Dear Damorada,

Not sure I have the full answer but you can start looking here:

On the use of the checker-board test to assess the resolution of

tomographic inversions by Jean-Jacques Leveque, Luis Rivera and Gerard Wittlinger in 1993.

Thank you sir. 

I have seen already the paper referred by you. From 1993 onward authors like Hearn et al 1994, C.Zelt 1998,1999, 2001 and many others are using this test extensively.

Is there any paper(s) available before 1993? 

Sparkman, W., and G. Nolet (1988), Imaging algorithms, accuracy and

resolution in delay time tomography, in Mathematical Geophysics, edited

by N. Vlarr et al., pp. 155 – 187, Springer, New York.

Thank you sir.

No problems, check this paper as well for a recent overview:

http://rses.anu.edu.au/~malcolm/papers/pdf/Rawlinson-etal-2014.pdf