广义散射层析成像反演

Generalized diffraction tomography

本文详细地给出了基于非均匀介质的体散射广义散射层析成像反演的基本理论.广义散射层析成像反演可以描述为波场的反向传播和对成像场进行局部波数域滤波的过程.在数值算例中,利用背景速度沿深度方向均匀变化的v(z)介质中的简单的方块作为速度异常体的模型,通过对该模型产生的低频的Born数据和声波的正演数据的测试,在对采集系统进行有限频率带宽和空间孔径的校正来进行局部成像矩阵谱的恢复中,可以看出模型中各点的谱在恢复后的质量无论从覆盖的面积范围还是幅值的均一性上都有着明显的提高;在对速度模型的重建中,广义散射层析成像反演能够很好地恢复速度模型的低频分量,即便是方块速度异常体相对于背景速度的平均速度扰动是23%也能很好地重建模型中的速度,且对于不同的背景速度模型基本上都能很好地恢复Marmousi速度模型的低频分量.所以该方法将基于Born模型的层析成像反演适应范围进行了一定程度的扩展.

In this paper, the methodology of generalized diffraction tomography is presented in detail. The generalized diffraction tomography is a process of backpropagation plus deconvolution filtering using the resolving kernel in the scattering tomography in the local wavenumber domain. We use forward scattering renormalized Green＇s function in the model and the forward modeling is based on the De Wolf approximation. Through numerical tests of data sets generated using both the Born approximation and the finite-difference simulations of scalar wave for low frequencies using background velocity model of v（z） media, the blind areas in the spectra domain are partially filled in with multi-frequency spectra and the qualities of the local spectra are considerably improved in both coverage and uniformity in the local wavenumber domain. Numerical tests demonstrate the capability of generalized diffraction tomography, it can recover the long wavelength components of velocity perturbations of up to 23% with respect to the background velocity in a simple square box model, and it can also reconstruct the Marmousi velocity model with low wavenumber component very well comparing the multi-scale representation ofthe exact Marmousi velocity model with those of the reconstruction results generated using different background velocity models.