一种基于自然梯度的地震盲反褶积方法

常规反褶积方法在地震子波和反射系数未知的情况下，需要做统计性假设，这样往往会降低地震数据处理的分辨率和可靠性。基于自然梯度的盲反褶积算法无需任何假设，利用自然梯度法估算地震子波，得到更接近于实际情况的混合相位子波，用于反褶积，使地震资料的分辨率得到了提高。首先介绍了源数据体可分离的数学依据；然后阐述了基于自然梯度盲反褶积算法的数学原理，并引入补偿函数，推导出适合地震盲反褶积的迭代公式；最后分别利用合成地震记录和实际地震数据对方法进行了验证，结果表明，基于自然梯度的盲反褶积算法能较好地适用于混合相位子波，最大可能地估算原始反射系数。

Seismic blind deconvolution based on natural gradient

In conventional deconvolution method, statistical assumptions are needed when the seismic wavelet and reflectivity is unknown, which usually decreases the resolution and reliability of seismic data processing. The blind deconvolution based on natural gradient does not need any assumption but uses natural gradient method to estimate seismic wavelet to obtain mixed phase seismic wavelet closer to actual situation. The mixed phase seismic wavelet is used for deconvolution to improve the resolution of seismic data. Firstly, the mathematical foundations of separable source data volumes are introduced; then, the blind deconvolution algorithm based on natural gradient is described, and the penalty function is inducted to fetch recurrence formula suitable for seismic blind deconvolution; finally, synthetic and actual seismic data is separately used to verify the method. The results show that the blind deconvolution algorithm based on natural gradient can well adapt to mixed phase system and estimate original reflectivity to maximum likelihood.