Service companies developed forward Nuclear Geophysical Models
like SNUPAR and MSTAR to assist in the design of their nuclear
logging tools and in the prediction of their response to porous
media that contain any minerals and any fluids in any combination.
Given a formation's mineral and fluid content, including chemical
formulas, densities, and volume fractions, a forward model can
predict logging tool responses to that formation. Forward models
are also used to help construct Chart Books with departure curves
and environmental corrections for unusual mineral and fluid conditions.

A big advantage is that these same models can be used to generate
the input information called "material specification cards" needed
to define a formation to the Monte Carlo program MCNP, thereby
maintainling the coherence between the nuclear geophysical models,
the charts and environmental corrections they provide, and the more
sophistocated MCNP models.

Clearly the most difficult/challenging aspect of these initial efforts
was describing the slowing down of fast neutrons and how this
process is related to formation porosity.

Earlier forward models assumed that the minerals and fluids of both
the pores and the host matrix are homogeneously distributed with
infinitesimal sizes in much the same way that oxygen, nitrogen,
carbon dioxide, water and other molecules form earth’s atmosphere;
also, no laminae were present. These assumptions were used
historically for mathematical convenience despite the obvious fact
that real earth formations contain minerals and fluids that are
inhomogeneously distributed throughout. After a time, even many
experts came to believe that pore size effects on nuclear logging
tools were negligible in every case.

To make matters worse, density, neutron, and pulsed neutron logging
tools are routinely calibrated in laboratory formations and shop
calibrators that are carefully constructed to be homogeneous with
no laminae and very small pore sizes.

Forward models are registered / calibrated with laboratory data
and also with Monte Carlo Methods. However, forward models
remain the method of choice in vuggy and laminated porous media
because the number of formation zones in these cases can present
formidable problems for Monte Carlo modelers and laboratory test
cell designers whenever pore size, laminae, and fractal dimension
are considered.