Waves: amplitude, frequency, wavelength
Learning objectives
- Build physical intuition for what a wave is and what moves when a wave moves
- Distinguish amplitude, frequency, period, and wavelength
- Compute wavelength from velocity and frequency (the key relation v = f·λ)
- Recognize why the Ricker wavelet — not a pure sine — represents real seismic
Every seismic image you will ever interpret is built out of waves. Before we talk about rocks, boundaries, or cubes, we need a clear mental picture of what a wave actually is.
What is a wave?
A wave is a disturbance that propagates through a medium while the medium itself stays roughly in place. When you clap your hands, you do not throw air at the listener — you briefly compress the air near your hands, that compression pushes the next bit of air, and the push travels outward at the speed of sound. The air molecules wobble a little and return to where they were. The disturbance moves across the room; the air does not.
A seismic wave is the same idea, in rock. A controlled source (a small explosion, a vibrator truck, or an air gun) briefly compresses the ground. That compression races outward through the earth at the rock's sound speed, typically 1500–6000 m/s depending on the rock. The rock particles wobble a tiny amount. What we record at the surface is the later arrival of those compressions after they bounce off subsurface boundaries.
The kind of wave that dominates reflection seismology is the P-wave (or compressional wave). The particle motion is along the direction of travel — back and forth like an accordion. P-waves travel fastest through rock, arrive first, and carry the energy we use to image the subsurface. Later in Part 5 we will meet S-waves (shear waves), which move perpendicular to travel and tell us different things. For now, picture P-waves only.
Four numbers describe any simple wave
- Amplitude — how big the disturbance is. Louder sound, stronger reflection, bigger number on your seismic trace. Units depend on what you are measuring (pressure, particle velocity, etc.).
- Frequency (f) — how many oscillations per second, in hertz (Hz). A 30 Hz wave completes 30 cycles every second.
- Period (T) — the time for one oscillation. It is just . A 30 Hz wave has period .
- Wavelength (λ, lambda) — the physical distance between two successive peaks, measured in metres.
These four are not independent. If the wave travels at velocity v, then in one period it moves a distance of one wavelength. Therefore:
This single equation is the most-used formula in seismology. It lets you go from "a 30 Hz wave in rock that travels at 3000 m/s" to "the wavelength is 100 m" without any further thought. A slower rock at the same frequency gives you shorter wavelengths; a higher-frequency wave in the same rock also gives you shorter wavelengths. Short wavelengths are what let you see small features — more on that when we cover resolution in §1.8.
Sines versus wavelets
A pure sine wave oscillates forever. Real seismic sources cannot do that — they produce a short pulse of energy and then stop. That pulse, when it arrives at a geophone, looks like a single central peak flanked by smaller troughs on either side. The Ricker wavelet is the standard mathematical model for this shape. It is parameterized by one number — its peak frequency — and it looks like a localized burst of a sine wave that quickly damps out.
Switch the toggle in the sandbox above between "Sine wave" and "Ricker wavelet" to see the difference. Every real seismic trace you ever look at is built from wavelets overlapping each other, not sinusoids.
A note on frequency content. Processed seismic typically contains energy across a band of frequencies — maybe 8 to 80 Hz for a land dataset, or 5 to 150 Hz for a high-resolution marine survey. We speak of the dominant frequency when we need a single number, but any real wavelet has a whole spectrum. Section 1.8 and Part 6 will return to this when we discuss resolution and spectral decomposition.
References
- Sheriff, R. E., & Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press.
- Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). Society of Exploration Geophysicists.
- Aki, K., & Richards, P. G. (2002). Quantitative Seismology (2nd ed.). University Science Books.
- Sheriff, R. E. (2002). Encyclopedic Dictionary of Applied Geophysics. Society of Exploration Geophysicists.