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Smoothing the Marmousi Model

机译：平滑Marmousi模型

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The only way to make an excessively complex velocity model suitable for application of ray-based methods, such as the Gaussian beam or Gaussian packet methods, is to smooth it. We have smoothed the Marmousi model by choosing a coarser grid and by minimizing the second spatial derivatives of the slowness. This was done by minimizing the relevant Sobolev norm of slowness. We show that minimizing the relevant Sobolev norm of slowness is a suitable technique for preparing the optimum models for asymptotic ray theory methods. However, the price we pay for a model suitable for ray tracing is an increase of the difference between the smoothed and original model. Similarly, the estimated error in the travel time also increases due to the difference between the models. In smoothing the Marmousi model, we have found the estimated error of travel times at the verge of acceptability. Due to the low frequencies in the wavefield of the original Marmousi data set, we have found the Gaussian beams and Gaussian packets at the verge of applicability even in models sufficiently smoothed for ray tracing.
机译：制作适用于基于射线的方法（例如高斯束或高斯包方法）的过于复杂的速度模型的唯一方法是对其进行平滑处理。我们通过选择更粗糙的网格并最小化慢度的第二空间导数来平滑Marmousi模型。这是通过最小化相关的Sobolev慢度规范来完成的。我们表明，最小化相关的慢速Sobolev范数是一种为渐近射线理论方法准备最佳模型的合适技术。但是，我们为适合光线追踪的模型支付的价格是平滑模型和原始模型之间差异的增加。同样，由于模型之间的差异，行进时间的估计误差也会增加。在平滑Marmousi模型时，我们发现行进时间的估计误差接近可接受性。由于原始Marmousi数据集的波场中频率较低，因此即使在足够平滑的光线跟踪模型中，我们也发现了高斯光束和高斯数据包处于适用范围的边缘。

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