Inversion is a tricky business. It involves predicting the cause from observations of the effects.
Inverse problems don’t have a unique solution so they need to be constrained via an “objective function” which basically says “let’s keep it simple” and match the observations.
Inversion algorithms differ by how they enforce the “keep it simple” rule. Mathematically speaking though, keeping it simple can sometimes be quite complex!
In geophysics the observations are typically the seismic data — the aim is to determine if the cause is indicative of valuable natural resources.
In oil and gas exploration, predictions are rarely black or white — it’s about quantifying the shade of grey. Independent sources of information can also add together non-linearly.
This is where Bayes’ Theorem comes into play.
Bayes’ Theorem is named after the Reverend Thomas Bayes, an 18th-century statistician, who made significant contributions to probability theory.
Bayes’ Theorem frames inversion (the tricky stuff) as a much easier forward modelling exercise — it’s beautiful!
- Aids in making informed decisions
- Updates understanding of probabilities with new information
- Distills complex information for easy digestion by decision makers
It has wide-ranging applications:
- Hypothesis testing
- Statistical inference
- Decision support
- Machine learning
In the example below we use a Bayesian classification framework to produce fluid and lithology probability volumes from 3D seismic data.
DUG was the first service company to produce these back in the early 2000s!
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