从化极算法误差方程看各种波数域低纬度化极方法

本文以化极算法误差方程为理论工具揭示了三类波数域低纬度化极方法各自的误差规律,并据此对三类方法进行了化极效果评估、功能定位和应用条件界定。压制类化极方法可以且只能用于低纬度磁异常定性解释;波数域反演化极法可以用于低纬度磁异常定量解释,其条件是数据完整覆盖异常,数据边界尽量简单;波数域偏移抽样化极方法也可以用于低纬度磁异常定量解释,其条件除数据完整覆盖异常,还要求数据精度高于0.2%,且磁偏角方向的数据网格规模不大于64×64。文中应用化极算法误差方程对波数域反演化极方法误差规律的揭示,是对该方法的重要理论补充,使之更加严谨和完善。本文导出的v轴分离法则丰富和发展了偏移抽样类化极方法。

低纬度磁异常波数域化极方法机理分析与功能定位

基于化极算法误差方程,对三类波数域低纬度化极方法进行机理分析和功能定位。压制型化极法不能用于低纬度磁异常数据的定量解释,但可用于定性解释;反演化极法理论上可用于定量解释,但要求资料窗外的未知数据很好地被模拟(实测资料难以满足),因此不具有实用性;偏移抽样化极法理论上也可以用于定量解释,但该方法要求磁偏角方向上的数据(网格数)不超过64,且数据相对精度不低于0.2%。三类波数域低纬度化极方法的功能定位,可对低纬度磁测资料的解释发挥重要的指导作用。

Fourier变换数值计算的偏移抽样理论

将DFT变换推广为DFT_(εη)变换,给出了DFT_(εη)(变换对)与FT(变换对)量值关系的Fourier变换离散化定理,并以此为基础导出了DFT_(εη)算法误差方程,论证了离散效应的极小化问题和截断效应的振荡性质,从而建立了Fourier变换数值计算的偏移抽样理论.

A survey on artificial boundary method Dedicated to Professor Shi Zhong-Ci on the Occasion of his 80th Birthday

The artificial boundary method is one of the most popular and effective numerical methods tor solving partial differential equations on unbounded domains, with more than thirty years development. The artificiM boundary method has reached maturity in recent years. It has been applied to various problems in scientific and engineering computations, and the theoretical issues such as the convergence and error estimates of the artificial boundary method have been solved gradually. This paper reviews the development and discusses different forms of the artificial boundary method.