基于L_(1)范数正则化约束的叠前数据衰减补偿方法

Prestack data attenuation compensation based on L_(1)-norm regularization constraint

由于地下介质的吸收作用,地震波在传播过程中经历了能量衰减、波形畸变及频带变窄的过程,严重降低了地震资料的分辨率。对于叠前地震数据而言,地层吸收衰减效应会随着传播路径发生变化,进而扭曲地震数据的AVA反射曲线特征。为此,提出一种针对叠前数据的衰减补偿方法。该方法考虑了射线路径对于衰减补偿的影响,首先在水平层状介质假设下推导出衰减介质中的叠前道集正演公式;然后将衰减补偿简化为一个反问题,并通过L_(1)范数进行正则化约束;最后采用交替方向乘子算法(ADMM)求取最优解,进而实现叠前数据的衰减补偿。数值测试结果表明,所提方法不仅能对振幅和相位进行补偿,而且还能恢复叠前道集的AVA反射特征。通过与叠后补偿、常规叠前反Q滤波方法对比分析,所提方法的精度更高、稳定性及抗噪能力更强。同时,Q值敏感度分析实验说明所提方法对Q值模型不敏感,仅借助低频Q值模型也能保持较高的补偿精度。实际资料处理结果也表明,该方法能够提高叠前道集的分辨率,有效还原数据的AVA反射特征,为高精度叠前地震反演奠定了基础。

Due to the absorption of the subsurface medium,seismic waves experience energy attenuation,waveform distortion,and frequency band narrowing during propagation,which severely reduces the resolution of seismic data.Meanwhile,the absorption effect of formations changes with the propagation path for prestack seismic wave,which distorts the amplitude variation with angle(AVA)reflection characteristics of the seismic data.Therefore,this paper considers the influence of the ray path on the attenuation compensation and proposes an attenuation compensation method for prestack data.Firstly,the forward modeling formula of prestack gathers in the attenuation medium is deduced on the assumption of a horizontally stratified medium.Then,the attenuation compensation is simplified to an inverse problem,and the L_(1)-norm regularization constraint is imposed.Finally,the optimal solution is obtained by the alternating direction method of multipliers(ADMM)to achieve the attenuation compensation for prestack data.Numerical tests show that the proposed method can compensate for the amplitude and phase and recover the AVA reflection characteristics of prestack gathers.The comparison with the poststack compensation and the conventional prestack inverse-Qfiltering method shows that the proposed method has higher precision,stronger stability,and more remarkable noise immunity.The Q-sensitivity analysis experiments illustrate that the method can also maintain high compensation precision with the help of the low-frequency Q model,and it is insensitive to the Q model.The processing results of measured data also reveal that the proposed method can improve the resolution of prestack gathers and effectively restore their AVA reflection characteristics,which provides a basis for high-precision prestack seismic inversion.