一种自适应增益限的反Q滤波

A self-adaptive approach for inverse Q-filtering

地层的Q吸收会造成地震波振幅衰减、相位畸变,分辨率和信噪比明显降低.反Q滤波可消除由于地层Q吸收造成的振幅衰减和相位畸变,从而提高地震资料的分辨率;但反Q滤波振幅补偿的数值不稳定性问题会严重降低地震资料的信噪比,并产生很多假象.截止频率法和稳定因子法反Q滤波振幅补偿方法虽可控制数值非稳定性问题,但振幅补偿函数的增益限为一个时不变的常数,且与地震数据动态范围无关,其经常会压制深层地震波的高频成分,反而降低地震资料的分辨率;因此,本文在研究截止频率法和稳定因子法的基础上,结合地震数据的动态范围对地震记录分辨率的影响,提出了一种自适应增益限的反Q滤波振幅补偿方法,其增益限和稳定因子都是时变的,且都自适应于地震数据有效频带的截止频率.合成数据和实际数据试算表明,本文的自适应增益限的反Q滤波方法可恢复地震信号有效频带范围内的能量,且能较好地控制数值非稳定性问题,最终获得高分辨率和高信噪比的地震数据.

The Earth Q-filter,with frequency-dependent amplitude attenuation and velocity dispersion,can distort seismic wavelet and reduce the seismic resolution.While the inverse Qfilter attempts to eliminate such effect and hence improve the seismic resolution.But the numerical instability of inverse Q-filter amplitude compensation can reduce the SNR（signal-tonoise ratio）and limit the spatial resolution.Although the gain-limit constrained cut-off frequencymethod and stable factor method for the inverse Q-filter can control the numerical instability and the SNR,in which the gain-limit is time-invariant and is not associated with the dynamic range of seismic data,it usually suppresses high frequencies at later time and reduces the seismic resolution.In order to solve this problem,we should fully compensate energy of seismic data in the effective frequency band and suppress noise beyond it.This work proposes a self-adaptive approach for inverse Q-filter amplitude compensation based on the cut-off frequency and stable factor methods.The gain-limit in this method is timevariant and self-adaptive to the cut-off frequency of the effective frequency band of seismic data;and the stabilizing factor changes in inverse proportion to the square of the self-adaptive gain-limit.The self-adaptive approach can restore energy of seismic data in the effective frequency band and control the numerical instability,and finally achieve high resolution and high SNR data.Synthetic and real data examples demonstrate that the self-adaptive inverse Q-filter can compensate for energy loss without boosting high frequency noise,and produce desirable seismic images with high quality.In order to achieve desirable resolution and high SNR of seismic data by the self-adaptive approach for inverse Q-filtering,the Qvalue and the cut-off frequency of the effective frequency band at any time should be relatively accurate.