# 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 $$q(t,\alpha_g)$$ = time-modulating 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 time-varying parameters are collected in the vector $$\lambda(\tau)$$; and $$\omega$$ = white-noise 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.

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## Properties

### Object Name

• Name of the object in Rtx
• Allowable characters are upper-case and lower-case letters, numbers, and underscore (“_”)
• The name is unique and case-sensitive

### 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 strike-slip fault and 1 if reverse fault.

### Moment Magnitude

• $$M$$ = moment magnitude

### Rupture Location

• Rupture location = coordinates of the rupture location

### Structure Location

• Structure location = coordinates of the structure location

### Shear Wave Velocity

• $$V_{s30} (m/s)$$ = shear-wave 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.