A multilayer level-set method for eikonal-based traveltime tomography

We present a novel multilayer level-set method (MLSM) for eikonal-based first-arrival traveltime tomography. Unlike classical level-set approaches that rely solely on the zero-level set, the MLSM represents multiple phases through a sequence of $i_n$-level sets ($n = 0, 1, 2, \cdots$). Near each $i_n$-level set, the function is designed to behave like a local signed-distance function, enabling a single level-set formulation to capture arbitrarily many interfaces and subregions. Within this Eulerian framework, first-arrival traveltimes are computed as viscosity solutions of the eikonal equation, and Fr\'{e}chet derivatives of the misfit are obtained via the adjoint state method. To stabilize the inversion, we incorporate several regularization strategies, including multilayer reinitialization, arc-length penalization, and Sobolev smoothing of model parameters. In addition, we introduce an illumination-based error measure to assess reconstruction quality. Numerical experiments demonstrate that the proposed MLSM efficiently recovers complex discontinuous slowness models with multiple phases and interfaces.