The MIIS Eprints Archive: No conditions. Results ordered -Date Deposited. 2019-08-20T02:55:10ZEPrintshttp://www.maths-in-industry.org/images/sitelogo.gifhttp://www.maths-in-industry.org/miis/2008-10-21Z2015-05-29T19:48:45Zhttp://www.maths-in-industry.org/miis/id/eprint/177This item is in the repository with the URL: http://www.maths-in-industry.org/miis/id/eprint/1772008-10-21ZA Seismic Inversion Problem for an Anisotropic, Inhomogeneous MediumIn this report, we consider the propagation of seismic waves through a medium that can be subdivided into of two distinct parts. The upper part is assumed to be azimuthally symmetric, linearly nonuniform with increasing depth, and the velocity dependence with direction consistent with elliptical anisotropy. The lower part, which is the layer of interest, is assumed to also be azimuthally symmetric, but uniform and nonelliptically anisotropic. Despite nonellipticity, we assume the angular dependence of the velocity can be described by a convex curve.

Our goal is to produce a single source-single receiver model which uses modern seismic measurements to determine the elastic moduli of the lower media. Once known, geoscientists could better describe the angular dependence of the velocity in the layer of interest and also would have some clues at to the actual material composing it.Chad Wheaton2008-10-13Z2015-05-29T19:48:41Zhttp://www.maths-in-industry.org/miis/id/eprint/173This item is in the repository with the URL: http://www.maths-in-industry.org/miis/id/eprint/1732008-10-13ZStitching IC ImagesImage stitching software is used in many areas such as photogrammetry, biomedical imaging, and even amateur digital photography. However, these algorithms require relatively large image overlap, and for this reason they cannot be used to stitch the integrated circuit (IC) images, whose overlap is typically less than 60 pixels for a 4096 by 4096 pixel image.

The report begins with a description of the data collection, followed by a description of the data processing required to align two back surfaces. A section is devoted to calculating the cosmetic score, a measure of deformity of the back. The paper concludes with a few suggestions for improvements on data collection and use.Jeff OrchardAdam Webber2008-10-13Z2015-05-29T19:48:48Zhttp://www.maths-in-industry.org/miis/id/eprint/179This item is in the repository with the URL: http://www.maths-in-industry.org/miis/id/eprint/1792008-10-13ZResistance MonitoringThe problem considered was that of estimating the temperature field in a contaminated region of soil, using measurements of electrical potential and current and also of temperature, at accessible points such as the wells and electrodes and the soil surface.

On the timescale considered, essentially days, the equation for the electrical potential is static. At any given time the potential satisfies the equation . Time enters the equation only as a parameter since is temperature and hence time dependent.

The problem of finding when both the potential and the current density are known on the boundary of the domain is a standard inverse problem of long standing. It is known that the problem is ill posed and hence that an accurate numerical solution will be difficult especially when the input data is subject to measurement errors.

In this report we examine a possible method for solving the electrical inverse problem which could possibly be used in a time stepping algorithm when the conductivity changes little in each step.

Since we are also able to make temperature measurements there is also the possibility of examining an inverse problem for the temperature equation. There seems to be much less literature on this problem, which in our case is essentially, a first order equation with a heat source.(We neglect thermal conductivity, which is small compared with the convection). Combining the results of both inverse problems might give a more robust method of estimating the temperature in the soil.Rex WestbrookSean C. Bohun