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Reflection points and surface points 1
Author(s) -
Levin Franklyn K.
Publication year - 1995
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1995.tb00283.x
Subject(s) - ellipse , midpoint , reflection (computer programming) , optics , perpendicular , geometry , surface (topology) , azimuth , plane (geometry) , reflector (photography) , physics , geology , mathematics , computer science , light source , programming language
A simple expression ties the midpoint of a surface spread to reflection points on a dipping plane. If we use two coordinate systems, an unprimed one with a z‐axis perpendicular to the surface and a primed one with a z‐axis perpendicular to the reflector, we havewhere θ is the dip angle, φ is the profile angle, X is the source‐to‐receiver separation, and D is the depth of the reflector. The reflection point is ( x , y p , D ) and the surface midpoint is ( x c , y c , 0). Using the expression, I show that if complete azimuthal coverage is required at a CMP position, the reflection points lie on an ellipse. Similarly, a fixed reflection point generates a circle of surface midpoints. A circle of CMP positions for fixed θ and φ becomes an ellipse of reflection points and a circle of reflection points becomes an ellipse of midpoints. A user can easily find the shape and location of the reflection area generated by a surface aperture.