Bayesian Markov chain Monte Carlo (MCMC) algorithms are introduced
for the analysis of one- and two-dimensional airborne frequency-domain
electromagnetic datasets. Substantial information about parameter
uncertainty, non-uniqueness, correlation, and depth of investigation
are revealed from the MCMC analysis that cannot be obtained using
traditional least-squares methods. In the one-dimensional analysis,
a trans-dimensional algorithm allows the number of layers to be unknown,
implicitly favouring models with fewer layers. Assessment of data
errors and systematic instrumentation errors can also be incorporated.
An example from western Nebraska shows that the MCMC analysis reveals
important details about the subsurface that are not identified using
a single ?best-fit? model. A geostatistical facies-based parameterization
is introduced in order to reduce the number of underlying parameters
for the two-dimensional MCMC analysis. This parameterization naturally
incorporates lateral constraints in the proposed models, which is
important for efficiently sampling the model space. A transdimensional
component can be optionally incorporated in the two-dimensional algorithm
by allowing the number of facies to vary, but with models that contain
fewer facies implicitly favoured.