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The Dehoop‐Knopoff representation theorem as a linear inverse problem
Author(s) -
Spudich P. K. P.
Publication year - 1980
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/gl007i009p00717
Subject(s) - geodetic datum , discontinuity (linguistics) , seismogram , inversion (geology) , inverse problem , representation (politics) , inverse , displacement (psychology) , geology , seismology , mathematics , geodesy , mathematical analysis , geometry , politics , political science , law , psychology , psychotherapist , tectonics
The deHoop‐Knopoff representation theorem, which relates observed seismic waves to a displacement discontinuity s defined on a surface S, is posed so that seismograms may be directly inverted for estimates of s and of the spatial and temporal resolution of s . Solutions s can be constructed either by parametrizing the fault surface as a number of point double couples or by representing s as an expansion of orthogonal functions. Of the infinite number of possible solutions satisfying a single seismic‐data set, methods for constructing particular solutions (e.g., best fitting, or closest to a desired solution) are given. Application of inverse theory to the deHoop‐Knopoff representation theorem leads to a convenient way to include various types of seismic data—e.g., long‐ and short‐period teleseismic, near field accelerogram, and geodetic—into a single inversion.