Compressing seismic migration parameters by B-spline surface fitting
Seismic migration needs many kinds of parameters. The parameters are scattered data and have a large amount of data points. In order to improve the numerical efficiency of seismic migration, the enormous parameter files need be compressed. The published methods for compressing scattered data have a few shortcomings, for example, some are not suitable for enormous data, some are time-consuming, and some can't provide high enough numerical precision. I propose a rapid algorithm to compress the enormous scattered migration parameters by B-spline surface fitting: A least surface is fitted by B-spline function which covers all the scattered data according to their coordinate range in 2D plane firstly. Then, on the basis of the linear interpolaton of B-spline smoothing function, the values of all the regular grids can be calculated by solving a liner system equation group with LU decomposition based on the multi-frontal method. Through storing these values of the regular grids, the value of every point from the original data can be estimated. In this way, the aim of scattered data compressing is achieved. The algorithm is practiced successfully in several models. The experiments show that the cubic B-spline function can be the best basal function for surface fitting because it makes the construction surface smooth, as well as has stable and effective compression with high approximate accuracy using regular grids. The compression algorithm has local relative errors as little as 0.0001, compressing ratio up to 300 and faster calculation efficiency than conventional iterative compressing methods. The algorithm is applicable for any seismic data with low gradient.
Filling polygonal holes using C1 cubic triangular spline patches
Abstract We use the method of energy minimization to fill polygonal holes by C 1 cubic triangular spline patches. We implement the method in MATLAB. Several numerical examples are shown.
An algorithm for least-squares fitting of cubic spline surfaces to functions on a rectilinear mesh over a rectangle
Abstract In this paper a method is presented for fitting, in the least-squares sense, a bivariate cubic spline function to values of a dependent variable, specified at points on a rectangular grid in the plane of the independent variables. Products of B-splines are used to represent the bicubic splines. The coefficients in this representation are determined by solving a set of one-dimensional least-squares problems.