Independent research notes on whether a generative, physics-grounded, uncertainty-calibrated model of the Earth's subsurface is possible — and on the specific reasons the current literature says it is not, yet.
A 3-D seismic survey illuminates the subsurface through a band-limited wavefield recorded at the surface. Wells sample the rock directly, and cover a vanishing fraction of the volume they are used to characterise. Everything in between is inference.
The field's answer for forty years has been forward-model-and-invert: assume physics, assume a parameterisation, regularise until the inverse problem converges, and produce a single deterministic image with error bars nobody believes.
It works. It is also structurally incapable of answering the question that matters: given everything known about this basin, what is the distribution over what is down there — and how much does the next observation move it? That question is a posterior.
A distribution over subsurface states, not a labelled section. Every sample geologically admissible on its own.
Condition on arbitrary partial evidence — a new well, a reprocessed survey, one core photograph — without retraining.
The state evolves: injection, depletion, thermal drawdown, stress redistribution. A world model has a transition function.
If the model says 20%, it must be right 20% of the time. The hardest of the four, and where every published effort stops.
Especially if you work on inverse problems, generative models for scientific data, or subsurface characterisation. Notes and results will be published here.