Conventional acceleration records do not properly account for the observed coseismic ground displacements, thus leading to an inaccurate definition of the seismic demand needed for the design of flexible (long period) structures. Large coseismic displacements observed during the 27 February 2010 Maule earthquake suggest that this effect should be included in the design of flexible structures by modifying the design ground motions and spectra considered. Consequently, Green’s functions are used herein to compute synthetic low‐frequency seismograms that are consistent with the coseismic displacement field obtained from interferometry using synthetic aperture radar (SAR) images. In this case, the coseismic displacement field was determined by interfering twenty SAR images of the Advanced Land Observation Satellite (ALOS)/PALSAR satellite taken between 12 October 2007 and 28 May 2010. These images cover the region affected by the 2010 Mw 8.8 Maule earthquake. Synthetic broadband seismograms are built by superimposing the low‐pass filtered synthetic low‐frequency seismograms with high‐frequency strong‐motion data. The broadband seismograms generated are then consistent with the coseismic displacement field and the high‐frequency content of the earthquake. A sensitivity analysis is performed using three different fault and slip parameters, the rupture velocity, the corner frequency, and the slip rise time. Results show that the optimal corner frequency of the low‐pass filter fc=1/Tc, leads to a trade‐off between acceleration and displacement accuracy. Furthermore, spectral response for long periods, say T≥8 s, is relatively insensitive to the value of Tc, whereas shorter periods are strongly dependent on both the slip rise time and Tc. In general, larger displacements consistent with coseismic data are obtained using this technique instead of digitally processing the acceleration ground‐motion records.