Noise and Signal-to-Noise
Learning objectives
- Define signal-to-noise ratio as signal RMS over noise RMS
- See that noise buries weak reflections first
- Explain why stacking improves SNR by the square root of the fold
- Relate a known-clean synthetic to a noisy real trace
Signal Plus Noise
Every synthetic so far has been perfectly clean, because we built it. Real traces are not. A recorded trace is signal plus noise, and the number that decides what you can believe is the signal-to-noise ratio, the ratio of the signal's strength to the noise's, usually as RMS amplitudes. Add noise to the clean trace and the strong reflections shrug it off while the weak ones, the two marked events, vanish first.
Why We Stack
Acquisition fights noise with a beautiful trick. Record the same subsurface point many times, from many source and receiver pairs, so each trace has the same signal but an independent noise realisation. Average them, which is what a stack is, and the signal survives untouched while the random noise partly cancels. The mathematics is exact: averaging traces divides the noise RMS by , so
Raise the fold and watch the two weak events climb back above the noise floor as the point on the right slides up the square-root curve. This is why a modern survey stacks tens of traces per point: fold buys signal-to-noise that no single shot can.
The Modelling Angle
There is a quieter lesson here about why we model at all. A convolutional synthetic of the clean earth is noise-free by construction, so it is often cleaner than any single real trace. That is exactly why a synthetic is the reference you tie to and the labelled truth you train on: it has the answer without the noise. When you do want realism, adding calibrated noise like this makes a synthetic behave like field data, which the feasibility and training-data uses from Part 0 depend on.