论文标题
简单的Riemannian流行歧管上的三个旅行时间反问题
Three travel time inverse problems on simple Riemannian manifolds
论文作者
论文摘要
我们根据Myers-Steenrod定理提供新的证明，以确认旅行时间数据，旅行时间差数据和破裂的散射关系决定了圆盘上简单的Riemannian度量，直到固定边界固定差异的自然量表。我们的证明方法导致了Lipschitz型稳定性估算，对于简单指标类中的前两个数据集。
We provide new proofs based on the Myers-Steenrod theorem to confirm that travel time data, travel time difference data and the broken scattering relations determine a simple Riemannian metric on a disc up to the natural gauge of a boundary fixing diffeomorphism. Our method of the proof leads to a Lipschitz-type stability estimate for the first two data sets in the class of simple metrics.
