The generalized pulse-spectrum technique (GPST) is a versatile and efficient iterative numerical algorithm for solving multiparameter inverse problems of a system of nonlinear partial differential equations. Here it is used to determine bulk modulus, shear modulus, and density variation from seismic data. Numerical simulations of simple but nontrivial examples are carried out on coarse uniform grids and adaptive grids to test and to study the general characteristics of GPST without the real measurements (seismograms). GPST does give reasonably good results. It can be made more efficient by implementing parallelism, automatic adaptive-grids, and methods of domain decomposition into the numerical algorithm.