# Traveltime

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

Title | Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing |

Author | Enders A. Robinson and Sven Treitel |

Chapter | 2 |

DOI | http://dx.doi.org/10.1190/1.9781560801610 |

ISBN | 9781560801481 |

Store | SEG Online Store |

Now let us turn to traveltime *t*. Traveltime represents the time it takes for seismic energy emanating from the source point to reach a given point (*x*,*y*). Traveltime has magnitude but no direction, and thus traveltime can be represented by the scalar function *t*(*x*,*y*). The traveltime surface is a plot of traveltime *t* against *x*, *y*. The traveltime function can be depicted by a surface plotted against horizontal coordinate *x* and vertical (depth) coordinate *y*.

An imaginary terrain, depicted by a topographic map, can be used to visualize the traveltime configuration. Topographic maps provide information about elevation of the terrain’s surface above sea level. Elevation is represented on a topographic map by contour lines. In effect, the contour map of the terrain represents a scalar function. Each point on a contour line has the same elevation. In other words, a contour line represents a horizontal slice through the land surface. A set of contour lines tells you the shape of the land. For example, hills are represented by concentric loops, whereas stream valleys are represented by V shapes. Steep slopes have closely spaced contour lines, whereas gentle slopes have very widely spaced contour lines. The contour interval is the difference in elevation between adjacent contour lines.

A wavefront is the locus of all points with a given traveltime. The contour line **Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle t\left(x,y\right){\rm =}T}**
represents the wavefront for traveltime *T*. We get an idea of what the traveltime surface looks like from a study of the contour lines (i.e., by a study of the wavefronts). The traveltime surface rises relatively steeply where wavefronts are close to one another, and it rises relatively gently when they are far apart.

## Continue reading

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

The unit tangent vector | The gradient |

Previous chapter | Next chapter |

Wave Motion | Visualization |

## Also in this chapter

- Reflection seismology
- Digital processing
- Signal enhancement
- Migration
- Interpretation
- Rays
- The unit tangent vector
- The gradient
- The directional derivative
- The principle of least time
- The eikonal equation
- Snell’s law
- Ray equation
- Ray equation for velocity linear with depth
- Raypath for velocity linear with depth
- Traveltime for velocity linear with depth
- Point of maximum depth
- Wavefront for velocity linear with depth
- Two orthogonal sets of circles
- Migration in the case of constant velocity
- Implementation of migration
- Appendix B: Exercises