In spite of the abundance of opening-mode fractures in the earth's upper crust, knowledge about their spatial arrangement remains limited. The spatial arrangement of fractures refers to the patterns of fracture positions in space. On one-dimensional analyses, fracture position can be obtained by combining fracture apertures, spacings, and their sequence along a one-dimensional scanline. Previous approaches failed to account for fracture position and fracture size, thus a new technique, normalized correlation count (NCC), was used to overcome these limitations. This technique was designed to distinguish random from non-random (fractal, inherited/imposed, periodically arranged fractures, or periodically arranged clusters) spatial arrangements of fractures. In addition, another method to quantify the attributes of microfractures in rock samples larger than a thin section was developed and used to quantify their spatial arrangements. NCC indicated that where statistically significant (non-random) clusters exist, large fractures are more clustered than small ones. Differential clustering according to fracture size was detected in data sets from different lithologies at outcrop and rock-sample scale, suggesting that this phenomenon is related to development of fracture systems as opposed to host rock lithology and scale. Fracture clusters with power-law variation of spatial correlation with length scale are not strictly natural fractals because clusters occur in cascades at discrete values of length scale and not in a continuous fashion. Some statistically significant clusters with a power-law of spatial correlation are formed by smaller clusters with a power-law of spatial correlation that are also periodically arranged. Fractures from the Cupido Fm. in the Monterrey salient were grouped in three categories based on their trace morphology, cement composition, and timing of fracture cements with respect to fracture opening. Fractures at outcrop scale in two of the categories exhibit low percentages of synkinematic cement and random arrangements, whereas fractures in the remaining category exhibit large amounts of synkinematic cement and periodically arranged clusters. An evolutionary model of fracture development based on subcritical propagation is proposed. This model suggests that mechanical layering increases during cluster development, explaining the non-random clustering within interclustering domains at outcrop scale and implies that cluster spacing increases with mechanical layering but decreases during evolution towards cluster saturation. / text

Digitization of medical data has become a very important part of the modern healthcare system. Data can be transmitted easily at any time to anywhere in the world using Internet to get the best diagnosis possible for a patient. This digitized medical data must be protected at all times to preserve the doctor-patient confidentiality. Watermarking can be used as an effective tool to achieve this. In this research project, image watermarking is performed both in the spatial domain and the frequency domain to embed a shared image with medical image data and the patient data which would include the patient identification number. For the proposed system, Structural Similarity (SSIM) is used as an index to measure the quality of the watermarking process instead of Peak Signal to Noise Ratio (PSNR) since SSIM takes into account the visual perception of the images compared to PSNR which uses the intensity levels to measure the quality of the watermarking process. The system response under ideal conditions as well as under the influence of noise were measured and the results were analyzed.