General Statistical Design of an Experimental Problem for Harmonics

Four years ago, the Michelin Tire Corporation proposed a problem on experimental design, to improve the manufacturing process for their tires. The idea is basically to determine the effects of placements for various layers built up in the construction of a tire, to allow the design of a smooth tire with a smooth ride. A highly success solution was developed, and it has been reported that this method introduced savings of over half a million dollars in their test processes. This year, Michelin returned to the workshop with an extension to the original problem, to address specific refinements in the testing method. This report summarizes the work completed in course of the five day workshop. It was clear early in the workshop that this problem could be handled quickly by reviewing the analysis which was done in 2000, and extending those ideas to the new problems at hand. We reviewed the required Fourier techniques to describe the harmonic problem, and statistical techniques to deal with the linear model that described how to accurately measure quantities that come from real experimental measurements. The “prime method” and “good lattice points method” were reviewed and re-analysed so we could understand (and prove) why they work so well. We then looked at extending these methods and successfully found solutions to problem 1) and 2) posed by Michelin. Matlab code was written to test and verify the algorithms developed. We have some ideas on problems 3) and 4), which are also described

Inversion for Anisotropic Velocity Parameter

The problem under study concerns the robust computation of a certain parameter of anisotropy from observed travel-times of a seismic shear wave propagating through a geological medium. We have obtained an exact mathematical description of a geoseismic signal propagating through an anisotropic medium using a constant coefficient wave equation as the basic model. This model captures exactly the elliptical velocity profile required in the formulation of the geophysical model from which we obtained exact formulas describing the travel-time through a two layer geological structure, and an exact inversion formula for computing the anisotropic velocity parameter (gamma). A robust numerical method based on a minimization technique was presented as an accurate method of computing both travel-time and the inverted gamma. The exact formulas and robust numerical methods are significant improvements over the approximations and root finding methods discussed in the background material, and we note our formulation is no more difficult than these background methods. We derived asymptotic formulas valid for the near vertical case, which describe accurately the high sensitivity of gamma to the input parameters in this case. Our numerical work also confirms this sensitivity, even using exact formulas and robust numerical methods. We conclude that the computation of the anisotropic velocity parameter (gamma) for the given physical measurements from a series of surface signals and single borehole receiver is intrinsically unstable. By changing to the alpha,beta velocity parameter space, we obtain an inversion method that is much less sensitive to input errors. For certain geophysical problems, the alpha,beta parameters may suffice for an accurate description of the material. When the anisotropic velocity parameter (gamma) is needed directly, a different measurement technique is required. This route will require further investigation, and we have proposed a number of promising possibilities involving a differential time measure

Profiting from Mass Incarceration: The History and Development of the Private Prison Industrial Complex in the United States

Undergraduate Textual or Investigativ

Seismic Image Analysis Using Local Spectra

This report considers a problem in seismic imaging, as presented by researchers from Calgary Scientific Inc. The essence of the problem was to understand how the S-transform could be used to create better seismic images, that would be useful in identifying possible hydrocarbon reservoirs in the earth. The important first step was to understand what aspect of the imaging problem we were being asked to study. However, since we would not be working directly with raw seismic data, traditional seismic techniques would not be required. Rather, we would be working with a two dimensional image, either a migrated image, a common mid-point (CMP) stack, or a common depth point (CDP) stack. In all cases, the images display the subsurface of the earth with geological structures evident in various layers. For a given image the local spectrum is computed at each point. The various peaks in the spectrum are used to classify each pixel in the original seismic image resulting in an enhanced and hopefully more useful seismic pseudosection. Thus, the objective of this project was to improve the identification of layers and other geological structures apparent in the two dimensional image (a seismic section, or CDP gather) by classifying and coloring image pixels into groups based on their local spectral attributes

Determining Geological Properties by a Hybrid Seismic-Magnetotelluric Approach

This paper concerns the controlled source audio magnetotelluric technique (CSAMT) for imaging subsurface structure. Given the short time available, we limited our investigation to a simple 1D earth model where regional seismic and well logs suggest discrete layers, each with constant seismic velocity and constant electrical conductivity. In addition, the well logs provide rough estimates of velocity and conductivity for use as a starting point in the seismic and MT inversions