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.
Surface fitting with hierarchical splines
We consider the fitting of tensor product parametric spline surfaces to gridded data. The continuity of the surface is provided by the basis chosen. When tensor product splines are used with gridded data, the surface fitting problem decomposes into a sequence of curve fitting processes, making the computations particularly efficient. The use of a hierarchical representation for the surface adds further efficiency by adaptively decomposing the fitting process into subproblems involving only a portion of the data. Hierarchy also provides a means of storing the resulting surface in a compressed format. Our approach is compared to multiresolution analysis and the use of wavelets.
Early Cretaceous Feathers from Victoria
Unusually well preserved fossil feathers from Lower Cretaceous (VaIanginian-Aptian) claystones at Koonwarra, Victoria, are the oldest (c. 110-125 million years) bird remains yet found in the southern hemisphere, They are among the oldest bird remains known in the world, being antedated only by the toothed Archaeopteryx from the late Jurassic of Bavaria, and being more or less the same age as Gallornis from the Lower Cretaceous of France. The Victorian fossil feathers are evidence for essentially worldwide distribution of birds soon after the beginning of the Cretaceous, if not before. The feathers could conceivably have come from toothed birds.