Formation matrix

Abstract: Transformation matrices are widely used in robotics for kinematic analysis and trajectory planning. Screw geome try offers better geometric insight into such analyses. In this article we unify the two approaches through the use of invariant properties of orthogonal matrices under simi larity transformations. We give a complete expression for the finite screw motion in terms of the entires of a 3 x 3 dual-number transformation matrix. Our analysis suggests that the finite screw is suitable for trajectory planning, and we develop a concise expression that gives the trans formation matrix describing the displacement at each point along the path of the finite screw motion.

Abstract: Formation matrix properties, such as matrix density, can be estimated from the elemental concentrations available from modern, openhole, nuclear spectroscopy logging techniques. Although this estimation is similar to that of mineral-based interpretation frequently practiced today, it can preempt the a priori selection of minerals by solving for matrix properties directly from the elements. This simple approach greatly enhances the ability to perform wellsite interpretations in both simple and complex formations. The interpretation for the matrix density is derived from a comprehensive database containing hundreds of core samples analyzed for both mineralogy and chemistry. The chemical analysis includes not only the major elements, but also the minor and trace elements that significantly influence wireline log responses. These data are used to forward model the matrix which is then solved as a linear combination of four elements (silicon, calcium, iron, sulfur) that are measured by prompt neutron capture spectroscopy. Comparisons are shown between measured and derived matrix density along with statistical measures of goodness of fit. Although in many cases the errors could be reduced by local optimization, the overall agreement is quite good.

Abstract: The present invention relates to a decoding method and a decoding apparatus in which, while the circuit scale is suppressed, the operating frequency can be suppressed within a sufficiently feasible range, and control of memory access can be performed easily, and to a program therefor. By using a transformation check matrix obtained by performing one of or both a row permutation and a column permutation on an original check matrix of LDPC (Low Density Parity Check) codes, the LDPC codes are decoded. In this case, by using, as a formation matrix, a P×P unit matrix, a quasi-unit matrix in which one or more 1s, which are elements of the unit matrix, are substituted with 0, a shift matrix in which the unit matrix or the quasi-unit matrix is cyclically shifted, a sum matrix, which is the sum of two or more of the unit matrix, the quasi-unit matrix, and the shift matrix, and a P×P 0-matrix, the transformation check matrix is represented by a combination of a plurality of the formation matrices. A check node calculator 302 simultaneously performs p check node calculations. A variable node calculator 304 simultaneously performs p variable node calculations.

Abstract: A method of interpreting petrophysical measurement data include arranging measurements of at least one physical property of formations into a matrix representing the measurements and selecting a range of number of unobserved factors or latent variables for factor analysis. Factor analysis is performed on the measurement matrix and comprises performing factorization of measurements matrix into a number of factors and performing rotation of the factorization results. Whether the factor loadings for each factor have achieved a simple structure is determined and either each of the selected number of factors is associated with a physical parameter of the formations, or one is added to the number of factors and factor analysis and rotation are repeated until factor loadings of all factors have achieved simple structure such that the each of the number of factors is associated with a physical property of the formations.