# Spatial sampling restrictions

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

Title | Problems in Exploration Seismology and their Solutions |

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

Chapter | 12 |

Pages | 469 - 484 |

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

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Contents

## Problem 12.1a

Show that the maximum spatial sampling can be written

**(**)

**where is the maximum frequency of interest, and is the maximum angle of approach.**

### Background

A wave is a function of time and space, e.g., (see problem 2.5); therefore it can be sampled in time at a fixed location (problem 9.4) or in space at a fixed time (see Sheriff and Geldart, 1995, section 8.3.10). In both cases the sampling theorem (see problem 9.4) states that the wave can be sampled at fixed intervals and be recovered exactly from the sampled data provided all frequencies are less than the Nyquist frequency , that is, less than half the sampling frequency:

**(**)

For spatial sampling, gives the number of waves per unit length and, hence, corresponds to frequency in the time domain. Therefore, for spatial sampling at intervals , the equivalent of equation (12.1b) is

**(**)

so

where , .

### Solution

The maximum sampling interval is associated with the minimum apparent wavelength. From equation (12.1c) we have

**(**)

## Problem 12.1b

Show that the maximum group spacing is

**(**)

**where the dip moveout is in milliseconds/unit distance.**

### Solution

Assuming , we replace in equation (12.1d) with [see equation (4.2b)]:

where time difference in milliseconds between two geophones separated by a distance .

## Continue reading

Previous section | Next section |
---|---|

Interpreting marine refraction data | Bin size in marine work |

Previous chapter | Next chapter |

Geologic interpretation of reflection data | Specialized techniques |

## Also in this chapter

- Spatial sampling restrictions
- Bin size in marine work
- Effect of crosscurrents
- Number of seismic sources
- Circle shooting
- Ocean-bottom cable surveys
- Vibroseis land survey
- Loop layout for a 3D survey
- Fault interpretation using time slices
- Acquisition direction for marine 3D surveys