In this paper, the computation of seismic responses of complex ridge topography is documented that can provide a reliable scenario of ridge amplification. This research work is inspired by the topography of the great Himalaya, wherein the increase of height from the south to north is in form of ups (anticlines) and downs (synclines). The viscoelastic SH- and SV-wave responses of triangular and elliptical complex ridge topography models are simulated using fourth-order finite-difference method. The complexity in the model is augmented by adding more number of sub-ridges and sub-valleys along the flanks of the reference mega-ridge. An increase in ridge amplification is obtained with an increase of complexity in both the triangular and elliptical ridge models for both the polarization of S-wave. The increase of amplification with complexity is drastically very high for the horizontal components of the SV-wave in the case of triangular ridges. It is concluded that the horizontal ground motion simulated at the crest of ridge very much depends on the shape and complexity of the topography as well as the polarization of the incident S-wave. It is concluded that the computed topography effects using the spectral ratio of earthquake records at the top and near its base generally overpredicts spectral amplifications and may not be reliable.

$\bf{Highlights}$

$\bullet$ In this paper, the increase of S-wave amplification at the crest of sub-ridges as well as the base of subvalleys with an increase of complexity in the topography models is observed. The increase of amplification of the horizontal components of the SV-wave with complexity was larger to that of the SH-wave in the case of triangular sub-ridges. The predicted ridge amplification using earthquake records at the top and base of a ridge generally over-predicts the ridge amplification.