面向模型空间地震反演成像的点扩散函数快速计算方法

Fast point spread function calculation scheme for seismic inversion in model space media

点扩散函数(PSF)反映了地震观测系统对地下一个成像点观测过程的模糊化。在反演理论下可以证明,偏移成像是真实反射率与PSF卷积的结果。将反演成像转化为模型空间的图像去模糊问题,其核心在于PSF算子的计算和PSF模糊化效应的消除。提出了通过散射点模型的一次正演和偏移高效求取控制点PSF,而后通过空间插值快速得到全成像空间PSF的方法。理论分析和数值实验结果表明,全成像空间的PSF是反演理论中Hessian算子的近似,将PSF与反射率模型卷积得到模糊化的图像。利用波数域反演成像的方法,对常规偏移成像结果进行解卷积处理可以得到模型空间的反演结果。模拟数据的测试结果表明,相较于传统的最小二乘偏移方法,面向模型空间地震反演成像的点扩散函数快速计算方法具有更高的计算效率,处理后的偏移剖面分辨率更高,同时具有更均衡的振幅。

The point spread function(PSF)represents the fuzzification of the observation process of an imaging point using a seismic observation system.In inversion theory,it can be proved that migration imaging is the convolution of real reflectivity and PSF.Regarding inverse imaging as an image-deblurring problem,the core of this problem is the calculation of the PSF operator and the elimination of the PSF blurring effect.In this study,a method was proposed to obtain the PSF of the control point efficiently by forward modeling and migration of the scattering point model,and the PSF of the full imaging space was quickly obtained by spatial interpolation.Theoretical analysis and numerical experiments showed that PSF in the full imaging space approximates the Hessian operator in inversion theory,and the blurred image can be obtained by convoluting the PSF and reflectivity models.Using the inversion imaging method in the wavenumber domain,the inversion results in the model space can be obtained by deconvolution of the conventional migration imaging results.The test results of the simulation data showed that compared with traditional least square migration,the proposed method has higher computational efficiency,higher resolution,and a more balanced amplitude.