Inverse numerical acoustics is a method which reconstructs the source surface normal velocity from the sound measured in the near-field around the source. This is of particular interest when the source is rotating or moving, too light or too hot to be instrumented by accelerometers. The use of laser vibrometers is often of no remedy due to the complex shape of the source.The Inverse Numerical Acoustics technique is based on the inversion of transfer relations (Acoustic Transfer Vectors) using truncated Singular Value Decomposition (SVD). Most of the time the system is underdetermined which results in a non unique solution. The solution obtained by the truncated SVD is the minimal solution in the RMS sense. This paper is investigating the impact of non homogeneities in the mesh density (local mesh refinement) on the retrieved solution for underdetermined systems. It will be shown that if transfer quantities are inverted as such, big elements get a higher weight in the inversion. An approach is proposed to alleviate this issue and is illustrated using multiple examples.