基于柯西分布的频率域全波形反演

Full waveform inversion with Cauchy distribution in the frequency domain

全波形反演利用了波形的整体特征,是一种高分辨率的成像方法。目前广泛使用的最小二乘法全波形反演隐含了地震数据处理中噪声服从正态分布,限制了实际应用的效果。本文在假设地震数据噪声误差服从柯西分布的前提下,提出了一种基于柯西分布的频率域目标函数构造方法,推导出了相应的梯度表达式,通过对理论模型的数值合成记录加入随机脉冲噪声、高斯噪声和线性噪声,验证本方法的正确性。反演过程中采用拟牛顿法从低频到高频进行了多尺度的全波形反演,并将低频反演结果作为高频反演的初始模型以便减少解的非唯一性。研究结果表明:该方法相对于最小二乘全波形反演方法,在噪声存在且不满足高斯正态分布的情况下,仍然能够得到较好的反演结果。

Applications of least squares full inversion are limited because this inversion is based on noise normal distribution.The full waveform inversion(FWI)with the whole waveform characteristics is a high-resolution imaging method.In this paper,we present a new approach,full wave inversion with Cauchy distribution in the frequency domain.Based on noise Cauchy distribution,objective functions in the frequency domain for this FWI depends on the Cauchy regularization restraint-based method.We also derive a formula for Cauchy function gradient.We test this new algorithm with Quasi-Newton method on synthetic data merged with random spike noise,coherent noise,and Gaussian noise.This multi-scale inversion is performed from low frequency to high frequency.And low-frequency inversion results are used as the starting model for higher frequency inversion,which can greatly reduce the non-uniqueness of their solutions.Compared with least square full wave inversion,the proposed approach can get good inversion results even with non noise normal distribution.