Spatial and Spectral Interpolation of Ground‐Motion Intensity Measure Observations

Research Article| February 13, 2018 Spatial and Spectral Interpolation of Ground‐Motion Intensity Measure Observations C. Bruce Worden; C. Bruce Worden aU.S. Geological Survey, Denver Federal Center, PO Box 25046, MS 966, Denver, Colorado 80225, cbworden@usgs.gov Search for other works by this author on: GSW Google Scholar Eric M. Thompson; Eric M. Thompson aU.S. Geological Survey, Denver Federal Center, PO Box 25046, MS 966, Denver, Colorado 80225, cbworden@usgs.gov Search for other works by this author on: GSW Google Scholar Jack W. Baker; Jack W. Baker bDepartment of Civil and Environmental Engineering, Stanford University, Stanford, California 94305‐4020 Search for other works by this author on: GSW Google Scholar Brendon A. Bradley; Brendon A. Bradley cStanford University, Stanford, California 94305‐4020dAlso at Department of Civil and Natural Resources Engineering, University of Canterbury, Private Bag 4800, Christchurch 8041, New Zealand. Search for other works by this author on: GSW Google Scholar Nicolas Luco; Nicolas Luco aU.S. Geological Survey, Denver Federal Center, PO Box 25046, MS 966, Denver, Colorado 80225, cbworden@usgs.gov Search for other works by this author on: GSW Google Scholar David J. Wald David J. Wald aU.S. Geological Survey, Denver Federal Center, PO Box 25046, MS 966, Denver, Colorado 80225, cbworden@usgs.gov Search for other works by this author on: GSW Google Scholar Author and Article Information C. Bruce Worden aU.S. Geological Survey, Denver Federal Center, PO Box 25046, MS 966, Denver, Colorado 80225, cbworden@usgs.gov Eric M. Thompson aU.S. Geological Survey, Denver Federal Center, PO Box 25046, MS 966, Denver, Colorado 80225, cbworden@usgs.gov Jack W. Baker bDepartment of Civil and Environmental Engineering, Stanford University, Stanford, California 94305‐4020 Brendon A. Bradley cStanford University, Stanford, California 94305‐4020dAlso at Department of Civil and Natural Resources Engineering, University of Canterbury, Private Bag 4800, Christchurch 8041, New Zealand. Nicolas Luco aU.S. Geological Survey, Denver Federal Center, PO Box 25046, MS 966, Denver, Colorado 80225, cbworden@usgs.gov David J. Wald aU.S. Geological Survey, Denver Federal Center, PO Box 25046, MS 966, Denver, Colorado 80225, cbworden@usgs.gov Publisher: Seismological Society of America First Online: 13 Feb 2018 Online Issn: 1943-3573 Print Issn: 0037-1106 © Seismological Society of America Bulletin of the Seismological Society of America (2018) 108 (2): 866–875. https://doi.org/10.1785/0120170201 Article history First Online: 13 Feb 2018 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation C. Bruce Worden, Eric M. Thompson, Jack W. Baker, Brendon A. Bradley, Nicolas Luco, David J. Wald; Spatial and Spectral Interpolation of Ground‐Motion Intensity Measure Observations. Bulletin of the Seismological Society of America 2018;; 108 (2): 866–875. doi: https://doi.org/10.1785/0120170201 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyBulletin of the Seismological Society of America Search Advanced Search Abstract Following a significant earthquake, ground‐motion observations are available for a limited set of locations and intensity measures (IMs). Typically, however, it is desirable to know the ground motions for additional IMs and at locations where observations are unavailable. Various interpolation methods are available, but because IMs or their logarithms are normally distributed, spatially correlated, and correlated with each other at a given location, it is possible to apply the conditional multivariate normal (MVN) distribution to the problem of estimating unobserved IMs. In this article, we review the MVN and its application to general estimation problems, and then apply the MVN to the specific problem of ground‐motion IM interpolation. In particular, we present (1) a formulation of the MVN for the simultaneous interpolation of IMs across space and IM type (most commonly, spectral response at different oscillator periods) and (2) the inclusion of uncertain observation data in the MVN formulation. These techniques, in combination with modern empirical ground‐motion models and correlation functions, provide a flexible framework for estimating a variety of IMs at arbitrary locations. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.