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.
THE ATLANTIC SLAVE TRADE AND COLONIALISM: REASONS FOR AFRICA’S UNDERDEVELOPMENT?
It is probably an understatement to assert that Africa, the world’s second largest continent, is underdeveloped compared with other continents. Two major exogenous factors often cited for Africa’s development crisis are the so called ‘dual historical injustices’ – the Atlantic slave trade and colonialism. It is often pointed out that while the former almost completely arrested and retarded Africa’s demographical growth for more than three centuries, evoked a perennial state of acrimony and warfare and created a tense and unprecedented atmosphere of insecurity which hindered economic activities and stifled local entrepreneurship and technological drive and dislocated Africa’s socio-economic and political structures and institutions; the latter tied African countries to the apron strings of western imperial powers thereby rendering the pre-conditions necessary for socio-economic and political transformation unachievable. This paper contends that while the history of Africa’s underdevelopment may be traceable to the Atlantic slave trade and colonialism, African leaders had made enormous contributions to the continent’s underdevelopment and backwardness. The paper concludes that irresponsible and irresponsive leadership, vampirism and prodigality, corruption, lack of respect for democratic ideals, insecurity, endemic civil wars, nepotism, etc are the fundamental causes of Africa’s underdevelopment.