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The use of laser ablation for cleaning stone is a tried-and-tested method for preserving outdoor artwork surfaces exposed to environmental stresses. However, it is of interest to spectroscopically characterize the sample surface before and during the laser ablation in order to implement automatic control of the cleaning process. To this aim, we have undertaken systematic LIBS analysis on various clean and dirty surfaces of marble fragments collected from ancient quarries in Mediterranean areas, without the characteristic patina that comes from the protective layers usually deposited on the final artwork. The effectiveness of the cleaning process was then monitored by following the disappearance from the LIBS spectra of the encrustation elements during successive laser shots. The LIBS analysis of the clean surfaces of the samples examined confirmed that main bulk composition is based on calcium and magnesium carbonates, with the addition of strontium and, to a minor extent, of manganese and copper substituents. On the other hand, the encrustations were rich in sodium, aluminum, iron, silicon, titanium, lithium, manganese, and chromium, probably coming from sand/soil deposition and, only to a minor extent, from atmospheric pollution. Although SEM imaging and SEM-EDX analyses performed on the same samples at different resolutions showed remarkable surface inhomogeneities from the crustal region deep into the bulk material, the work demonstrates the possibility of a quantitative, minimally invasive, LIBS stratigraphy. The results from the technique are suitable for monitoring cleaning processes by determining appropriate elemental markers present on the surface at trace level (of the order of 100 ppm). [ABSTRACT FROM AUTHOR]