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Medellin is a 3.5 M inhabitant city located in an Andean valley in northwestern Colombia. Its initial prosperity was due to agriculture and cattle-raising carried out in the valley itself and sold to the surrounding gold mining fields. The investment of these monies in coffee plantations and industry boosted the city development, accelerated urban growth, and since the middle of twentieth century, relegated food production to surrounding regions, which are also responsible for almost the totality of natural resource supply: water, electricity, food, building and industrial raw materials. Among the problems which will have to be solved in order to reach a sustainable development are relocation of population living in areas exposed to natural risks, improvement of road communications with surrounding regions and of internal public transportation and pollution control.
This paper aims at describing the theoretical fundamentals of a
reciprocity-based ultrasonic measurement model. This complete inspection
simulation can be decomposed in two modeling steps, one dedicated to transducer
radiation and one to flaw scattering and echo synthesis. The physical meaning
of the input/output signals used in these two modeling tools is defined and the
theoretical principles of both field calculation and echo computation models
are then detailed. The influence on the modeling results of some changes in the
simulated configuration (as the incident angle) or some input signal parameters
(like the frequency) are studied: it is thus theoretically established that the
simulated results can be compared between each other in terms of amplitude for
numerous applications when changing some inspection parameters in the simulation
but that a calibration for echo calculation is generally required.