Retrieving source characteristics for moderate-sized earthquakes in sparsely instrumented regions has been made possible in recent years, through the modeling of waveforms at regional distances. The techniques used in such studies model waveforms successfully at long period, using Green's functions for simple 1D crustal models. For small earthquakes (M < 4), however, long-period signals are usually noisy, and modeling short-period waveforms requires refined Green's functions such as used in the empirical Green's function (eGf) approach. In this article, we present a new technique that generates such Green's functions by perturbing individual generalized ray responses calculated from a 1D model. The model is divided into blocks, and velocities in the blocks are allowed to vary, which shifts the arrival time of the individual rays similar to conventional tomography. The amplitudes of the rays are perturbed independently to accommodate local velocity variations in the structure. For moderate-sized earthquakes with known source mechanism and time history, the velocity variation in each block and the amplification factor for individual rays can be optimized using a simulated annealing algorithm. The resulting modified Green's functions, pseudo Green's functions (pGfs), can be used to study the relative location and characteristics of neighboring events. The method is also useful in retrieving 2D structure, which is essentially waveform tomography.