Physical Sciences and Mathematics Commons^™

Software Development For A Three-Dimensional Gravity Inversion And Application To Study Of The Border Ranges Fault System, South-Central Alaska, Rolando Cardenas

Open Access Theses & Dissertations

The Border Ranges Fault System (BRFS) bounds the Cook Inlet and Susitna Basins, an important petroleum province within south-central Alaska. A primary goal in the research is to test several plausible models of structure along the Border Ranges Fault System using a novel three-dimensional inversion utilizing gravity and magnetic data, constrained with other geophysical, borehole and surface geological information. This research involves the development of inversion modeling software using a Borland C++ compiler as part of the Rapid Application Development (RAD) Studio. The novel inversion approach directly models known geology, and "a priori" uncertainties on the geologic model to allow …

Solving The Partial Differential Equation Of Vibrations With Interval Parameters Using The Interval Finite Difference Method, Brenda G. Medina

Open Access Theses & Dissertations

Accuracy and efficiency are among the main factors that drive today's innovative disciplines. As technology rapidly advances, efficiency takes on new meanings but what about accuracy? How accurate is accurate? Human error, uncertainties in measurement, and rounding errors are just some causes of inaccuracy. Interval Computations is an area that allows for such issues to be taken into account; for each measurement attained (for example), an interval can be built by considering the error associated with the measurement, and such an interval can be utilized in the mathematical computations of interest.

We consider the partial differential equation (PDE) of vibrations …

Digital Image Processing Based On Sparse Representation And Convex Programming, Carlos Andres Ramirez

Open Access Theses & Dissertations

Sparse representation models have been of central interest in recent years due to important achievements in computational harmonic analysis, such as wavelet transformations, and the most recent sampling theory, compressed sensing. Numerous applications based on sparse models have been studied in the last decade leading to promising results. These applications include areas in seismology, image processing, wireless sensor networks, computed tomography and magnetic resonance imaging just to mention a few.

In this work, we propose to extend such applications in the area of image processing, particularly for the image segmentation problem, and examine algorithms involved in sparse modeling from both …

A Sparse Representation Technique For Classification Problems, Reinaldo Sanchez Arias

Open Access Theses & Dissertations

In pattern recognition and machine learning, a classification problem refers to finding an algorithm for assigning a given input data into one of several categories. Many natural signals are sparse or compressible in the sense that they have short representations when expressed in a suitable basis. Motivated by the recent successful development of algorithms for sparse signal recovery, we apply the selective nature of sparse representation to perform classification. In order to find such sparse linear representation, we implement an l₁-minimization algorithm. This methodology overcomes the lack of robustness with respect to outliers. In contrast to other classification …

On Constrained Optimization Schemes For Joint Inversion Of Geophysical Datasets, Uram Anibal Sosa Aguirre

Open Access Theses & Dissertations

In the area of geological sciences, there exist several experimental techniques used to advance in the understanding of the Earth. We implement a joint inversion least-squares (LSQ) algorithm to characterize one dimensional Earth's structure by using seismic shear wave velocities as a model parameter. We use two geophysical datasets sensitive to shear velocities, namely Receiver Function and Surface Wave dispersion velocity observations, with a choice of an optimization method: Truncated Singular Value Decomposition (TSVD) or Primal-Dual Interior-Point (PDIP). The TSVD and the PDIP methods solve a regularized unconstrained and a constrained minimization problem, respectively. Both techniques include bounds into the …