Variation of reflection point with offset

From SEG Wiki
Jump to navigation Jump to search

Problem 4.11a

Equation (4.3a) for an offset geophone can be written


where is the offset and is the slant depth at the midpoint between the source and receiver (see Figure 4.11a). The point of reflection is displaced updip the distance from the zero-dip position . Show that the coordinates of a point on the line must satisfy the relation


where is the image point, are the direction cosines of , is the slant depth at the source, and is a parameter fixing the location of a point on .


Referring to Figure 4.11a, are the direction cosines of where

To get the coordinates of , a point on , we draw and perpendicular to . Then, using the similar triangles and , we have , that is,


being the horizontal distance from . If we write

Figure 4.11a.  Displacement of reflection point for offset geophone.

we can vary to get different points on .

Problem 4.11b

Verify the following relations:




To get , the point of intersection of and , we first find the equation of ; the line has slope and passes through , so the equation is


We now solve equations (4.11c) and (4.11f) as simultaneous equations. Eliminating gives

Using the equations ,  ; this reduces to



From equation (4.11f) we get

Since ,

We now have

Continue reading

Previous section Next section
Cross-dip Functional fits for velocity-depth data
Previous chapter Next chapter
Partitioning at an interface Seismic velocity

Table of Contents (book)

Also in this chapter

External links

find literature about
Variation of reflection point with offset
SEG button search.png Datapages button.png GeoScienceWorld button.png OnePetro button.png Schlumberger button.png Google button.png AGI button.png