A method to construct statistical prior models of geology for probabilistic inversion of geophysical data

In probabilistic inversion of geophysical data, one must describe the expected noise in the system, and any prior information. In a geoscience context, prior information can provide a quantitative description of the expected spatial variability and correlations of the geology. But in practical inversion cases, driven by difficulty in quantifying geological information and computational complexity, an analytical mathematical smooth prior model is often chosen to describe the spatial variability. This is one of the primary reasons that realistic geological structures are difficult to resolve in geophysical models. Thus, there is currently a need for investigating and proposing practical ways of capturing complex (and often qualitative) geological information in statistical prior models that can be used in probabilistic inversion, which satisfies both the geologist, geophysicist, engineer and the geostatistician. In this research we show how a 1D statistical prior model can be designed that emulates the spatial distribution found in 188 boreholes with Miocene and Quaternary deposits from a study area (approx. 177,5 km2) near Horsens, Denmark. The prior model is built in two major steps 1) a multidimensional distribution describing the sub-division of major geological elements (here represented by lithologies from defined geological periods) and 2) a truncated pluri-Gaussian distribution describing the internal structure of lithologies within each element. The presented prior model can both be used to generate independent realizations, which can be used as part of the extended rejection sampler, as well as allowing the possibility of doing a "random walk" in the model space, as required by the extended Metropolis algorithm. We demonstrate, as an example, how the developed prior model can be used in a probabilistic inversion of airborne transient electromagnetic (AEM) data and discuss the implications the use of such informed prior models can have.