Wavefronts and raypaths

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	1
DOI	http://dx.doi.org/10.1190/1.9781560801610
ISBN	9781560801481
Store	SEG Online Store

A homogeneous medium is a material with properties independent of position. An isotropic medium is a material with properties independent of direction of travel. An anisotropic medium is a material in which a physical property (such as velocity) depends on the direction. A homogeneous and isotropic medium is a material with properties independent of both position and direction of travel. The simplest type of wave propagation can be illustrated by a disturbance originating at a point in a homogeneous and isotropic medium. In particular, the velocity is constant and independent of direction everywhere in the medium. In Figure 2, S is the location of the point source of the disturbance. The source itself could be a shot of dynamite, for instance. The wave proceeds outward in all directions from the source, and its successive positions will assume the form of expanding concentric spheres with S as center. The successive positions of the wave after equal intervals of elapsed time will be equally spaced spheres - spheres whose radii differ by equal increments. In Figure 2, the fifth wavefront, which represents the locus of the disturbance after five time intervals of equal length, is the spherical arc ABC. If the total elapsed time is t and the velocity is v, then the radius SB is equal to vt.

For our present purpose, we define the leading-edge wavefront as the most forward position of the advancing region of the disturbance at any particular instant in time. Behind the leading-edge wavefront, the medium has been disturbed. Ahead of the leading-edge wavefront, the medium is undisturbed. This is the physical effect of the original disturbance as it propagates from its source point.

Figure 2.  Illustration of spherical wavefronts and radial raypaths from a point source in a uniform medium.

In Figure 2, the radii SA, SB, and SC are three of the raypaths associated with the spherical wavefronts. They can be given physical significance by thinking of them as the paths over which the energy of the disturbance travels from the source S to any wavefront or from any wavefront to a later one. It is evident in this simple case that the raypaths are everywhere at right angles to the wavefronts. This geometry (that is, the orthogonality of raypaths and wavefronts) is true for any isotropic medium whether the medium is homogeneous or not.

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Table of Contents (book)

Also in this chapter

• Introduction
• d’Alembert’s solution
• One-dimensional waves
• Sinusoidal waves
• Phase velocity
• Wave pulses
• Geometric seismology
• The speed of light
• Huygens’ principle
• Reflection and refraction
• Ray theory
• Fermat’s principle
• Fermat’s principle and reflection and refraction
• Diffraction
• Analogy
• Appendix A: Exercise

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