The aim of this article is to investigate a possible way to improve ambient noise tomography by expanding the data base of useful cross-correlation measurements. We show that the curvelet transform makes it possible to compute synthetic noise correlations by simulating directly seismic ambient noise using the spectral element method. These synthetic correlations can in turn be used to identify surface waves and overtones even on correlations having a signal to noise ratio much lower than one. We hope that the possibility to compute SEM synthetic correlations and to extract more information from correlations will be useful to improve ambient noise tomography and monitoring.