A hybrid adaptive phase space method for reflection traveltime tomography
This work addresses a challenging inverse problem for geophysics or nondestructive testing, but the method is incremental as it combines existing techniques (layer stripping and direct imaging) with data classification.
The paper presents a hybrid three-step method for reflection traveltime tomography that recovers both the unknown medium and scatterer boundaries from boundary scattering data. Numerical tests show the method efficiently and robustly reconstructs the medium and not-too-concave scatterers.
We present a hybrid imaging method for a challenging travel time tomography problem which includes both unknown medium and unknown scatterers in a bounded domain. The goal is to recover both the medium and the boundary of the scatterers from the scattering relation data on the domain boundary. Our method is composed of three steps: 1) preprocess the data to classify them into three different categories of measurements corresponding to non-broken rays, broken-once rays, and others, respectively, 2) use the the non-broken ray data and an effective data-driven layer stripping strategy--an optimization based iterative imaging method--to recover the medium velocity outside the convex hull of the scatterers, and 3) use selected broken-once ray data to recover the boundary of the scatterers--a direct imaging method. By numerical tests, we show that our hybrid method can recover both the unknown medium and the not-too-concave scatterers efficiently and robustly.