Sediment Concentration Estimation via Multiscale Inverse Problem and Stochastic Homogenization

Abstract

We develop a multiscale framework for estimating sediment concentration in water flow from acoustic wave measurements. At the microscopic scale, the sediment distribution is modeled by a spatially inhomogeneous Poisson cloud, while the quantity of interest is its macroscopic concentration. For the associated random wave model, we derive an effective medium whose coefficient is explicitly related to the local probability of sediment occurrence. This effective description avoids resolving individual sediment particles and provides a computationally tractable forward model for inversion. We then formulate the recovery of the effective medium, and hence the sediment concentration, as an inverse medium problem from partial boundary measurements, and investigate numerical strategies including model mollification and shot averaging. Numerical experiments demonstrate that the effective model captures the macroscopic wave behavior and can be used to obtain accurate estimates of sediment concentration.