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International audience; The objective of this article is to present the nonlinear response of a soft sedimentary site based on a one-dimensional inversion by a genetic algorithm of the shear-wave velocity structure and damping factors of a borehole soil column during the 2005 Fukuoka Prefecture Western Offshore earthquake. First, we confirm that, according to the source rupture mechanism, the major and minor axes in the horizontal plane at the borehole station are the transverse and radial directions, respectively. Then, in order to corroborate in the linear domain the S-wave transfer function of the borehole's logging, we perform time-dependent spectral ratios analyses on small aftershocks. Finally, we show qualitative evidence of nonlinearity during the mainshock associated with a significant shift toward low frequencies of several resonant modes, and we evaluate the degree of nonlinearity by inverting the shear-wave velocity structure and damping factors. Because of a directional effect present only in the major axis around 8 Hz, which prevents the use of the conventional objective function that minimizes the integrated residuals between observed and theoretical ratios, we introduce a simple objective function that depends only on peaks' frequency and amplitude. The efficiency of the objective function and the robustness of the inversion are shown by performing eight independent inversions converging to very similar minima.