An iterative construction-based experimental design algorithm is presented, using a determinant-based design objective function of the approximate Hessian for the linearized problem at each model parameter iterant. The approach is a modified version of the sequential algorithm first presented by Coles and Morgan. In the context of measurement spaces partitioned into subsets (e.g. according to the initial condition of the constitutive PDE), a potentially faster and more scalable search algorithm is proposed which uses the rank-revealing QR factorization to identify a particular measurement subset that possesses the approximate best collection of $p$ new measurements for $p \geq 1$, without having to optimize exhaustively over the full measurement set. Once a subset is found, $p$ measurements are then added from it via the exhaustive approach of Coles et al. We then apply this approach to experimental design for 2-D travel time tomography, where the forward problem is solved via the fast sweeping method (FSM). The inverse problem is solved numerically using a TV-regularized inexact conjugate gradient Gauss Newton method, where the approximate Hessian is computed via matrix-free products implemented via algorithmic differentiation of the FSM.