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Turbidity currents are one of the main drivers for sediment transport from the continental shelf to the deep ocean. The resulting sediment deposits can reach hundreds of kilometres into the ocean. Computer models that simulate turbidity currents and the resulting sediment deposit can help to understand their general behaviour. However, in order to recreate real-world scenarios, the challenge is to find the turbidity current parameters that reproduce the observations of sediment deposits. This paper demonstrates a solution to the inverse sediment transportation problem: for a known sedimentary deposit, the developed model reconstructs details about the turbidity current that produced these deposits. The reconstruction is constrained here by a shallow water sediment-laden density current model, which is discretised by the finite element method and an adaptive time-stepping scheme. The model is differentiated using the adjoint approach and an efficient gradient-based optimisation method is applied to identify turbidity parameters which minimise the misfit between modelled and observed field sediment deposits. The capabilities of this approach are demonstrated using measurements taken in the Miocene-age Marnoso Arenacea Formation (Italy). We find that whilst the model cannot match the deposit exactly due to limitations in the physical processes simulated, it provides valuable insights into the depositional processes and represents a significant advance in our toolset for interpreting turbidity current deposits. [ABSTRACT FROM AUTHOR]