Wavefronts, rays, and Huygens

Every piece of acquisition physics rests on one picture: a point source releases energy that travels outward as an expanding wavefront. In a uniform isotropic medium, the wavefront is a sphere (a circle in 2D), and it expands at speed V.

The three equivalent views

• Wavefronts — the set of points the wave has reached at time t. These are surfaces of constant travel time (isochrons).
• Rays — arrows in the direction of energy flow. In an isotropic medium, rays are everywhere orthogonal to wavefronts. Rays are the right tool when we want to know where a given packet of energy is going.
• Huygens construction — every point on the current wavefront is itself a source of secondary spherical wavelets. The envelope of those secondary wavelets is the next wavefront. This is what lets us reason about wavefront propagation into complex media and around edges.

Why all three matter for acquisition

You will design a survey by picking offsets and azimuths that let your receivers intercept rays reflected from your target. You will verify coverage by drawing wavefronts at the target depth and checking you have illuminated enough of it. You will reason about diffractions (the edges of salt, faults, and reservoirs) using Huygens: each point along the edge behaves as a secondary source.

Three vocabularies, one physics. Get comfortable with all three.

References

• Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press.
• Aki, K., Richards, P. G. (2002). Quantitative Seismology (2nd ed.). University Science Books.
• Yilmaz, Ö. (2001). Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data (2 vols.). SEG Investigations in Geophysics 10.