稳定高效的时域反Q滤波方法

A stable and efficient approach of inverse Q filtering in the time domain

本文提出了一种全新的基于等效Q值的时域反Q滤波算法,其允许等效Q值在垂向上随时间连续变化,在空间上存在弱变化;将加权最小平方方法优化设计思想引入到时域反Q补偿短算子设计当中,给出最优时域短算子设计,将大量的频率域乘法工作转化为少量的时域褶积运算;采取表驱动方案,将短算子的构建与反Q补偿运算相剥离,极大地提升了计算效率;提出了一种新的稳定性控制方法,其既保证算法具有良好的稳定性,又满足短算子设计精度的要求.数值计算表明:时域反Q滤波算法可以取得与频域算法相同的补偿效果,并保证算法具备良好的稳定性和较高的计算效率.

A method of inverse Q filtering in the time domain based on the effective quality factor is presented for the first time. The effective quality factor can vary continuously along two-way traveltime and vary weakly in spatial direction. The optimum strategy of the weighted least squares method is introduced into designing inverse Q compensation short operator in time domain for calculating the optimum factors of short operator, which can translate large amount of multiplication operation in the frequency dowaininto less convolution operation in the time domain. The scheme of table-driven is adopted to split short operator construction from operation of inverse Q compensation for raising the efficiency of calculation. A new method of stabilization controlling is proposed which can ensure the stablitity of arithmetic as well as can satisfy the demand of designing precision of short operators. Numerical examples indicate that the inverse Q filtering in the time domain can achieve the same compensation result as the arithmetic in the frequency domain and ensure the stabitity and efficiency of the arithmetic.