Traveltime sensitivity kernels for wave equation tomography using the unwrapped phase

Handle URI:
http://hdl.handle.net/10754/554371
Title:
Traveltime sensitivity kernels for wave equation tomography using the unwrapped phase
Authors:
Djebbi, Ramzi ( 0000-0003-0415-0092 ) ; Alkhalifah, Tariq Ali ( 0000-0002-9363-9799 )
Abstract:
Wave equation tomography attempts to improve on traveltime tomography, by better adhering to the requirements of our finite-frequency data. Conventional wave equation tomography, based on the first-order Born approximation followed by cross-correlation traveltime lag measurement, or on the Rytov approximation for the phase, yields the popular hollow banana sensitivity kernel indicating that the measured traveltime at a point is insensitive to perturbations along the ray theoretical path at certain finite frequencies. Using the instantaneous traveltime, which is able to unwrap the phase of the signal, instead of the cross-correlation lag, we derive new finite-frequency traveltime sensitivity kernels. The kernel reflects more the model-data dependency, we typically encounter in full waveform inversion. This result confirms that the hollow banana shape is borne of the cross-correlation lag measurement, which exposes the Born approximations weakness in representing transmitted waves. The instantaneous traveltime can thus mitigate the additional component of nonlinearity introduced by the hollow banana sensitivity kernels in finite-frequency traveltime tomography. The instantaneous traveltime simply represents the unwrapped phase of Rytov approximation, and thus is a good alternative to Born and Rytov to compute the misfit function for wave equation tomography. We show the limitations of the cross-correlation associated with Born approximation for traveltime lag measurement when the source signatures of the measured and modelled data are different. The instantaneous traveltime is proven to be less sensitive to the distortions in the data signature. The unwrapped phase full banana shape of the sensitivity kernels shows smoother update compared to the banana–doughnut kernels. The measurement of the traveltime delay caused by a small spherical anomaly, embedded into a 3-D homogeneous model, supports the full banana sensitivity assertion for the unwrapped phase.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Citation:
Traveltime sensitivity kernels for wave equation tomography using the unwrapped phase 2014, 197 (2):975 Geophysical Journal International
Publisher:
Oxford University Press (OUP)
Journal:
Geophysical Journal International
Issue Date:
18-Feb-2014
DOI:
10.1093/gji/ggu025
Type:
Article
ISSN:
0956-540X; 1365-246X
Additional Links:
http://gji.oxfordjournals.org/cgi/doi/10.1093/gji/ggu025
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorDjebbi, Ramzien
dc.contributor.authorAlkhalifah, Tariq Alien
dc.date.accessioned2015-05-21T07:00:44Zen
dc.date.available2015-05-21T07:00:44Zen
dc.date.issued2014-02-18en
dc.identifier.citationTraveltime sensitivity kernels for wave equation tomography using the unwrapped phase 2014, 197 (2):975 Geophysical Journal Internationalen
dc.identifier.issn0956-540Xen
dc.identifier.issn1365-246Xen
dc.identifier.doi10.1093/gji/ggu025en
dc.identifier.urihttp://hdl.handle.net/10754/554371en
dc.description.abstractWave equation tomography attempts to improve on traveltime tomography, by better adhering to the requirements of our finite-frequency data. Conventional wave equation tomography, based on the first-order Born approximation followed by cross-correlation traveltime lag measurement, or on the Rytov approximation for the phase, yields the popular hollow banana sensitivity kernel indicating that the measured traveltime at a point is insensitive to perturbations along the ray theoretical path at certain finite frequencies. Using the instantaneous traveltime, which is able to unwrap the phase of the signal, instead of the cross-correlation lag, we derive new finite-frequency traveltime sensitivity kernels. The kernel reflects more the model-data dependency, we typically encounter in full waveform inversion. This result confirms that the hollow banana shape is borne of the cross-correlation lag measurement, which exposes the Born approximations weakness in representing transmitted waves. The instantaneous traveltime can thus mitigate the additional component of nonlinearity introduced by the hollow banana sensitivity kernels in finite-frequency traveltime tomography. The instantaneous traveltime simply represents the unwrapped phase of Rytov approximation, and thus is a good alternative to Born and Rytov to compute the misfit function for wave equation tomography. We show the limitations of the cross-correlation associated with Born approximation for traveltime lag measurement when the source signatures of the measured and modelled data are different. The instantaneous traveltime is proven to be less sensitive to the distortions in the data signature. The unwrapped phase full banana shape of the sensitivity kernels shows smoother update compared to the banana–doughnut kernels. The measurement of the traveltime delay caused by a small spherical anomaly, embedded into a 3-D homogeneous model, supports the full banana sensitivity assertion for the unwrapped phase.en
dc.publisherOxford University Press (OUP)en
dc.relation.urlhttp://gji.oxfordjournals.org/cgi/doi/10.1093/gji/ggu025en
dc.rightsArchived with thanks to Geophysical Journal International © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Societyen
dc.subjectInverse theoryen
dc.subjectSeismic tomographyen
dc.subjectWave propagationen
dc.titleTraveltime sensitivity kernels for wave equation tomography using the unwrapped phaseen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalGeophysical Journal Internationalen
dc.eprint.versionPublisher's Version/PDFen
kaust.authorAlkhalifah, Tariq Alien
kaust.authorDjebbi, Ramzien
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