Seismic inversion techniques fundamentally intend to estimate subsurface properties from wavefield data and provide an outline of their spatial distributions. A conventional scheme for approaching the seismic inversion problem is FWI (full-waveform inversion). FWI has serious drawbacks such as the computational cost of executing new simulations at each iteration as well as the built-in stiffness to evolve from inaccurate initial scenarios to the target ones. Alternative approaches based on deep learning have been recently developed in which deep convolutional neural networks determine a property distribution from scarce sensor data. Meanwhile, train a neural network for seismic inversion may involve a costly hyperparameter tuning. That way, such approaches have still been applied to limited and considerably well-behaved cases. We propose WRI (Wave Reconstruction Inversion) where the forward stage uses the Kansa method with RBF (Radial Basis Functions) to approximate the wavefield. RBF interpolations allow the construction of sparse operators. The inversion step of WRI solves a constrained minimization problem through a two-step penalty method.