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速度函数的低波数分量可以根据Beam叠加数据用层析方法进行估算。该法不要求进行数据拾取工作,而是使由速度模型预测的地面位置和旅行时间处Beam叠加能量为最大值求取。用显式射线跟踪计算有关该速度模型的目标函数的梯度,依次地使用共轭梯度算法和拟牛顿算法获得目标函数的最大值。前者收敛到速度模型的低波数分量的稳定估计值,而后者解出根据Beam叠加确定的速度模型的较精细的分量。这个反演方法用于估计水平层状介质的合成数据的速度函数是成功的。
The low-wavenumber component of the velocity function can be estimated by the tomographic method based on the Beam superimposed data. The law does not require a data pick-up but rather maximizes the maximum Beam stacking energy at the ground location and travel time predicted by the velocity model. The gradient of the objective function with respect to the velocity model is calculated using explicit ray tracing, and the maximum value of the objective function is obtained using the conjugate gradient algorithm and the quasi-Newton algorithm in turn. The former converges to a stable estimate of the low wavenumber component of the velocity model, while the latter yields the finer components of the velocity model determined from Beam stacking. This inversion method is successful in estimating the velocity function of synthetic data in horizontal stratiform media.