# Search in KarstBase

**fractal dimension**(Keyword) returned

**10**results for the whole karstbase:

Limestone Pavements are highly significant components of the physiographic and ecological landscapes of the UK. As relict glacial features they are subject to destruction by natural processes but also by human intervention. This thesis identifies the most effective methods to monitor such change at a variety of temporal and spatial scales, based on the Morecambe Bay pavements at Hutton Roof and Farleton Fell. The starting point for such a study is a methodology to define the baseline on which to base change detection and the key to this is the development of a suitably detailed scene model. This must reflect the environment at the macro-, meso- and micro- scales and also incorporate considerations of the dynamics involved in the landscape evolution. The scene model (the Land Surface Classification Hierarchy (LSCH)) was developed by field measurement of the reflectance spectra of the main elements, biotic and abiotic, with measurements of the pavement surface in terms of the scale of karren development and the texture of the limestone itself. Study of the DEM allowed a fractal dimension to be established and also the nature of ice-flow and its contribution to pavement development, with extending flow, entraining fractured limestone blocks above a plastic, impermeable shale band, being the main mechanism. At the meso scale pavements were classified according to clint form derived from intra-pavement trends in grike direction calculated by Preferred Direction Analysis. Measurements of the key karren forms, runnels, solution pits and pipes and grikes allow assessment of their contribution to the variability of the pavement surface as an element of the scene model through the identification of solution domains. Identification of different lithologies allowed an investigation of spatial variation across the study area, although lithological control on karren form and magnitude is weaker than variability from age of exposure as shown by statistical analysis of karren morphometry using univariate comparative methods and Link diagrams, bivariate and multivariate regression, discriminant analysis, cluster analysis, multi-dimensional scaling and star diagrams with the derived Star Index. Pavements were classified according to karren morphometry. The traditional view of pedestals as an indicator of solution rates, and hence the concentration of solution at the surface, is challenged through the investigation of water flow over the pavement surface and the consideration of the role of lichen as a protective agent as well as the size of solution pits and grike width. It is suggested that only 10% of solution potential is achieved at the surface with 43% in the immediate epikarst. From this solution rate diagrams were developed, allowing the dating of exposure of pavements. These were shown to be within the period when human impact in the area was becoming significant and confirms an early anthropogenic impact on this element of the landscape. Further to this the development of grikes as emergent features was confirmed and this linked to the concept of breakthrough, allowing a model of grike development to be proposed, an important consideration in the dynamics of pavement change. At the micro scale texture analysis allowed the calculation of fractal measures which are related to variations in reflectance. The radiometric response of biotic and abiotic elements of the scene model was analysed confirming the facility of the baseline scene reflectance model of the pavement. Remotely sensed images from the Airborne Digital Camera were linked to ATM, CASI and TM images assessing the effect of scale on change detection and the evaluation of the pavement environment.

The lengths of the Slovenian caves follow the power-law distribution through several orders of magnitude, which implies that the caves can be considered as natural fractal objects. Fractal dimensions obtained from distribution of all caves are about 1.07, and vary within different tectonic and hydrogeological units. Some deviations from the ideal best fit line in log-log plots (i.e. lower and upper cut-off limits) can be explained by underestimation, as many very short caves are not registered. The study of tectonic and hydrogeological setting indicates that the greatest dimensions occur in the rocks with karstic-fracture and fracture porosity and the lowest in low-permeability rocks. Proximity to major tectonic structures shows a detectable effect on the cave length distribution, and the influence is greatest for the caves closer to the faults and thrust fronts. Dimensions are lower than those of fracture networks and faults, which can be most probably explained by flow channeling along the fracture networks, which causes the decrease of fractal dimension. The physical causes of power law scaling and variations in fractal dimensions (power law exponents) are still poorly understood, but the behaviour of fracture networks is believed to be caused by a scale-independent fractal fragmentation of the blocks, and during the process of forming the caves inherit some fractal geometrical properties of the networks.

The main idiosyncrasy of a typical karst system is the presence of a three-dimensional network of conduits behaving as drains in the system and being responsible of both the quick response of karst springs to rainfall events and the complex distribution of solutes in the system. A morphometric analysis of the three-dimensional geometry of conduits provides quantitative measures that can be used in a range of applications. These morphometric parameters can be used as descriptors of the underground geomorphology, they provide information on speleogenesis processes, they can be correlated with karst denudation ratios, they can be used to control the simulation of realistic stochastic karst networks of conduits, and they can be correlated with hydrogeologic behaviour of the karst system. The main purpose of this paper is to define, describe and illustrate a range of morphometric indexes and morphometric functions that can be calculated nowadays because the availability of three-dimensional topographies provided by speleological work and the availability of the computational and graphical power provided by modern computers. Some of the morphometric parameters describe the existence of preferential directions of karstification, others describe the kartification along the vertical and the possible presence of inception horizons. Other indexes describe the shape complexity of the karstic network, whilst other indexes describe spatial variability of the conduit geometry, and other parameters give account of the connectivity of the three-dimensional network. The morphometric analysis is illustrated with a three-dimensional karstic network in Southern France.

Research highlights

**1**to

**10**of 10