{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T03:27:14Z","timestamp":1767929234363,"version":"3.49.0"},"reference-count":23,"publisher":"Society of Exploration Geophysicists","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The computational tools for imaging in transversely isotropic media with tilted axes of symmetry (TTI) are complex and in most cases do not have an explicit closed-form representation. Developing such tools for a TTI medium with tilt constrained to be normal to the reflector dip (DTI) reduces their complexity and allows for closed-form representations. The homogeneous-case zero-offset migration in such a medium can be performed using an isotropic operator scaled by the velocity of the medium in the tilt direction. For the nonzero-offset case, the reflection angle is always equal to the incidence angle, and thus, the velocities for the source and receiver waves at the reflection point are equal and explicitly dependent on the reflection angle. This fact allows for the development of explicit representations for angle decomposition as well as moveout formulas for analysis of extended images obtained by wave-equation migration. Although setting the tilt normal to the reflector dip may not be valid everywhere (i.e., on salt flanks), it can be used in the process of velocity model building, in which such constrains are useful and typically are used.<\/jats:p>","DOI":"10.1190\/1.3409114","type":"journal-article","created":{"date-parts":[[2010,6,17]],"date-time":"2010-06-17T18:28:20Z","timestamp":1276799300000},"page":"A19-A24","source":"Crossref","is-referenced-by-count":28,"title":["A transversely isotropic medium with a tilted symmetry axis normal to the reflector"],"prefix":"10.1190","volume":"75","author":[{"given":"Tariq","family":"Alkhalifah","sequence":"first","affiliation":[{"name":"1King Abdulah University of Science and Technology, Thuwal, Saudi Arabia. E-mail: tkhalfah@kacst.edu.sa."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul","family":"Sava","sequence":"additional","affiliation":[{"name":"2Colorado School of Mines, Center for Wave Phenomena, Golden, Colorado, U.S.A. E-mail: E-mail: psava@mines.edu."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"186","published-online":{"date-parts":[[2010,5,26]]},"reference":[{"key":"2025121113260305700_R1","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1190\/1.1444175","article-title":"Seismic data processing in vertically inhomogeneous TI media","volume":"62","author":"Alkhalifah","year":"1997","journal-title":"Geophysics"},{"key":"2025121113260305700_R2","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1190\/1.1444361","article-title":"Acoustic approximations for processing in transversely isotropic media","volume":"63","author":"Alkhalifah","year":"1998","journal-title":"Geophysics"},{"key":"2025121113260305700_R3","first-page":"965","article-title":"Building a 3-D anisotropic model: Its implications to traveltime calculation and velocity analysis","volume-title":"70th Annual International Meeting","author":"Alkhalifah","year":"2000"},{"key":"2025121113260305700_R4","first-page":"2899","article-title":"Angle gathers in wave-equation imaging for VTI media","volume-title":"79th Annual International Meeting","author":"Alkhalifah","year":"2009"},{"key":"2025121113260305700_R5","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1190\/1.1443698","article-title":"Migration error in transversely isotropic media","volume":"59","author":"Alkhalifah","year":"1994","journal-title":"Geophysics"},{"key":"2025121113260305700_R6","doi-asserted-by":"crossref","first-page":"1550","DOI":"10.1190\/1.1443888","article-title":"Velocity analysis for transversely isotropic media","volume":"60","author":"Alkhalifah","year":"1995","journal-title":"Geophysics"},{"key":"2025121113260305700_R7","first-page":"P185","article-title":"TTI anisotropic depth migration: Which tilt estimate should we use?","volume-title":"68th Conference and Exhibition","author":"Audebert","year":"2006"},{"key":"2025121113260305700_R8","doi-asserted-by":"crossref","first-page":"1495","DOI":"10.1190\/1.1443883","article-title":"Estimation of anisotropy and anisotropic 3-D prestack depth migration, offshore