Where 2D Convolution Lies
Learning objectives
- Name the specific events a 2D convolutional section omits
- Locate the missing diffraction at a fault tip and bowtie under a syncline
- State the honest verdict: faithful geometry, silent about wave effects
- Turn that knowledge into judgement about when to reach past convolution
Faithful and Incomplete
Part 3 has given you a real capability: build a 2D earth, fault it, fluid it, and convolve it into a section, fast and at scale. This closer makes sure you carry the capability with clear eyes, by marking exactly where the section misleads.
The model below has a syncline and a fault. Convolution renders both geometries perfectly. Turn on the overlay and two ghosts appear where a real wavefield would put events that convolution simply cannot.
The Two Ghosts, and the Rest
The upper ghost is a diffraction: a real fault tip is a sharp scatterer and radiates a hyperbola, one of the strongest cues an interpreter uses to place a fault. Convolution truncates the reflector and stops. The lower ghost is a bowtie: under a syncline sharper than the wavefield can focus, a real time section crosses over and images the trough three times. Convolution just draws the syncline. Neither ghost is in the section; they are sketches of the absence.
And these two are only the visible members of a longer list. A 2D convolutional section also omits multiples, any angle or offset behaviour, mode conversions, and the velocity pull-up and push-down that lateral velocity changes impose on a real time section. That is a lot of missing physics. Yet the verdict is not distrust, it is judgement: the section is trustworthy for structure, well ties, tuning, and training data, and silent about everything that needs a wave to travel between traces. Knowing precisely where it lies is what lets you use it fearlessly where the omissions do not matter and reach past it where they do. Part 4 builds exactly that reach, the acoustic wave equation, which turns every one of these ghosts into a computed event.