Two-point paraxial traveltime formula for inhomogeneous isotropic and anisotropic media: Tests of accuracy

Handle URI:
http://hdl.handle.net/10754/562955
Title:
Two-point paraxial traveltime formula for inhomogeneous isotropic and anisotropic media: Tests of accuracy
Authors:
Waheed, Umair bin ( 0000-0002-5189-0694 ) ; Psencik, Ivan; Cerveny, Vlastislav; Iversen, Einar; Alkhalifah, Tariq Ali ( 0000-0002-9363-9799 )
Abstract:
On several simple models of isotropic and anisotropic media, we have studied the accuracy of the two-point paraxial traveltime formula designed for the approximate calculation of the traveltime between points S' and R' located in the vicinity of points S and R on a reference ray. The reference ray may be situated in a 3D inhomogeneous isotropic or anisotropic medium with or without smooth curved interfaces. The twopoint paraxial traveltime formula has the form of the Taylor expansion of the two-point traveltime with respect to spatial Cartesian coordinates up to quadratic terms at points S and R on the reference ray. The constant term and the coefficients of the linear and quadratic terms are determined from quantities obtained from ray tracing and linear dynamic ray tracing along the reference ray. The use of linear dynamic ray tracing allows the evaluation of the quadratic terms in arbitrarily inhomogeneous media and, as shown by examples, it extends the region of accurate results around the reference ray between S and R (and even outside this interval) obtained with the linear terms only. Although the formula may be used for very general 3D models, we concentrated on simple 2D models of smoothly inhomogeneous isotropic and anisotropic (~8% and ~20% anisotropy) media only. On tests, in which we estimated twopoint traveltimes between a shifted source and a system of shifted receivers, we found that the formula may yield more accurate results than the numerical solution of an eikonal-based differential equation. The tests also indicated that the accuracy of the formula depends primarily on the length and the curvature of the reference ray and only weakly depends on anisotropy. The greater is the curvature of the reference ray, the narrower its vicinity, in which the formula yields accurate results.
KAUST Department:
Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program; Environmental Science and Engineering Program
Publisher:
Society of Exploration Geophysicists
Journal:
Geophysics
Issue Date:
Sep-2013
DOI:
10.1190/GEO2012-0406.1
Type:
Article
ISSN:
00168033
Sponsors:
We would like to express our gratitude to Joachim Mispel, three anonymous referees and the associate editor, Claudia Vanelle, for their stimulating comments. We are grateful to Seismic Wave Analysis Group (SWAG) of KAUST, Saudi Arabia, project "Seismic waves in complex 3-D structures" (SW3D), to Research Projects 210/11/0117 and 210/10/0736 of the Grant Agency of the Czech Republic and to Research Project MSM0021620860 of the Ministry of Education of the Czech Republic for support. E. Iversen acknowledges support from the Research Council of Norway and from the European Community's FP7 Consortium Project AIM "Advanced Industrial Microseismic Monitoring," Grant Agreement no. 230669.
Appears in Collections:
Articles; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorWaheed, Umair binen
dc.contributor.authorPsencik, Ivanen
dc.contributor.authorCerveny, Vlastislaven
dc.contributor.authorIversen, Einaren
dc.contributor.authorAlkhalifah, Tariq Alien
dc.date.accessioned2015-08-03T11:16:54Zen
dc.date.available2015-08-03T11:16:54Zen
dc.date.issued2013-09en
dc.identifier.issn00168033en
dc.identifier.doi10.1190/GEO2012-0406.1en
dc.identifier.urihttp://hdl.handle.net/10754/562955en
dc.description.abstractOn several simple models of isotropic and anisotropic media, we have studied the accuracy of the two-point paraxial traveltime formula designed for the approximate calculation of the traveltime between points S' and R' located in the vicinity of points S and R on a reference ray. The reference ray may be situated in a 3D inhomogeneous isotropic or anisotropic medium with or without smooth curved interfaces. The twopoint paraxial traveltime formula has the form of the Taylor expansion of the two-point traveltime with respect to spatial Cartesian coordinates up to quadratic terms at points S and R on the reference ray. The constant term and the coefficients of the linear and quadratic terms are determined from quantities obtained from ray tracing and linear dynamic ray tracing along the reference ray. The use of linear dynamic ray tracing allows the evaluation of the quadratic terms in arbitrarily inhomogeneous media and, as shown by examples, it extends the region of accurate results around the reference ray between S and R (and even outside this interval) obtained with the linear terms only. Although the formula may be used for very general 3D models, we concentrated on simple 2D models of smoothly inhomogeneous isotropic and anisotropic (~8% and ~20% anisotropy) media only. On tests, in which we estimated twopoint traveltimes between a shifted source and a system of shifted receivers, we found that the formula may yield more accurate results than the numerical solution of an eikonal-based differential equation. The tests also indicated that the accuracy of the formula depends primarily on the length and the curvature of the reference ray and only weakly depends on anisotropy. The greater is the curvature of the reference ray, the narrower its vicinity, in which the formula yields accurate results.en
dc.description.sponsorshipWe would like to express our gratitude to Joachim Mispel, three anonymous referees and the associate editor, Claudia Vanelle, for their stimulating comments. We are grateful to Seismic Wave Analysis Group (SWAG) of KAUST, Saudi Arabia, project "Seismic waves in complex 3-D structures" (SW3D), to Research Projects 210/11/0117 and 210/10/0736 of the Grant Agency of the Czech Republic and to Research Project MSM0021620860 of the Ministry of Education of the Czech Republic for support. E. Iversen acknowledges support from the Research Council of Norway and from the European Community's FP7 Consortium Project AIM "Advanced Industrial Microseismic Monitoring," Grant Agreement no. 230669.en
dc.publisherSociety of Exploration Geophysicistsen
dc.titleTwo-point paraxial traveltime formula for inhomogeneous isotropic and anisotropic media: Tests of accuracyen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEarth Science and Engineering Programen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.identifier.journalGeophysicsen
dc.contributor.institutionAcademy of Sciences of the Czech Republic, Institute of Geophysics, Praha, Czech Republicen
dc.contributor.institutionCharles University, Faculty of Mathematics and Physics, Department of Geophysics, Praha, Czech Republicen
kaust.authorWaheed, Umair binen
kaust.authorAlkhalifah, Tariq Alien
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.