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We develop an inversion strategy for seismic full waveform inversion (FWI) for 2D vertical transversely isotropic media (VTI). In our strategy, we use LamA© constants (I» and I¼) instead of C33 (= I» + 2I¼) and C44 (= I¼). For C11 and C13, we redefine them by LamA© constants and residuals between anisotropic parameters (C11 and C13) and LamA© constants. Accordingly, these residuals represent anisotropic characteristics. In FWI, we invert LamA© constants and residuals, and then we extract C11, C13, C33 and C44 from the inverted parameters. We validate our new strategy by comparing inversion results obtained by the new inversion strategy to those obtained by the isotropic inversion and the conventional VTI inversion for a modified version of the overthrust geological model. Results obtained by the isotropic inversion are reliable only for isotropic layers. On the other hand, anisotropic layers cannot be recovered well by only I» and I¼. In case of the conventional VTI inversion, C33 and C44 are well inverted. These results agree well with the isotropic inversion results. The C11 and C13 models inverted by the conventional VTI inversion are reasonable, but their resolutions are poorer than those of the C33 and C44. On the other hand, the C11 and C13 models inverted by the new inversion strategy are much improved compared to those of the conventional VTI inversion. From these results, we note that anisotropic properties in subsurface media cannot be recovered by the isotropic inversion, whereas the developed inversion strategy can provide reasonable anisotropic characteristics. In addition, elastic parameters by the new inversion strategy are more precise and stable than those of the conventional isotropic and VTI FWIs.