Optical probing of glaciers has the potential for tremendous impact on environmental science. However, glacier ice is turbid, which prohibits the use of most established optical measurements for determining a glacier's interior structure. Here, we propose a method for determining the depth, scattering and absorption length based upon diffuse propagation of short optical pulses. Our model allows us to extract several characteristics of the glacier. Performing Monte Carlo simulations implementing Mie scattering and mixed boundary conditions, we show that the proposed approach should be feasible with current technology. The results suggest that the optical properties and geometry of the glacier can be extracted from realistic measurements, which could be implemented with a low cost and small footprint.