Closed form solutions for the geometrical spreading in inhomogeneous media

Research output: Contribution to journalArticle

Abstract

True-amplitude migration is a subject of great interest to exploration geophysicists. The procedure should provide a means of computing angle-dependent reflection coefficients of reflectors within the Earth and is therefore essential in any AVO analysis. The migration weighting functions in the Kirchhoff integral include geometrical spreading factors whose determination in terms of travel-time functions and their end point derivatives are the main subject of this paper. Such "closed form" solutions for the geometrical spreading of an acoustic P-wave in an isotropic and inhomogeneous medium are presented, and their symmetry properties are used to simplify the Kirchhoff integral migration weight functions. Emphasis is put on derivation of the equations based on simple physical and mathematical requirements. The result of applying the derived forms to a synthetic example comprised of a velocity field that varies linearly with depth and dipping reflectors is also included. It is suggested that the migration weight functions could be simplified substantially for smooth velocity backgrounds.

Original languageEnglish (US)
Pages (from-to)1189-1192
Number of pages4
JournalGeophysics
Volume61
Issue number4
StatePublished - Jan 1 1996

Fingerprint

hyaluronate lyase
Travel time
acoustic wave
travel time
P-wave
symmetry
Acoustics
Earth (planet)
Derivatives
analysis

ASJC Scopus subject areas

  • Geochemistry and Petrology

Cite this

Closed form solutions for the geometrical spreading in inhomogeneous media. / Najmi, Amir.

In: Geophysics, Vol. 61, No. 4, 01.01.1996, p. 1189-1192.

Research output: Contribution to journalArticle

@article{4804e7e12f5c479984f9208b3df62a3d,
title = "Closed form solutions for the geometrical spreading in inhomogeneous media",
abstract = "True-amplitude migration is a subject of great interest to exploration geophysicists. The procedure should provide a means of computing angle-dependent reflection coefficients of reflectors within the Earth and is therefore essential in any AVO analysis. The migration weighting functions in the Kirchhoff integral include geometrical spreading factors whose determination in terms of travel-time functions and their end point derivatives are the main subject of this paper. Such {"}closed form{"} solutions for the geometrical spreading of an acoustic P-wave in an isotropic and inhomogeneous medium are presented, and their symmetry properties are used to simplify the Kirchhoff integral migration weight functions. Emphasis is put on derivation of the equations based on simple physical and mathematical requirements. The result of applying the derived forms to a synthetic example comprised of a velocity field that varies linearly with depth and dipping reflectors is also included. It is suggested that the migration weight functions could be simplified substantially for smooth velocity backgrounds.",
author = "Amir Najmi",
year = "1996",
month = "1",
day = "1",
language = "English (US)",
volume = "61",
pages = "1189--1192",
journal = "Geophysics",
issn = "0016-8033",
publisher = "Society of Exploration Geophysicists",
number = "4",

}

TY - JOUR

T1 - Closed form solutions for the geometrical spreading in inhomogeneous media

AU - Najmi, Amir

PY - 1996/1/1

Y1 - 1996/1/1

N2 - True-amplitude migration is a subject of great interest to exploration geophysicists. The procedure should provide a means of computing angle-dependent reflection coefficients of reflectors within the Earth and is therefore essential in any AVO analysis. The migration weighting functions in the Kirchhoff integral include geometrical spreading factors whose determination in terms of travel-time functions and their end point derivatives are the main subject of this paper. Such "closed form" solutions for the geometrical spreading of an acoustic P-wave in an isotropic and inhomogeneous medium are presented, and their symmetry properties are used to simplify the Kirchhoff integral migration weight functions. Emphasis is put on derivation of the equations based on simple physical and mathematical requirements. The result of applying the derived forms to a synthetic example comprised of a velocity field that varies linearly with depth and dipping reflectors is also included. It is suggested that the migration weight functions could be simplified substantially for smooth velocity backgrounds.

AB - True-amplitude migration is a subject of great interest to exploration geophysicists. The procedure should provide a means of computing angle-dependent reflection coefficients of reflectors within the Earth and is therefore essential in any AVO analysis. The migration weighting functions in the Kirchhoff integral include geometrical spreading factors whose determination in terms of travel-time functions and their end point derivatives are the main subject of this paper. Such "closed form" solutions for the geometrical spreading of an acoustic P-wave in an isotropic and inhomogeneous medium are presented, and their symmetry properties are used to simplify the Kirchhoff integral migration weight functions. Emphasis is put on derivation of the equations based on simple physical and mathematical requirements. The result of applying the derived forms to a synthetic example comprised of a velocity field that varies linearly with depth and dipping reflectors is also included. It is suggested that the migration weight functions could be simplified substantially for smooth velocity backgrounds.

UR - http://www.scopus.com/inward/record.url?scp=0030183080&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030183080&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030183080

VL - 61

SP - 1189

EP - 1192

JO - Geophysics

JF - Geophysics

SN - 0016-8033

IS - 4

ER -