Black hole visualization is a problem of raytracing over curved spacetimes. This paper discusses the physics of light in curved spacetimes, the geometry of black holes, and the appearance of objects as viewed through a relativistic camera (the Penrose-Terrell effect). It then discusses computational issues of how to generate images of black holes with a computer. A method of determining the most efficient series of steps to calculate the value of a mathematical expression is described and used to improve the speed of the program. The details of raytracing over curved spaces not covered by a single chart are described. A method of generating images of several black holes in the same spacetime is discussed. Finally, a series of images generated by these methods is given and interpreted. / text

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Inversion for refraction statics is a key part of three-dimensional (3D) reflection seismic processing. The present thesis has two primary goals directed toward improvement of refraction statics inversion. First, I attempt to improve the quality of the travel-time data right at the beginning of the processing sequence and before any inversion. Any error in the travel times or geometry caused during acquisition or processing would propagate into the resulting model and may harm the resulting image. To implement rigorous, model-independent data quality control, I view the first-arrival travel times as surfaces in 3D, which allows utilization of the travel-time reciprocity condition to check for errors in geometry and in first-arrival picking.<p> The second goal of this study is in development of a new inversion approach for refraction statics specifically for 3D seismic datasets. The first-break travel-times are decomposed by using a ô-p parameterization, which allows an automatic derivation of a high-quality initial subsurface model. This model is further improved by using accurate, multi-layer ray-tracing and inversion techniques to obtain accurate refraction statics. An iterative inversion scheme based on the Simultaneous Iterative Reconstruction Technique is utilized, and its performance is measured and discussed. To assess the quality of the inverse and establish the optimal grid sizes, I use several types of resolution tests. Finally, the surface consistent statics is calculated and applied to a real dataset from southern Saskatchewan. A comparison of the resulting statics model with statics calculated by using standard industry software is made, and the statics correction is incorporated in seismic processing.<p> An overall result of this study is in demonstration that the fully 3D, ô-p based travel-time inversion method works, is applicable to large seismic datasets, and results in detailed shallow subsurface models and reliable statics solutions. Several recommendations for extending and improving the proposed approaches are also made.

When intellectual properties are distributed over a broadcast network, the content is usually encrypted in a way such that only authorized users who have a certain set of keys, can decrypt the content. Some authorized users may be willing to disclose their keys in constructing a pirate decoder which allows illegitimate users to access the content. It is desirable to determine the source of the keys in a pirate decoder, once one is captured. Traitor tracing schemes were introduced to help solve this problem. A traitor tracing scheme usually consists of: a scheme to generate and distribute each user's personal key, a cryptosystem used to protect session keys that are used to encrypt/decrypt the actual content, and a tracing algorithm to determine one source of the keys in a pirate decoder. In this thesis, we survey the traitor tracing schemes that have been suggested. We group the schemes into two groups: <i>symmetric</i> in which the session key is encrypted and decrypted using the same key and <i>asymmetric</i> schemes in which the session key is encrypted and decrypted using different keys. We also explore the possibility of a truly public scheme in which the data supplier knows the encryption keys only. A uniform analysisis presented on the efficiency of these schemes using a set of performance parameters.

When intellectual properties are distributed over a broadcast network, the content is usually encrypted in a way such that only authorized users who have a certain set of keys, can decrypt the content. Some authorized users may be willing to disclose their keys in constructing a pirate decoder which allows illegitimate users to access the content. It is desirable to determine the source of the keys in a pirate decoder, once one is captured. Traitor tracing schemes were introduced to help solve this problem. A traitor tracing scheme usually consists of: a scheme to generate and distribute each user's personal key, a cryptosystem used to protect session keys that are used to encrypt/decrypt the actual content, and a tracing algorithm to determine one source of the keys in a pirate decoder. In this thesis, we survey the traitor tracing schemes that have been suggested. We group the schemes into two groups: <i>symmetric</i> in which the session key is encrypted and decrypted using the same key and <i>asymmetric</i> schemes in which the session key is encrypted and decrypted using different keys. We also explore the possibility of a truly public scheme in which the data supplier knows the encryption keys only. A uniform analysisis presented on the efficiency of these schemes using a set of performance parameters.

Inversion for refraction statics is a key part of three-dimensional (3D) reflection seismic processing. The present thesis has two primary goals directed toward improvement of refraction statics inversion. First, I attempt to improve the quality of the travel-time data right at the beginning of the processing sequence and before any inversion. Any error in the travel times or geometry caused during acquisition or processing would propagate into the resulting model and may harm the resulting image. To implement rigorous, model-independent data quality control, I view the first-arrival travel times as surfaces in 3D, which allows utilization of the travel-time reciprocity condition to check for errors in geometry and in first-arrival picking.<p> The second goal of this study is in development of a new inversion approach for refraction statics specifically for 3D seismic datasets. The first-break travel-times are decomposed by using a ô-p parameterization, which allows an automatic derivation of a high-quality initial subsurface model. This model is further improved by using accurate, multi-layer ray-tracing and inversion techniques to obtain accurate refraction statics. An iterative inversion scheme based on the Simultaneous Iterative Reconstruction Technique is utilized, and its performance is measured and discussed. To assess the quality of the inverse and establish the optimal grid sizes, I use several types of resolution tests. Finally, the surface consistent statics is calculated and applied to a real dataset from southern Saskatchewan. A comparison of the resulting statics model with statics calculated by using standard industry software is made, and the statics correction is incorporated in seismic processing.<p> An overall result of this study is in demonstration that the fully 3D, ô-p based travel-time inversion method works, is applicable to large seismic datasets, and results in detailed shallow subsurface models and reliable statics solutions. Several recommendations for extending and improving the proposed approaches are also made.

In our thesis, we investigate the detection of malicious behavior in cooperative networks. Our model contain one source, one destination and two relays where relays adopt Orthogonal Space Time Block Code (OSTBC) to achieve spatial diversity. Cooperative communication takes two phases to forward signal to the destination. During first phase, source broadcasts data symbols to relay and destination, and a few tracing symbols are inserted randomly in data symbols. The values and positions of tracing symbols are known at source and destination. The random placement of tracing symbols is to prevent relays evade the detection of malicious behavior. In second phase, relays adopt orthogonal space time block code to forward the received signals after decoding source message successfully. We consider two scenarios based on the decoding capability at relays. The first scenario assumes perfect source¡Vrelay links. So, relays can always decode symbols correctly. Second scenario considers decoding failures at relays. In both scenarios, relays have a certain probability to perform maliciously. After receiving symbols at destination, the destination extracts and detect the tracing symbols. The malicious behavior of relay is detected depending on the value of the correlation between detected and exact tracing symbols. Moreover, depending on the average received energy, we can distinguish whether relays behaves as in outage. Through computer simulation, we can verify that our proposed tracing algorithm and decoding strategy reduce bit error rate.

Zugl.: Aachen, Techn. Hochsch., Diss., 2009

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