Muography is an imaging tool based on the attenuation of cosmic muons for observing
density anomalies associated with 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 along special
challenges. The detector field of view covering must be as balanced as possible, considering
the muon flux drop at high zenith angles and the detector placement possibilities.
The inversion from directional muon fluxes to a 3D density map is usually underdetermined
(more voxels than measurements). Therefore, the solution of the inversion can be unstable
due to partial coverage. The instability can be solved by geologically relevant Bayesian
constraints. However, the Bayesian principle results in parameter bias and artifacts.
In this work, linearized (density-length based) inversion is applied by 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 resulting
tomographic imaging provides details on the complicated internal structures of karstic
fracture zone. The existence of low density zones in the imaged space was verified
by samples from core drills, which consist of altered dolomite powder within the intact
high density dolomite.