This thesis addresses accessibility questions through five case studies in two different contexts. Two case studies take place in the rural Peruvian Amazonia (Loreto region) where the extensive river network forms the backbone of regional transportation and peoples daily mobility. The other three case studies are conducted in the capital region in Finland (Greater Helsinki), and the focus of these studies is on urban environments.

The contribution of my work is both methodological and contextual; I aim at finding novel data sources for spatial accessibility analyses and further developing methods for quantifying accessibility as distances and travel times. On the other hand, I aim at (visually) describing and understanding the spatial patterns of accessibility in my study areas and at analysing and discussing the implications of accessibility for the spatial organisation of land-use and peoples daily mobility.

My results show that realistic accessibility analyses require a consideration of different travel modes and regionally specific transport network properties. In fluvial transport networks, travel time analysis is particularly sensitive to river channel types, direction of movement and seasonality. In urban settings the door-to-door approach for multimodal travel time calculations gives more realistic results than in-vehicle travel time only, and it also makes the different travel modes mutually comparable. The value of the more advanced quantification methods becomes particularly visible when the results obtained from the accessibility calculations are further applied in new analyses. The use of simple Euclidean distances may, however, be justified in situations where appropriate data for more advanced analysis is lacking, but knowing the limitations and simplifying assumptions of these measures is important when applying them.

The key contextual findings of this thesis are based on quantitative descriptions and visualisations of the spatial patterns of accessibility in the case study areas. Quantitative data on accessibility also serve as an input for analyses of human livelihoods (such as modelling of potential production zones for different agricultural produce in Loreto) and land-use pressure (such as Amazonian deforestation modelling). My results furthermore show how accessibility to services and other daily activities is an important factor influencing urban residents travel behaviour and its environmental sustainability in Greater Helsinki.

Finally, this thesis provides examples of how different types of data sources and their innovative combinations can be used in accessibility analyses. In the case studies I utilize and thus also introduce freely available computational tools for detailed multimodal travel time analysis.

]]>The research related to inverse problems is spread out from purely theoretical mathematics to engineering. Theorists try to find uniqueness results and the steps to reconstruct the solution, applied mathematicians implement and test these theoretical findings using computers. This work is then put to practice by modifying the theoretical algorithms to handle noisy data. Finally we need engineering work to enhance the measurement process and to design the devices for our new inverse problem solution method.

In this thesis we are testing some theoretical concepts numerically. More specifically, we are testing new direct reconstruction methods. They rely on the use of analysis on the mathematical model of the (physical) problem itself, producing information about the solution via equations and relations.

Different tomographic methods use different physical properties of matter. In underground prospecting we use the scattered acoustic waves in the form of Acoustic tomography (AT). Electrical impedace tomography (EIT) is based on electrical measurements, whereas Diffusive optical tomography (DOT) measures scattered light. Heat probing is done by measuring heat flux through the boundary of the object of interest. Each type of tomography has its strengths and weaknesses.

The new scientific work presented in this thesis is three-fold: (1) we numerically test a boundary correction procedure in the D-bar method for EIT, (2) we develop a new computational method of the D-bar method for reconstructing a potential at positive energy applicable to AT and numerically find exceptional points, and (3) we numerically test new probing methods for either a stationary or moving inclusion in a background heat conductivity.

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