Rezaeian DerKiureghian Artificial Ground Motion
Class Name
 RRezaeianDerKiureghianArtificialGroundMotionModel
Location in Objects Pane
 Model > Hazard > Earthquake > Intensity > Rezaeian DerKiureghian Artificial Ground Motion
Model Description
Model Form
This model generates random artificial ground motions using the method presented by Rezaeian and Der Kiureghian (2010). This model generates the artificial ground motion using the following equation:
$$ \eqalign{
&{x}(t) = q(t,\alpha_g)\cdot {1 \over \sigma_h(t)} \int^t_ {\infty}h[t\tau,\lambda(\tau)]\omega(\tau)d\tau
}$$
where \(q(t,\alpha_g) \) = timemodulating function in which the \(\alpha_g\) vector controls the intensity, shape, and duration of the motion; \(\sigma^2_h(t)\) = variance of the integral process; \(h[t\tau,\lambda(\tau)]\) = impulse response function of the filter whose timevarying parameters are collected in the vector \(\lambda(\tau)\); and \(\omega\) = whitenoise process. The elements of the αg and \(\lambda(\tau)\) vectors depend on six key characteristics of the ground motion. The \(\alpha_g\) vector includes three elements that depend on the Arias intensity, \(\bar{I_a}\), the effective duration of the motion, \(D_{5−95}\), and the time at the middle of the strong motion phase, \(t_{mid}\). The \(\lambda(\tau)\) vector includes two time functions that depend on the filter frequency at \(t_{mid}\), \(\omega_{mid}\), the rate of the change of the filter frequency in time, \(\omega'\), and the filter damping, \(\xi_f\). Each of these six key characteristics is computed using the predictive equations proposed by Rezaeian and Der Kiureghian (2010). The inputs of the equations are: fault type, distance to the rupture location, shear wave velocity, and moment magnitude.
DDM sensitivities
Properties
Object Name
 Name of the object in Rtx
 Allowable characters are uppercase and lowercase letters, numbers, and underscore (“_”)
 The name is unique and casesensitive
Display Output
 Determines whether the model is allowed to print messages to the Output Pane
White Noise Variable List
 List of independent standard normal random variables
Fault Type
 \(F\) = 0 if strikeslip fault and 1 if reverse fault.
Moment Magnitude
Rupture Location
 Rupture location = coordinates of the rupture location
Structure Location

Structure location = coordinates of the structure location
Shear Wave Velocity
 \(V_{s30} (m/s)\) = shearwave velocity of the top 30 meters of the soil.
Intervent Model Error
 \(v_i\) model error \((i=1,…,6)\) = realizations of the model errors for six key characteristics based on the distributions presented in Rezaeian Der Kiureghian (2010)
Duration
 d = Duration of the motion
Time Step
 ∆t = time increments in the ground motion time history
Output (Automatically generated generic response object)
 A vector of simulated ground motion in unit of ground acceleration (g). It is saved in the form of a text file near the input file.
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