Contouring

Structural maps display the top (and sometimes the base) of the reservoir surface below the datum level. The depth values are always true vertical sub sea. One could say that the contours of structure maps provide a picture of the subsurface topography. They display the shape and extent of a hydrocarbon accumulation and indicate the dip and strike of the structure. The dip is defined as the angle of a plane with the horizontal, and Is perpendicular to the strike, which runs along the plane. 

Reservoir quality maps are used to illustrate the lateral distribution of reservoir parameters such as net sand, porosity or reservoir thickness. It is important to know whether thickness values are isochore or isopach (see Figure 5.46). Isochore maps are useful if properties related to a fluid column are contoured, e.g. net oil sand. Isopach maps are used for sedimentological studies, e.g. to show the lateral thinning out of a sand body. In cases of low structural dip (<12°) isochore and isopach thickness are virtually the same. 

The stylus of the planimeter is guided around the depth to be measured and the respective area contained within this contour can then be read off. The area is now plotted for each depth as shown in Figure 6.2 and entered onto the area - depth graph. Since the structure is basically cut into slices of increasing depth the area measured for each depth will also increase. 

We can now planimeter the thickness of the different NOS contours, plot thickness versus area and then integrate both with the planimeter. The resulting value is the volume of net oil sand (4) and not the GRV ... 

The extraction of characteristics contains the determination of properties and characteristics which describe the casting defect. Within this investigations three different groups of characteristics were determined which include information about the geometry, the distribution of gray values, and the contour of the defects (fig. 9). 

Secondly, the linearized inverse problem is, as well as known, ill-posed because it involves the solution of a Fredholm integral equation of the first kind. The solution must be regularized to yield a stable and physically plausible solution. In this apphcation, the classical smoothness constraint on the solution [8], does not allow to recover the discontinuities of the original object function. In our case, we have considered notches at the smface of the half-space conductive media. So, notche shapes involve abrupt contours. This strong local correlation between pixels in each layer of the half conductive media suggests to represent the contrast function (the object function) by a piecewise continuous function. According to previous works that we have aheady presented [14], we 2584... 

With 3D-CTVicwer the export of slice-contours from parts inside the data volume is possible via the DXF-format. From these contours a two-dimensional comparison to the CAD geometry is possible if the coordinate system and the absolute scaling between both methods are well known. 

The aim of this work which enter in a research project on NDT, is to conceive a system of aid for interpretation and taking decisions, on imperfections in metallic fusion welds, we have studied and tested several segmentation techniques based on the two approaches ( contour and regions ). A quantitative analysis will be applied to extract some relatives geometricals parameters. To the sight of these characteristics, a first classification will be possible. 

Good detection The operator has to give a response to the vicinity of a contour ... 

Unique response A contour has to provoke an unique response of the operator. 

The basic idea is to extract firstly "sure" contours contour segment extremities are identified by studying the local neighbourhood of each pixel. The aim of closing contours algorithm is to find the best path between two points that are extremities of the gap to fulfil. 

We have implemented all segmentation techniques described above, in an interactive software. The operator can chose and adapt the appropriate segmentation technique with the desired parameters. Some geometrical features can be extracted using a contour following such as length, width, surface, form, median axes of the selected defect. The selection is easy and can be done interactively using the mouse. 

The squares visible in figure 5 represent the position of hard particles at the moment of recording. Therefore the time distance between two video records is about 1,3 ms at a record rate of 750 Hz. With these data it is possible to calculate particle velocity. Figure 8 shows the particle movement in the molten bath caused by flow processes. The particles are captured at the contour of the molten bath and transported into the liquid phase. 

Depth measurement possibility on complex-contour parts (in the corners, grooves etc.) by training the device in the dialog mode on control items with certain depth cracks... 

The image without treatment (Fig lb) should be compared with the deconvolved image of the rod (Fig. 2b). The dimension of the rod is well restored and the contour is reinforced by the signal processing. 

For this purpose a special probe was designed whose contour fits exactly to the actual turbine blade - it has to be positioned on the foot platform and around the comer of the blade, see figure 2. 

The advantage of this dedicated form is that the operator must not optimize the position of the probe. As the probe fits exactly to the blade contour, the positioning can be performed very quickly. 

In both cases special probes were designed and manufactured For the first ease a special probe which fits geometrically exactly to the contour of the turbine blade and in the other case a combined transducer system was developed which enables a continuous measurement of... 

A two-dimensional slice may be taken either parallel to one of the principal co-ordinate planes (X-Y, X-Z and Y-Z) selected from a menu, or in any arbitrary orientation defined on screen by the user. Once a slice through the data has been taken, and displayed on the screen, a number of tools are available to assist the operator with making measurements of indications. These tools allow measurement of distance between two points, calculation of 6dB or maximum amplitude length of a flaw, plotting of a 6dB contour, and textual aimotation of the view. Figure 11 shows 6dB sizing and annotation applied to a lack of fusion example. 

Interesting pattern formations also occur in surfactants spreading on water due to a hydrodynamic instability [52]. The spreading velocity from a crystal may vary with direction, depending on the contour and crystal facet. There may be sufficient imbalance to cause the solid particle to move around rapidly, as does camphor when placed on a clean water surface. The many such effects have been reviewed by Stemling and Scriven [53]. 

Rowell and co-workers [62-64] have developed an electrophoretic fingerprint to uniquely characterize the properties of charged colloidal particles. They present contour diagrams of the electrophoretic mobility as a function of the suspension pH and specific conductance, pX. These fingerprints illustrate anomalies and specific characteristics of the charged colloidal surface. A more sophisticated electroacoustic measurement provides the particle size distribution and potential in a polydisperse suspension. Not limited to dilute suspensions, in this experiment, one characterizes the sonic waves generated by the motion of particles in an alternating electric field. O Brien and co-workers have an excellent review of this technique [65]. 

The microscopic contour of a meniscus or a drop is a matter that presents some mathematical problems even with the simplifying assumption of a uniform, rigid solid. Since bulk liquid is present, the system must be in equilibrium with the local vapor pressure so that an equilibrium adsorbed film must also be present. The likely picture for the case of a nonwetting drop on a flat surface is... 

Fig. XVII-18. Contours of constant adsorption energy for a krypton atom over the basal plane of graphite. The carbon atoms are at the centers of the dotted triangular regions. The rhombuses show the unit cells for the graphite lattice and for the commensurate adatom lattice. (From Ref. 8. Reprinted with permission from American Chemical Society, copyright 1993.)...

We confine ourselves here to scanning probe microscopies (see Section VIII-2B) scanning tunneling microscopy (STM) and atomic force microscopy (AFM), in which successive profiles of a surface (see Fig. VIII-1) are combined to provide a contour map of a surface. It is conventional to display a map in terms of dark to light areas, in order of increasing height above the surface ordinary contour maps would be confusing to the eye. 

Figure Al.6.27. Equipotential contour plots of (a) the excited- and (b), (c) ground-state potential energy surfaces. (Here a hamionic excited state is used because that is the way the first calculations were perfomied.) (a) The classical trajectory that originates from rest on the ground-state surface makes a vertical transition to the excited state, and subsequently undergoes Lissajous motion, which is shown superimposed, (b) Assuming a vertical transition down at time (position and momentum conserved) the trajectory continues to evolve on the ground-state surface and exits from chaimel 1. (c) If the transition down is at time 2 the classical trajectory exits from chaimel 2 (reprinted from [52]).

Figure A3.7.1. Two-dimensional contour plot for direct collinear reaction A + BC —> AB + C. Transition state is indicated by J.

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