Convolving a Section
Learning objectives
- Build a section trace by trace from independent columns
- See that each trace depends only on its own column of the model
- Explain why total trace independence makes the model fast and parallel
- Connect that independence to the model's lateral blindness
A Stack of Solo Traces
You have now dipped, folded, faulted, and fluid-filled a 2D model. This section steps back to the mechanics of turning any such model into a section, because the way it is built explains both what the model is good at and what it cannot do.
The rule is exactly the 1D convolutional model applied once per column. Take a column of the impedance grid, difference it into reflectivity, convolve with the wavelet, and you have one trace. Do that for every column and place the traces side by side. Nothing more. Sweep the build bar and watch it happen, one trace at a time.
Independence, for Better and Worse
The defining property is on display as you sweep: the traces are completely independent. Adding a new trace never changes the ones already placed, because no trace depends on any other. This has two faces, and both matter for modelling.
On the good side, independence makes the model gloriously cheap and embarrassingly parallel: a thousand-trace section is a thousand tiny problems that can run at once, which is why convolution generates 2D training data at scale. On the limiting side, independence is exactly why the model is laterally blind. A diffraction, a multiple, a bowtie, every one of them is energy travelling between traces, and there is no mechanism in a column-by-column convolution to carry it. The strength and the limit are the same fact seen from two sides. The next section cashes the strength in by building a fault-detection dataset; the closer, and Part 5, confront the limit.