Traditional geoacoustic inversions are generally solved by matched-field processing in combination with metaheuristic global searching algorithms which usually need massive computations.This paper proposes a new physical framework for geoacoustic retrievals.A parabolic approximation of wave equation with non-local boundary condition is used as the forward propagation model.The expressions of the corresponding tangent linear model and the adjoint operator are derived,respectively,by variational method.The analytical expressions for the gradient of the cost function with respect to the control variables can be formulated by the adjoint operator,which in tum can be used for optimization by the gradient-based method.