Glossary

This glossary defines key terms used in pyRVT and random vibration theory.

Acceleration Response Spectrum

A plot showing the maximum acceleration response of single-degree-of-freedom oscillators with different natural periods when subjected to a specific ground motion. Typically computed for a fixed damping ratio (commonly 5%).

Damping

A measure of energy dissipation in a vibrating system. In structural dynamics, typically expressed as a fraction of critical damping (e.g., 0.05 for 5% damping).

Duration

The effective duration of strong ground motion. Different definitions exist, including significant duration (time between 5% and 95% of cumulative energy) and RMS duration used in random vibration theory calculations.

Fourier Amplitude Spectrum (FAS)

The frequency-domain representation of a time series, showing the amplitude of different frequency components. For ground motions, typically expressed in units of g-s (acceleration times time).

Ground Motion Prediction Equation (GMPE)

An empirical or semi-empirical equation that predicts ground motion intensity measures (such as peak ground acceleration or response spectral values) based on earthquake source, path, and site parameters.

Kappa (κ)

A parameter describing high-frequency attenuation of seismic waves, particularly important for site effects. Often modeled as an exponential decay factor in the form exp(-πκf) where f is frequency.

Moment Magnitude

A logarithmic scale used to measure earthquake size, based on the seismic moment. Denoted as Mw, it provides a physically meaningful measure of earthquake strength.

Peak Factor

A statistical parameter relating the peak value of a random process to its root-mean-square (RMS) value. Central to random vibration theory calculations.

Power Spectral Density (PSD)

The frequency-domain representation of a random process showing how power is distributed across different frequencies. Related to the square of the Fourier amplitude spectrum.

Random Vibration Theory (RVT)

A statistical approach for relating frequency-domain characteristics of ground motion (Fourier amplitude spectrum) to peak response characteristics (response spectrum) using probabilistic methods.

Response Spectrum

See Acceleration Response Spectrum. May also refer to velocity or displacement response spectra computed similarly.

RMS (Root Mean Square)

A statistical measure of the magnitude of a varying quantity. For random processes, it represents the square root of the mean of the squared values.

Seismic Moment

A measure of earthquake size based on the area of fault rupture, average slip, and rock rigidity. Used to calculate moment magnitude.

Single-Degree-of-Freedom (SDOF)

A simplified structural model with one degree of freedom, characterized by mass, damping, and stiffness. Used as the basis for response spectrum calculations.

Spectral Acceleration

The maximum acceleration response of a single-degree-of-freedom oscillator with a specific natural period and damping ratio when subjected to ground motion.

Stochastic Simulation

A method for generating synthetic ground motions using random processes constrained by statistical properties (such as Fourier amplitude spectra and durations) derived from empirical data or theoretical models.

Strong Motion

The portion of earthquake ground shaking that is of primary engineering interest, typically characterized by significant amplitude and frequency content that can cause structural damage.

VS30

The time-averaged shear-wave velocity in the upper 30 meters of the subsurface. A commonly used parameter for site characterization in earthquake engineering.

Mathematical Terms

Autocorrelation Function

A mathematical function that describes the correlation of a signal with a delayed copy of itself as a function of delay time.

First-Passage Time

In probability theory, the first time a stochastic process reaches a specified threshold level. Important for calculating peak factor distributions.

Gaussian Process

A stochastic process where any finite collection of random variables has a multivariate normal distribution. Often assumed in random vibration theory.

Rayleigh Distribution

A probability distribution often used to model the magnitude of a vector whose components are normally distributed. Relevant for modeling peaks in random processes.

Rice Distribution

A probability distribution that generalizes the Rayleigh distribution to include a non-zero mean. Sometimes used in advanced peak factor calculations.

Stationary Process

A stochastic process whose statistical properties do not change over time. Ground motions are often modeled as approximately stationary over their strong motion duration.

Acronyms and Abbreviations

ASCE

American Society of Civil Engineers

BSSA

Bulletin of the Seismological Society of America

CLI

Command-Line Interface

FAS

Fourier Amplitude Spectrum

GMPE

Ground Motion Prediction Equation

HVSR

Horizontal-to-Vertical Spectral Ratio

NGAWest2

Next Generation Attenuation West 2 project

PGA

Peak Ground Acceleration

PGV

Peak Ground Velocity

PSA

Pseudo-Spectral Acceleration (often used synonymously with Spectral Acceleration)

PSHA

Probabilistic Seismic Hazard Analysis

RVT

Random Vibration Theory

SA

Spectral Acceleration

SDOF

Single-Degree-of-Freedom

USGS

United States Geological Survey

Contributing to the Glossary

If you encounter terms in pyRVT documentation that are not defined here, or if you think additional terms should be included:

  1. Create an issue on GitHub

  2. Suggest the term and provide a definition

  3. Consider contributing a pull request to add the term

The glossary aims to be accessible to users with varying backgrounds in earthquake engineering and random vibration theory.