  Geophysical inversion should ideally produce geologically realistic
subsurface models that explain the available data. Multiple-point statistics is
a geostatistical approach to construct subsurface models that are consistent
with site-specific data, but also display the same type of patterns as those
found in a training image. The training image can be seen as a conceptual model
of the subsurface and is used as a non-parametric model of spatial variability.
Inversion based on multiple-point statistics is challenging due to high
nonlinearity and time-consuming geostatistical resimulation steps that are
needed to create new model proposals. We propose an entirely new model proposal
mechanism for geophysical inversion that is inspired by texture synthesis in
computer vision. Instead of resimulating pixels based on higher-order patterns
in the training image, we identify a suitable patch of the training image that
replace a corresponding patch in the current model without breaking the
patterns found in the training image, that is, remaining consistent with the
given prior. We consider three cross-hole ground-penetrating radar examples in
which the new model proposal mechanism is employed within an extended
Metropolis Markov chain Monte Carlo (MCMC) inversion. The model proposal step
is about 40 times faster than state-of-the-art multiple-point statistics
resimulation techniques, the number of necessary MCMC steps is lower and the
quality of the final model realizations is of similar quality. The model
proposal mechanism is presently limited to 2-D fields, but the method is
general and can be applied to a wide range of subsurface settings and
geophysical data types.
