Computer Engineering Commons^™

Efficient Geophysical Technique Of Vertical Line Elements As A Natural Consequence Of General Constraints Techniques, Rolando Cardenas, Martine Ceberio

Departmental Technical Reports (CS)

One of the main objectives of geophysics is to find how density d and other physical characteristics depend on a 3-D location (x,y,z). In general, in numerical methods, a way to find the dependence d(x,y,z) is to discretize the space, and to consider, as unknown, e.g., values d(x,y,z) on a 3-D rectangular grid. In this case, the desired density distribution is represented as a combination of point-wise density distributions. In geophysics, it turns out that a more efficient way to find the desired distribution is to represent it as a combination of thin vertical line elements that start at some …

Monte-Carlo-Type Techniques For Processing Interval Uncertainty, And Their Geophysical And Engineering Applications, Matthew G. Averill, Kate C. Miller, George R. Keller, Vladik Kreinovich, Jan Beck, Roberto Araiza, Roberto Torres, Scott A. Starks

Departmental Technical Reports (CS)

To determine the geophysical structure of a region, we measure seismic travel times and reconstruct velocities at different depths from this data. There are several algorithms for solving this inverse problem, but these algorithms do not tell us how accurate these reconstructions are.

Traditional approach to accuracy estimation assumes that the measurement errors are independently normally distributed. Problem: the resulting accuracies are not in line with geophysical intuition. Reason: a typical error is when we miss the first arrival of the seismic wave; it is not normal (bounded by the wave period T) and not independent.

Typically, all we know …

Kolmogorov Complexity, Statistical Regularization Of Inverse Problems, And Birkhoff's Formalization Of Beauty, Vladik Kreinovich, Luc Longpre, Misha Kosheleva

Departmental Technical Reports (CS)

Most practical applications of statistical methods are based on the implicit assumption that if an event has a very small probability, then it cannot occur. For example, the probability that a kettle placed on a cold stove would start boiling by itself is not 0, it is positive, but it is so small, that physicists conclude that such an event is simply impossible.

This assumption is difficult to formalize in traditional probability theory, because this theory only describes measures on sets (e.g., for an inverse problem, on the set of all functions) and does not allow us to divide functions …

Multi-Spectral Inverse Problems In Satellite Image Processing, Scott A. Starks, Vladik Kreinovich

Departmental Technical Reports (CS)

Satellite imaging is nowadays one of the main sources of geophysical and environmental information. It is, therefore, extremely important to be able to solve the corresponding inverse problem: reconstruct the actual geophysics- or environment-related image from the observed noisy data.

Traditional image reconstruction techniques have been developed for the case when we have a single observed image. This case corresponds to a single satellite photo. Existing satellites (e.g., Landsat) take photos in several (up to 7) wavelengths. To process this multiple-spectral information, we can use known reasonable multi-image modifications of the existing single-image reconstructing techniques. These modifications, basically, handle each …