  Muography is an imaging tool based on the attenuation of cosmic muons to
observe the density distribution of large objects, such as underground caves or
fractured zones. Tomography based on muography measurements -- that is, three
dimensional reconstruction of density distribution from two dimensional muon
flux maps -- brings up special challenges. The detector field of view covering
must be as balanced as possible, considering the muon flux drop at higher
zenith angles and the detector placement possibilities. The inversion from
directional muon fluxes to 3D density map is usually underdetermined (more
voxels than measurements) which can be unstable due to partial coverage. This
can be solved by geologically relevant Bayesian constraints. The Bayesian
principle results in parameter bias and artifacts. In this work, the linearized
(density-length based) inversion is applied, the methodology is explained,
formulating the constraints associated with inversion to ensure the stability
of parameter fitting. After testing the procedure on synthetic examples, an
actual high quality muography measurement data set from 7 positions is used as
input for the inversion. The result demonstrates the tomographic imaging of a
complex karstic crack zone and provides details on the complicated internal
structures. The existence of low density zones in the imaged space was verified
by samples from core drills, which consist altered dolomite powder within the
intact high density dolomite.
