This contribution comprises true-3D volume datasets ("Digital drill cores"), acquired by a X-ray Computed Microtomography (μ-CT) survey on reference drill core material recovered from Hole 5059-1-D (354 m length to a depth of 290 m, inclined 35° from vertical) on Surtsey volcano (Vestmannaeyjar archipelago, Iceland), drilled by the SUSTAIN drilling project (Surtsey Underwater volcanic System for Thermophiles, Alteration processes and INnovative Concretes, see Jackson et al. 2019 for details).Thirteen reference samples (see Weisenberger et al. 2019 for preparational details) (ranging from 220.35 to 344.47 inclined depth / 180.47 to 282.12 m vertical depth, sampling roughly every 10 m) were scanned as quarter cores. The X-ray μ-CT scans were performed using the ProCon CT-ALPHA system of the Petrology of the Ocean Crust research group at the University of Bremen, Germany.This μ-CT survey has been conducted as part of the DFG SPP 1006 grant "Rates and Processes of Tephra Alteration on Surtsey: Observations and Experiments". In order to avoid imaging of void space due to the quarter core shape, and to achieve a higher magnification, the scans were performed as "out-of-area"-scans (see, e. g. Kahl et al., 2016), restricting observations to the inner regions of the samples. The reconstructed image material is of cylindrical shape with a resolution of ca. 7.5 μm/voxel, and represents virtual drill cores of ca. 15 mm diameter and 15 mm height.The μ-CT-derived image volumes comprise the true 3-D spatial arrangement of fabric compounds in the rock. In the reconstructed 16-bit greyscale volume data, areas of highly attenuating phases (e.g. magnetite, olivine) are encoded in light grey values, whereas areas of low X-ray absorption are color-coded in dark grey (e.g. clays) or black (e.g. voids, cracks). In order to facilitate straightforward access to the digital drill core image material, the volume data is provided as a zipped stack of tif images. In addition, each digital drill core is characterized by three types of visualization: (i) shaded and classical texture-based volume rendering (volren), (ii) maximum intensity projection (volren-MIP): visualization of the highest or lowest intensity in a data volume along the current line of sight, and (iii) three perpendicular virtual cutting planes (3-slices).As an added value to the non-destructive visualization procedure, the reconstructed X-ray micro-CT scans of the studied reference drill core material provide volume reconstructions which can serve as digitypes that may be studied as digital facsimile without the necessity of consulting / modifying / destructive interactions of the actual type specimens (e. g. by physical permeability tests). These image data can be used for quantitative 3D image analysis, e. g. to derive empirical relations between porosity, the extent of replacement of primary phases, and the distribution of secondary phases (and many more).