We present a scheme for random summation of an empirical Green's function to synthesize ground motions from future large events. This scheme obeys the ω2 scaling law at all frequencies and produces time histories whose envelopes are realistic. Assuming that the source parameters of the empirical Green's function are known, one needs only to specify the stress parameter of the target event. In the method, the extended target area is approximated by a point source, whose rupture duration, however, is in accordance with its dimension. Although the method does not account for directivity of the source, tests with Mexican data show a good agreement between observed and synthesized motions. We use this approach to compute expected ground motions in the Valley of Mexico from a hypothetical M 8.2 event in the Guerrero gap.