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A geometrical approach to seismic processing:
the method of discontinuities
Sergey Goldin
Author has no known email address
Introduction
1: WHAT IS A DISCONTINUITY?
Functions with discontinuities
Fourier transformations
Equivalence of the order r
2: THE STANDARD DISCONTINUITIES (OF INTEGER ORDER)
Definition
The simplest properties
Examples
The operators
and
Hilbert transformation
Fourier-transformation
Convolution
Discontinuities and high-frequency band filters
3: WHY DISCONTINUITIES?
Characteristics
Characteristics and discontinuities
Eikonal equation
Elastic medium
4: CONNECTION WITH RAY METHOD
Ray method
Zero-approximation.
Fundamental solutions
6: WHY SO MANY ALGORITHMS FOR MIGRATION ?
The method of time fields (Common Source Pattern)
Zero-offset case
Migration
7: GEOMETRICAL PROBLEMS OF WAVE-FIELD CONTINUATION
Interference analysis
Untying loops
Geometrical analysis of imaging
A. Homogenous layer with a planar reflector
B. Two-layer media
C. 15-degree algorithm in one-layer model
D. CSP-depth migration in one-layer medium
8: CLASSIFICATION OF K-OPERATORS
Differential K-operators
One-way propagation (PDKO)
9: INTEGRAL OPERATORS OF WAVE-FIELD CONTINUATIONS
Formulas for amplitudes (3D case)
2D case
Amplitude equivalence
Very simple but important property
10: EXTREMAL VELOCITIES
11: TRUE AMPLITUDE MIGRATION
CSP migration, 3D case
Zero-offset migration
12: OPERATOR OF INTEGRAL GEOMETRY (IGO)
Geometry of the main discontinuity
Dynamics of the main discontinuity
Application to tomography
15: COMPARISON OF PRE- AND POST-STACK MIGRATION
Criteria for comparison:
Prestack migration
Post-stack migration
References
About this document ...
Stanford Exploration Project
1/13/1998
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