A new Bayesian framework for the interpretation of geophysical data

Providing images of the subsurface from ground-based datasets is at the heart of
the geophysicist’s work. Multiple approaches have been applied to tackle this task.
Most of the time, this task is performed in a deterministic framework, meaning
that for a given dataset, a single model is provided to explain the data. However,
those deterministic approaches lack the ability to provide reasonable uncertainty
estimations, that take into account the non-unicity of the solution, noise in the data
and modelling error. To provide precise and accurate models of the subsurface along
with uncertainty, geophysicists use probabilistic approaches. Those approaches are
able to sample the ensemble of a priori possible models (the prior) in order to extract
models that can reasonably explain the datasets (the posterior). Such approaches,
even though superior in terms of the reliability of their results, are rarely applied
in practice due to their significant computational requirements.
In this manuscript, the aim is to propose a new Bayesian framework to interpret
those geophysical datasets. This new framework, called Bayesian Evidential Learning, promises to enable a fast, precise and accurate estimation of the uncertainty.
This framework is applied and adapted for 1D geophysical datasets (BEL1D). The
new and adapted framework presents several advantages when compared to classical probabilistic approaches: from fast computations due to the limited number
of forward runs needed, to providing insight about the experiment sensitivity and
the validity of the prior. Moreover, it benefits from its construction as a Machine
Learning algorithm, leading to quasi-instantaneous models of uncertainty.