The surface of fractures and pore volumes in rocks affect many of the physico-chemical processes important to geothermal reservoirs and provides a record of the evolution of reservoir rock. Its geometric characterization is important. Computer tomographic imaging is developed into a technique for characterizing multiscale and fractal surfaces of pore-matrix interface of porous rock as well as inner fracture surfaces embedded in core samples. Horizontal slice images of surfaces and through the core images of vug structures are demonstrated by synthetic test cases.

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