An empirical method is used to simulate spectrum compatible time histories for a megathrust earthquake scenario in Peru. The Pisco earthquake (Mw 8.0) is the earthquake scenario. An empirical attenuation formula for acceleration response spectra provides the target spectrum. Moreover, empirical formulas to evaluate the mean and the variance of group delay time are used. The empirical formulas use site coefficients to represent local characteristics of ground motions due to underlying soil structure. Deep shear-wave velocity profiles in Lima, Peru and soil profile information from the KiK-net seismic network in Japan are used to calculate transfer functions and evaluate the site effect. Although there is good agreement with response spectra in a certain range of periods and peak acceleration values in time domain for observed and simulated ground motions, it is not advisable the direct use of empirical formulas. However, the procedure to construct waveforms, based on the phase content, used has proven to be a good technique to simulate ground motions.