Perturbation kernels for generalized seismological data functionals (GSDF)

Po Chen, Thomas H. Jordan, En-Jui Lee

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In seismic waveform analysis and inversion, data functionals can be used to quantify the misfit between observed and model-predicted (synthetic) seismograms. The generalized seismological data functionals (GSDF) of Gee & Jordan quantify waveform differences using frequency-dependent phase-delay times and amplitude-reduction times measured on time-localized arrivals and have been successfully applied to tomographic inversions at different geographic scales as well as to inversions for earthquake source parameters. The seismogram perturbation kernel is defined as the Fréchet kernel of the data functional with respect to the seismic waveform from which the data functional is derived. The data sensitivity kernel, which is the Fréchet kernel of the data functional with respect to structural model parameters, can be obtained by composing the seismogram perturbation kernel with the Born kernel through the chain rule. In this paper, we extend GSDF analysis to broad-band waveforms by removing constraints on two control parameters defined in Gee & Jordan and derive the seismogram perturbation kernels for the modified GSDF analysis. The modifications given in this paper are consistent with the original GSDF theory in Gee & Jordan around the centre frequency and improve the stability of GSDF analysis towards the edges of the passband. We also present numerical examples of perturbation kernels for the modified GSDF analysis and their data sensitivity kernels using a homogenous half-space structure model and a complex 3-D structure model.

Original languageEnglish
Pages (from-to)869-883
Number of pages15
JournalGeophysical Journal International
Volume183
Issue number2
DOIs
Publication statusPublished - 2010 Nov 1

Fingerprint

functionals
perturbation
seismograms
Model structures
Jordan
waveforms
seismogram
Waveform analysis
inversions
Time delay
Earthquakes
waveform analysis
data inversion
synthetic seismogram
sensitivity
source parameters
half space
arrival time
half spaces
arrivals

All Science Journal Classification (ASJC) codes

  • Geophysics
  • Geochemistry and Petrology

Cite this

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abstract = "In seismic waveform analysis and inversion, data functionals can be used to quantify the misfit between observed and model-predicted (synthetic) seismograms. The generalized seismological data functionals (GSDF) of Gee & Jordan quantify waveform differences using frequency-dependent phase-delay times and amplitude-reduction times measured on time-localized arrivals and have been successfully applied to tomographic inversions at different geographic scales as well as to inversions for earthquake source parameters. The seismogram perturbation kernel is defined as the Fr{\'e}chet kernel of the data functional with respect to the seismic waveform from which the data functional is derived. The data sensitivity kernel, which is the Fr{\'e}chet kernel of the data functional with respect to structural model parameters, can be obtained by composing the seismogram perturbation kernel with the Born kernel through the chain rule. In this paper, we extend GSDF analysis to broad-band waveforms by removing constraints on two control parameters defined in Gee & Jordan and derive the seismogram perturbation kernels for the modified GSDF analysis. The modifications given in this paper are consistent with the original GSDF theory in Gee & Jordan around the centre frequency and improve the stability of GSDF analysis towards the edges of the passband. We also present numerical examples of perturbation kernels for the modified GSDF analysis and their data sensitivity kernels using a homogenous half-space structure model and a complex 3-D structure model.",
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Perturbation kernels for generalized seismological data functionals (GSDF). / Chen, Po; Jordan, Thomas H.; Lee, En-Jui.

In: Geophysical Journal International, Vol. 183, No. 2, 01.11.2010, p. 869-883.

Research output: Contribution to journalArticle

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