Traveltime

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

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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Table of Contents (book)

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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