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To be able to resolve tomographic inversion problems in travel time, it is necessary the construction of distance matrices containing information of survey array geometry, the discretized domain shape and the distance traveled by rays in each area elements that compose it. Domain considered are generally rectangular for ease of geometric resolution. In this work is circular due to the need to carry out investigation in columns of this shape. Distance matrices are used to solve the linear system, which leads to the determination of velocity values in each element of the domain. Taking in mind discretization, there are several possibilities for the construction of arrays of pixels: may those be defined in one quadrant and obtaining the rest by symmetry; build arrays using any size pixels independent of the quadrant, and finally construct distance matrices with square pixels. Each option will provide access to new research possibilities. In this work an original procedure was developed for the construction of matrices with elements of the last type. The procedure was validated with simulated data using the damped least squares solution (DLSS) method, which demonstrated the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

In the paper the results of the combined strategy formed by Robust Principal Component Analysis and CUR matrix decomposition are applied to a practical problem for adjusting a regression model by using Partial Least Squares (PLS). The conclusions concerning their advantages of such an approach as well information about the adjusted models are given. [ABSTRACT FROM AUTHOR]