# Variation of reflection point with offset

Series | Geophysical References Series |
---|---|

Title | Problems in Exploration Seismology and their Solutions |

Author | Lloyd P. Geldart and Robert E. Sheriff |

Chapter | 4 |

Pages | 79 - 140 |

DOI | http://dx.doi.org/10.1190/1.9781560801733 |

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## 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 .**

### Solution

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

we can vary to get different points on .

## Problem 4.11b

Verify the following relations:

**(**)

**(**)

### Solution

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

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Cross-dip | Functional fits for velocity-depth data |

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Partitioning at an interface | Seismic velocity |

## Also in this chapter

- Accuracy of normal-moveout calculations
- Dip, cross-dip, and angle of approach
- Relationship for a dipping bed
- Reflector dip in terms of traveltimes squared
- Second approximation for dip moveout
- Calculation of reflector depths and dips
- Plotting raypaths for primary and multiple reflections
- Effect of migration on plotted reflector locations
- Resolution of cross-dip
- Cross-dip
- Variation of reflection point with offset
- Functional fits for velocity-depth data
- Relation between average and rms velocities
- Vertical depth calculations using velocity functions
- Depth and dip calculations using velocity functions
- Weathering corrections and dip/depth calculations
- Using a velocity function linear with depth
- Head waves (refractions) and effect of hidden layer
- Interpretation of sonobuoy data
- Diving waves
- Linear increase in velocity above a refractor
- Time-distance curves for various situations
- Locating the bottom of a borehole
- Two-layer refraction problem