# Difference between revisions of "Spatial sampling"

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[[Spatial aliasing]] was discussed in detail in [[the 2-D Fourier transform]] and in relation to [[migration]] in [[further aspects of migration in practice]]. The [[spatial aliasing]] problem is caused by spatial undersampling of the wavefield to be migrated — for example, the stacked section. The spatial sampling of stacked data (without [[trace interpolation]]) is defined by the recording parameters. Therefore, receiver spacing, crossline spacing, and the crossline direction in relation to dominant dip direction used in the field must be chosen carefully. | [[Spatial aliasing]] was discussed in detail in [[the 2-D Fourier transform]] and in relation to [[migration]] in [[further aspects of migration in practice]]. The [[spatial aliasing]] problem is caused by spatial undersampling of the wavefield to be migrated — for example, the stacked section. The spatial sampling of stacked data (without [[trace interpolation]]) is defined by the recording parameters. Therefore, receiver spacing, crossline spacing, and the crossline direction in relation to dominant dip direction used in the field must be chosen carefully. | ||

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+ | [[file:ch01_fig2-21.png|left|thumb|{{figure number|1.2-21}} A plane wave reflecting at normal incidence from a dipping reflector with a dip angle ''θ'' arrives at two consecutive receiver locations A and B at the surface with a separation Δ''x''. Geometry of this plane wave is used to derive equation ({{EquationNote|6}}).]] | ||

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+ | {{NumBlk|:|<math>\sin\theta = \frac{v\Delta t}{2\Delta x},</math>|{{EquationRef|6}}}} | ||

From Figure 1.2-21, note that a relationship exists between the trace spacing on a stacked section, dip, and the frequency at which [[spatial aliasing]] begins to occur. Imagine normal-incidence rays recorded at two receivers, ''A'' and ''B''. In the constant-velocity case, the angle between the surface and the wavefront is the true dip of the reflector from which these rays emerged. There is a time delay equivalent to travelpath ''CB'' between the receivers at ''A'' and ''B''. If this time delay is half the period of a given frequency component of the signal arriving at the receivers, then that frequency is at the threshold of being aliased. | From Figure 1.2-21, note that a relationship exists between the trace spacing on a stacked section, dip, and the frequency at which [[spatial aliasing]] begins to occur. Imagine normal-incidence rays recorded at two receivers, ''A'' and ''B''. In the constant-velocity case, the angle between the surface and the wavefront is the true dip of the reflector from which these rays emerged. There is a time delay equivalent to travelpath ''CB'' between the receivers at ''A'' and ''B''. If this time delay is half the period of a given frequency component of the signal arriving at the receivers, then that frequency is at the threshold of being aliased. | ||

From the relationship given by equation (1-7), note that the maximum frequency that is not aliased gets smaller at increasingly steeper dips, lower velocities, and coarser trace spacing. From this relationship, an optimum trace spacing can be derived for the inline and crossline directions based on the knowledge of a regional velocity field and subsurface dips. Typical trace spacings in the inline and crossline directions in 3-D surveys are 12.5 to 25 m, and 25 to 50 m, respectively. Even if the trace spacing in the crossline direction is as small as possible, for economic reasons, it usually is greater than that in the inline direction. Because of this, [[trace interpolation]] may be required along the crossline direction before migrating the data. | From the relationship given by equation (1-7), note that the maximum frequency that is not aliased gets smaller at increasingly steeper dips, lower velocities, and coarser trace spacing. From this relationship, an optimum trace spacing can be derived for the inline and crossline directions based on the knowledge of a regional velocity field and subsurface dips. Typical trace spacings in the inline and crossline directions in 3-D surveys are 12.5 to 25 m, and 25 to 50 m, respectively. Even if the trace spacing in the crossline direction is as small as possible, for economic reasons, it usually is greater than that in the inline direction. Because of this, [[trace interpolation]] may be required along the crossline direction before migrating the data. | ||

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==See also== | ==See also== |

## Latest revision as of 16:48, 30 September 2014

Series | Investigations in Geophysics |
---|---|

Author | Öz Yilmaz |

DOI | http://dx.doi.org/10.1190/1.9781560801580 |

ISBN | ISBN 978-1-56080-094-1 |

Store | SEG Online Store |

Spatial aliasing was discussed in detail in the 2-D Fourier transform and in relation to migration in further aspects of migration in practice. The spatial aliasing problem is caused by spatial undersampling of the wavefield to be migrated — for example, the stacked section. The spatial sampling of stacked data (without trace interpolation) is defined by the recording parameters. Therefore, receiver spacing, crossline spacing, and the crossline direction in relation to dominant dip direction used in the field must be chosen carefully.

**(**)

From Figure 1.2-21, note that a relationship exists between the trace spacing on a stacked section, dip, and the frequency at which spatial aliasing begins to occur. Imagine normal-incidence rays recorded at two receivers, *A* and *B*. In the constant-velocity case, the angle between the surface and the wavefront is the true dip of the reflector from which these rays emerged. There is a time delay equivalent to travelpath *CB* between the receivers at *A* and *B*. If this time delay is half the period of a given frequency component of the signal arriving at the receivers, then that frequency is at the threshold of being aliased.

From the relationship given by equation (1-7), note that the maximum frequency that is not aliased gets smaller at increasingly steeper dips, lower velocities, and coarser trace spacing. From this relationship, an optimum trace spacing can be derived for the inline and crossline directions based on the knowledge of a regional velocity field and subsurface dips. Typical trace spacings in the inline and crossline directions in 3-D surveys are 12.5 to 25 m, and 25 to 50 m, respectively. Even if the trace spacing in the crossline direction is as small as possible, for economic reasons, it usually is greater than that in the inline direction. Because of this, trace interpolation may be required along the crossline direction before migrating the data.

## See also

- Migration aperture
- Other considerations
- Marine acquisition geometry
- Cable feathering
- 3-D binning
- Crossline smearing
- Strike versus dip shooting
- Land acquisition geometry

## External links