Traveltime
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| 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 $ 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.
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| The unit tangent vector | The gradient |
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| 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
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