基于偏微分方程的模型光滑处理在偏移成像中的应用

The applications of model smoothing based on partial differential equation in migration imaging

本文针对射线类偏移成像当中的速度模型光滑处理问题,借鉴数字图像处理当中的偏微分方程法,基于能量泛函,应用变分方法导出基于速度模型的偏微分方程实现射线类偏移成像当中的速度模型的光滑处理.由于偏微分方程法具有线性叠加特性、模型解的唯一性和局部特征保持性,因此,应用该算法可以实现基于原始速度模型空间结构的模型光滑处理.通过在原始速度模型以及光滑处理后的速度模型上计算速度的空间分布以及地震波走时、射线路径可以得出,偏微分方程法对速度模型的光滑处理能够很好地保持原始模型的空间结构,偏移成像结果也证明了该方法的实用性.

In view of the problem of velocity model smoothing in ray type migration imaging,by reference to partial differential equation method in digital image processing,and based on the energy functional,we derived the partial differential equations based on velocity model,using the variational method to achieve velocity model smoothing in ray type migration imaging.Because the partial differential equations have the characteristics of linear superposition,model solution uniqueness and local features retention,therefore,the application of the algorithm can be very good to keep edge characteristics and the characteristics smoothing of velocity model,without breaking the spatial structure of the original velocity model.By calculating the spatial distribution of velocity,the travel time,and the ray paths of the seismic waves on the original and smoothed velocity model,it can be concluded that the smoothing of the velocity model using PDE method is good for keeping the spatial structure of the original model,the results of migration imaging also prove the practicability of this method.