Appendix
=====

Below are tables from the PEER report by Rezaeian & Der Kiureghian ([:ref:`bib9 <bib9>`], p.93-94) where average values as well as the distributions of earthquake model parameters were estimated from the American database NGA for a selection of earthquakes recorded on medium to hard ground and :math:`D>10\mathrm{km}`.

**Legend:**

:math:`{I}_{a}` *: Arias intensity;* :math:`{D}_{5\mathrm{-}95}` *: duration of the strong phase (here* :math:`{T}_{\mathit{SM}}` *);* :math:`{\zeta }_{f}` *: reduced damping of the filter (here* :math:`{\xi }_{0}` *);* :math:`{\omega }_{\mathrm{mid}}` *: natural frequency of the filter at the time* :math:`{t}_{0.45}` *: natural frequency of the filter at the time* *(here we work with the pulsation* :math:`{\omega }_{0}` *at the instant* :math:`{t}_{0.05}` *);* :math:`\omega \text{'}` *: ratio of variation of the natural frequency of the filter (the slope of the function describing the evolution of the natural pulsation of the filter) .*


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