Surface fitting in geomorphology - examples for regular-shaped volcanic landforms

In nature, several types of landforms have simple shapes: as they evolve they tend to take on an ideal, simple geometric form such as a cone, an ellipsoid or a paraboloid. Volcanic landforms are possibly the best examples of this ?ideal? geometry, since they develop as regular surface features due to the point-like (circular) or fissure-like (linear) manifestation of volcanic activity. In this paper, we present a geomorphometric method of fitting the ?ideal? surface onto the real surface of regular-shaped volcanoes through a number of case studies (Mt. Mayon, Mt. Somma, Mt. Semeru, and Mt. Cameroon). Volcanoes with circular, as well as elliptical, symmetry are addressed. For the best surface fit, we use the minimization library MINUIT which is made freely available by the CERN (European Organization for Nuclear Research). This library enables us to handle all the available surface data (every point of the digital elevation model) in a one-step, half-automated way regardless of the size of the dataset, and to consider simultaneously all the relevant parameters of the selected problem, such as the position of the center of the edifice, apex height, and cone slope, thanks to the highly performing adopted procedure. Fitting the geometric surface, along with calculating the related error, demonstrates the twofold advantage of the method. Firstly, we can determine quantitatively to what extent a given volcanic landform is regular, i.e. how much it follows an expected regular shape. Deviations from the ideal shape due to degradation (e.g. sector collapse and normal erosion) can be used in erosion rate calculations. Secondly, if we have a degraded volcanic landform, whose geometry is not clear, this method of surface fitting reconstructs the original shape with the maximum precision. Obviously, in addition to volcanic landforms, this method is also capable of constraining the shapes of other regular surface features such as aeolian, glacial or periglacial landforms.

An analysis of installation of submarine pipelines

There are different methods of construction of outfall pipelines, all of them have to solve the problem of placing a tube over a known location in sea bed. This process has sometimes to be done in difficult conditions as waves, current or depths greater than 30 metres, where a diver cannot go safely beyond. Also the placement of the pipeline must be carried out without any damage to the tube, therefore a close control of the deflections and stresses in the structure must be performed. The importance of this control should be not diminished because a damage during the construction would imply a very difficult and expensive repair, that should be avoided with a proper design of the construction process. This paper is focused in the analysis of the tube during its placement according to a very well known construction method consisting in placing the tube from a boat, where all the connections between consecutive tube segments are performed, and also the whole process is controlled. This method is used for outfall as well as offshore pipelines, and it will be described in Section 2