The broadband seismograms recorded at stations near the epicenter of the Landers, California earthquake of 28 June 1992 exhibit observed amplitudes of the spheroidal modes of the Earth that are nearly one order of magnitude larger than those calculated for a spherically symmetric Earth model. We show that these anomalous observations at stations close to the epicenter can be explained by coupling between the normal modes due to the Earth's asphericity. We calculate and sum fully coupled normal modes for three-dimensional shear-wave velocity models of the Earth's mantle to calculate synthetic seismograms. Our coupled-mode synthetic seismograms explain the observed anomalously large amplitude of spheroidal modes and indicate that the coupling between the normal modes due to laterally heterogeneous elastic structure of the Earth causes this anomalous observation. Our results also show that the present three-dimensional Earth models give qualitative fits to this observation. ¿ American Geophysical Union 1993