**3.3 Creation of H/V spectrum and transfer function**

The H/V spectrum can be obtained by using the amplitude spectrum for each direction obtained by the Fourier transform in the following equation.

The period in which the H/V spectral ratio shows the maximum value is the natural period of the surface layer ground, and the maximum value is the estimated value of the amplification factor. In this study, the period of the maximum value of the H/V spectrum is treated as the constant ground predominant period of the surface layer. In addition, the transfer function is obtained by the following equation when the dynamic interaction between the ground and the structure is taken into consideration. The period of the maximum value of the transfer function is the building natural period:

*Perspective Chapter: Building Damage Estimation and Renovation Proposal System Using... DOI: http://dx.doi.org/10.5772/intechopen.112457*

$$\mathbf{S}\_{i} = \sqrt{\frac{{\mathbf{X}\_{i}}^{2} + {\mathbf{Y}\_{i}}^{2}}{{\mathbf{Z}\_{i}}^{2}}} \tag{1}$$

Si : H/V spectral ratio at i Xi : Spectrum in the X direction at i Yi : Y-direction spectrum at i Zi : Z-direction spectrum at i

$$\mathbf{T}f\_i^\circ = \mathbf{B}i / \mathbf{G}i \tag{2}$$

Tfi : Transfer function at i

Bi : Fourier spectrum of the building at i

Gi : Fourier spectrum of the ground at i
