基于多参量的模拟退火全局优化傅里叶有限差分算子

傅里叶有限差分法(FFD)能够处理复杂地质构造中的波传播问题,但对陡倾角成像仍有明显的误差.优化参数的方法能够在保持计算效率的前提下进一步提高陡倾角的成像精度.本文在有理近似的基础上,将FFD算子展开式中的常系数由两个拓展为四个,然后采用模拟退火算法对这四个参数进行全局优化.本方法除了考虑速度对比度以外,还考虑了频率和延拓步长等参量的影响.理论误差分析和脉冲响应测试均表明该方法能极大地提高FFD算子的精确传播角度.二维SEG/EAGE盐丘模型实验表明本文方法对陡倾角以及盐下构造的成像精度明显高于未优化的FFD法.将本文的方法与交替方向加插值的方法结合应用于三维脉冲响应测试更进一步证实了本文方法的有效性.

Globally optimized Fourier finite-difference operator using simulated annealing algorithm based on multi-parameter

Fourier finite-difference(FFD) method can handle wave propagations in the complex media with large lateral velocity contrasts and wide propagation angles.However,the FFD method has obvious error for wider angles.The optimization method can obviously improve the image accuracy of wider angles without additional computational cost.Based on the rational approximation of the FFD operator,we extend the two coefficients to be optimized to four coefficients,then we optimize them globally using simulated annealing algorithm.Besides the velocity contrast,we consider the effects of both frequency and depth interval.The theoretical analyses and the impulse responses demonstrate that our method significantly extends the accurate propagation angle of the FFD method.Migration results on the 2D SEG/EAGE salt model show that our method resolves the wider angles and the sub-salt weak reflectors more accurately than the unoptimized FFD method.Combination of the FFD method and alternative-direction-implicit plus interpolation method on 3D impulse responses further proved the validity of our method.