“…Here we would like to discuss the relationship between the resolving kernel derived in this paper and the Hessian matrix in least-square inversion because they are closely related to each other. In the leastsquare inversion (Beylkin, 1985;Chavent and Plessix, 1999;Clapp et al, 2005;Hu et al, 2001;Kuhl and Sacchi, 2003;Lailly, 1983;Plessix and Mulder, 2004;Pratt et al, 1998;Rickett, 2003;Tarantola, 1984a;ten Kroode et al, 1994;Valenciano et al, 2005Valenciano et al, , 2006, which is based on the minimizing the misfit function using adjoint operator in the Hessian matrix, the backpropagation operator is defined as the gradient of the least-square error function, and the Hessian matrix is the second derivative of the error function (Plessix and Mulder, 2004). There are several differences between the formula of the resolving kernel and that of Hessian matrix.…”