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<p>In this paper, we are concerned with two inverse density and potential scattering problems for elastic waves using Dirichlet boundary measurements. A logarithmic stability estimate for determining the unknown inhomogeneity is derived at a single frequency by using point-source boundary measurements. The proof utilizes the construction of complex geometric optics solutions. Furthermore, given the multi-frequency data generated by incident plane waves, we derive an increasing stability for the inverse potential problem. The stability improves as the bandwidth of the frequency increases, which exhibits the phenomenon of the increasing stability. The proof relies on resolvent estimates of the elliptic operator and an application of a novel analytic continuation. As multi-frequency data are available, the analysis does not resort to complex geometric optics solutions.</p>

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Stability estimates for inverse scattering problems in elasticity

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • Rong Sun,
  • Ganghua Yuan,
  • Yue Zhao

摘要

In this paper, we are concerned with two inverse density and potential scattering problems for elastic waves using Dirichlet boundary measurements. A logarithmic stability estimate for determining the unknown inhomogeneity is derived at a single frequency by using point-source boundary measurements. The proof utilizes the construction of complex geometric optics solutions. Furthermore, given the multi-frequency data generated by incident plane waves, we derive an increasing stability for the inverse potential problem. The stability improves as the bandwidth of the frequency increases, which exhibits the phenomenon of the increasing stability. The proof relies on resolvent estimates of the elliptic operator and an application of a novel analytic continuation. As multi-frequency data are available, the analysis does not resort to complex geometric optics solutions.