Zaire","volume":"60","author":"Ball","year":"1995","journal-title":"Geophysics"},{"key":"2025121113260305700_R9","doi-asserted-by":"crossref","DOI":"10.1115\/1.3162563","article-title":"Seismic migration: Imaging of acoustic energy by wave field extrapolation","author":"Berkhout","year":"1982"},{"key":"2025121113260305700_R10","article-title":"Imaging the earth's interior","author":"Claerbout","year":"1985"},{"key":"2025121113260305700_R11","article-title":"Basic earth imaging","author":"Claerbout","year":"1995"},{"key":"2025121113260305700_R12","doi-asserted-by":"crossref","first-page":"1559","DOI":"10.1190\/1.1441162","article-title":"A Born-WKBJ inversion method for acoustic reflection data","volume":"46","author":"Clayton","year":"1981","journal-title":"Geophysics"},{"key":"2025121113260305700_R13","author":"Goldin","year":"1986"},{"key":"2025121113260305700_R14","first-page":"222","article-title":"The benefit of TTI tomography for dual azimuth data in Gulf of Mexico","volume-title":"78th Annual International Meeting","author":"Huang","year":"2008"},{"key":"2025121113260305700_R15","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1190\/1.1759454","article-title":"A practical method for estimating effective parameters of anisotropy from reflection seismic data","volume":"69","author":"Isaac","year":"2004","journal-title":"Geophysics"},{"key":"2025121113260305700_R16","first-page":"149","article-title":"A strategy for anisotropic P-wave prestack imaging","volume-title":"71st Annual International Meeting","author":"Martinez","year":"2002"},{"key":"2025121113260305700_R17","first-page":"1600","article-title":"Elliptical anisotropy: Regression or advance?","volume-title":"68th Annual International Meeting","author":"Ohlsen","year":"1999"},{"key":"2025121113260305700_R18","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1190\/1.1484531","article-title":"Offset and angle-domain common image-point gathers for shot-profile migration","volume":"67","author":"Rickett","year":"2002","journal-title":"Geophysics"},{"key":"2025121113260305700_R19","first-page":"2052","article-title":"Coordinate-independent angle-gathers for wave equation migration","volume-title":"75th Annual International Meeting","author":"Sava","year":"2005"},{"issue":"6","key":"2025121113260305700_R20","doi-asserted-by":"crossref","first-page":"S209","DOI":"10.1190\/1.2338824","article-title":"Time-shift imaging condition in seismic migration","volume":"71","author":"Sava","year":"2006","journal-title":"Geophysics"},{"key":"2025121113260305700_R21","doi-asserted-by":"crossref","first-page":"2458","DOI":"10.1190\/1.1441877","article-title":"Migration and inversion of seismic data","volume":"50","author":"Stolt","year":"1985","journal-title":"Geophysics"},{"key":"2025121113260305700_R22","doi-asserted-by":"crossref","first-page":"950","DOI":"10.1190\/1.1438416","article-title":"Migration-inversion revisited (1999)","volume":"18","author":"Weglein","year":"1999","journal-title":"The Leading Edge"},{"key":"2025121113260305700_R23","first-page":"2347","article-title":"Tomographic velocity analysis in strongly anisotropic TTI media","volume-title":"73rd Annual International Meeting","author":"Zhou","year":"2004"}],"container-title":["Geophysics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.geoscienceworld.org\/seg\/geophysics\/article-pdf\/75\/3\/A19\/3133893\/gsgpy_75_3_A19.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.geoscienceworld.org\/seg\/geophysics\/article-pdf\/75\/3\/A19\/3133893\/gsgpy_75_3_A19.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T18:26:12Z","timestamp":1765477572000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.geoscienceworld.org\/geophysics\/article\/75\/3\/A19\/261304\/A-transversely-isotropic-medium-with-a-tilted"},"secondary":[{"URL":"http:\/\/geophysics.geoscienceworld.org\/cgi\/doi\/10.1190\/1.3409114","label":"geoscienceworld"}]},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1,1]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,1,1]]}},"URL":"https:\/\/doi.org\/10.1190\/1.3409114","relation":{},"ISSN":["1942-2156","0016-8033"],"issn-type":[{"value":"1942-2156","type":"electronic"},{"value":"0016-8033","type":"print"}],"subject":[],"published-other":{"date-parts":[[2010]]},"published":{"date-parts":[[2010,1,1]]}}}