最小二乘傅立叶有限差分偏移

一般偏移算法是用反演算子通过解析方法求解.最小二乘偏移方法采用另一种思路,即采用数值方法,通过解一个线性离散反问题来索求解.这样我们试着寻找一个模型匹配地震数据并能表现出其某些特点来得到偏移图像.最小二乘法能减少偏移赝像,得到更精确的偏移效果.Kirchhoff算子在最小二乘偏移方法中应用较广,但需要较多的迭代次数,而且具有Kirchhoff偏移的缺点.本文把最小二乘方法运用到基于波长延拓的波动方程偏移方法中,为提高最小二乘偏移的效率,可采用效率较高的正传播算子和反传播算子.我们利用效率较高,能适应剧烈横向变速的傅立叶有限差分正传播和反传播算子来做叠后最小二乘偏移.数值实例表明,通过少数的共轭梯度法迭代,就能得到与真实模型差别很微小的偏移效果.对于傅式变换我们采用了数值软件FFTW,其变换速度比常规FFT算法一般要快六倍以上,进一步提高了效率.本文算法很容易在并行机上实现,这些特点在处理大型数据时大有裨益.

Least-squares Fourier finite-difference migration

Conventional migration algorithms utilize the inversion of a forward modeling operator by analytical means.Alternatively,least-squares migration method involves a numerical approach where the solution is retrieved by solving a linear discrete inverse problem.In this case,we intend to seek a model that fits the seismic data and exhibits some certain features.Least-squares migration reduces migration artifacts and generally produces very accurate seismic images.Kirchhoff operator is popularly used in the least-squares migration.However,many iterations are required and the methods have the drawbacks belong to the Kirchoff migration method.In this paper,we apply the least-squares technique to the wave equation migration methods based on wave extrapolation.An key to improve the efficiency of lease-squares migration is adopting efficient modeling and migrations operator.We perform least-squares migration using efficient Fourier finite-difference modeling and migration operators.Numerical examples show that the least-squares images can be efficiently retrieved in a few iterations of conjugate gradients method.In addition,we adopt the numerical software FFTW to perform Fourier transformation,which generally is more than six times quicker than conventional FFT programs,therefore the algorithm become more efficient.The algorithm can be easily implemented in parallel architecture.These features make the algorithm very attractive.