We analyzed 14 local earthquakes of the Mexico basin (2.3≤Mw≤3.8), recorded on hill sites at local distances (8.0≤R≤60.5 km), to study the spectral attenuation of seismic waves, spectral decay parameter kappa κ, quality factor Q, source spectra, and Brune stress drop. We found an average κ0‐value of 0.0457 s in hill sites, which is similar to values reported in other regions. Assuming a 1/R geometrical spreading, we obtain a quality factor given by Q(f )=72f 0.83. Source spectra of all studied events are in good agreement with the ω2 model. From the synthetic modeling of ground motions at local distances, we explain an anomalous behavior of the corner frequency versus seismic moment and also explain the relatively low values observed for stress drop (5 MPa). The resulting high spectral attenuation values obtained may be responsible for the low acceleration values of ground motions observed for crustal earthquakes occurring inside and near to the Mexico basin.