Bandwidth and Resolution

Part 1, Part 1: Wavelets, the Source

Learning objectives

State the vertical-resolution limit as about a quarter wavelength
See two reflectors resolve into two events or merge into one
Relate a wider wavelet bandwidth to a thinner resolvable bed
Read the resolution law: limit falls as peak frequency rises

The Question Resolution Asks

Part 1 has built the wavelet from the ground up: its shape, its family, its phase, and its sampling. This closer cashes all of it in for the number interpreters care about most, vertical resolution: the thinnest bed a wavelet can show as two events rather than one blur.

Put two reflectors a chosen distance apart, convolve with a wavelet, and look. While the separation beats the wavelet's resolution limit, the two peaks stand apart with a dip between them. The classic rule of thumb is the quarter-wavelength limit,

$\text{limit} \approx \dfrac{\lambda}{4} = \dfrac{v}{4 f}$

which in two-way time is about $1/(2 f)$ . Below it the dip fills in and the pair collapses into a single event.

Why Bandwidth Is Worth Fighting For

Thin the bed and it eventually merges; that is geology you cannot change. But raise the peak frequency, and with it the bandwidth, and the resolution limit drops, so the same bed that was merged now resolves. That is the payoff of the time-bandwidth tradeoff from the first section: a broader band gives a shorter wavelet gives thinner resolvable beds. Every dollar spent on acquisition bandwidth and every processing step that broadens the spectrum buys resolution by this law.

One caution the widget also teaches: this quarter-wavelength number is the limit of separation, not of detection. A bed thinner than the limit does not vanish; its top and base interfere into a single tuned event whose amplitude carries thickness information. Reading that tuned amplitude is the subject that opens the convolutional model in the next part.