Covariance, Geodesy, Mathematics, Laplacian matrix, Incidence matrix, Residual, Interferometric synthetic aperture radar
Related Organizations
Funded by
NSF| Collaborative Research: Improving the Generic Mapping Tools for Seismology, Geodesy, Geodynamics and Geology
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1347190
  • Funding stream: Directorate for Geosciences | Division of Earth Sciences
,
NSF| Graduate Reserach Fellowship Program (GRFP)
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1256259
  • Funding stream: Directorate for Education & Human Resources | Division of Graduate Education
,
NSF| COLLABORATIVE RESEARCH: Geodetic measurements and mechanical models of the volcano deformation cycle
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 0943965
  • Funding stream: Directorate for Geosciences | Division of Earth Sciences
49 references, page 1 of 4

Agram PS, Simons M (2015) A noise model for InSAR time series. J Geophys Res Solid Earth. doi:10.1002/2014JB011271

Aster, RC, Borchers, B, Thurber, CH. Parameter estimation and inverse problems. 2013: 360

Beauducel, F, Briole, P, Froger, J-L. Volcano-wide fringes in ERS synthetic aperture radar interferograms of Etna (1992–1998): deformation or tropospheric effect?. J Geophys Res Solid Earth. 2000; 105 (B7): 16391-16402 [OpenAIRE] [DOI]

Berardino, P, Fornaro, G, Lanari, R, Sansosti, E. A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms. IEEE Trans Geosci Remote Sens. 2002; 40 (11): 2375-2383 [OpenAIRE] [DOI]

Biggs, J, Wright, T, Lu, Z, Parsons, B. Multi-interferogram method for measuring interseismic deformation: Denali Fault, Alaska. Geophys J Int. 2007; 170 (3): 1165-1179 [DOI]

Biggs J, Lu Z, Fournier T, Freymueller JT (2010) Magma flux at Okmok volcano, Alaska, from a joint inversion of continuous GPS, campaign GPS, and interferometric synthetic aperture radar. J Geophys Res Solid Earth 115(B12). doi:10.1029/2010JB007577

Byrd, HR, Gilbert, CJ, Nocedal, J. A trust region method based on interior point techniques for nonlinear programming. Math Program. 2000; 89 (1): 149-185 [DOI]

Casu, F, Manzo, M, Pepe, A, Lanari, R. SBAS-DInSAR analysis of very extended areas: first results on a 60,000-km\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^2$$\end{document}2 test site. Geosci Remote Sens Lett IEEE. 2008; 5 (3): 438-442 [OpenAIRE] [DOI]

Deo, N. Graph theory with applications to engineering and computer science. 2004: 478

Emardson TR, Simons M, Webb FH (2003) Neutral atmospheric delay in interferometric synthetic aperture radar applications: statistical description and mitigation. J Geophys Res Solid Earth 108(B5). doi:10.1029/2002JB001781

Feigl, KL, Lee, WHK, Kanamoori, H, Jennings, PC. Measurement of coseismic deformation by satellite geodesy. International handbook of earthquake and engineering seismology. 2002: 607-620

Feigl, KL, Thurber, CH. A method for modelling radar interferograms without phase unwrapping: application to the M 5 Fawnskin, California earthquake of 1992 December 4. Geophys J Int. 2009; 176 (2): 491-504 [OpenAIRE] [DOI]

Feigl, KL, Sergent, A, Jacq, D. Estimation of an earthquake focal mechanism from a satellite radar interferogram: application to the December 4, 1992 Landers aftershock. Geophys Res Lett. 1995; 22 (9): 1037-1040 [OpenAIRE] [DOI]

Feigl, KL, Le Mével, H, Ali, ST, Córdova, L, Andersen, NL, DeMets, C, Singer, BS. Rapid uplift in Laguna del Maule volcanic field of the Andean Southern Volcanic zone (Chile) 2007–2012. Geophys J Int. 2014; 196 (2): 885-901 [OpenAIRE] [DOI]

Fialko, Y, Sandwell, D, Agnew, D, Simons, M, Shearer, P, Minster, B. Deformation on nearby faults induced by the 1999 Hector Mine earthquake. Science. 2002; 297 (5588): 1858-1862 [OpenAIRE] [PubMed] [DOI]

49 references, page 1 of 4
Related research
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publication . Article . 2016

Graph theory for analyzing pair-wise data: application to geophysical model parameters estimated from interferometric synthetic aperture radar data at Okmok volcano, Alaska

Reinisch, Elena C.; Cardiff, Michael; Feigl, Kurt L.;