Formula & Calculator
Peak Ground Acceleration Attenuation (Simplified)
Simplified empirical attenuation relationship estimating how strongly the ground shakes at a given distance from an earthquake, based on magnitude.
Interpretation
PGA = a × 10^(bM) / (R+c)^d. Empirical attenuation relationship for PGA. M is magnitude, R is distance. Used to predict ground shaking for seismic design.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| PGA | Peak ground acceleration | g |
| M | Earthquake magnitude | |
| R | Distance from epicenter | km |
| a, b, c, d | Empirical regional attenuation constants |
What it means
Peak Ground Acceleration (PGA) attenuation relationships are empirical equations that predict the maximum ground shaking at a given distance from an earthquake. The simplified form uses constants a, b, c, d fitted to data. PGA decreases with distance and increases with magnitude. This is used in engineering seismology to design buildings, bridges, and infrastructure to withstand earthquakes. It is also used in hazard mapping and risk assessment. Understanding these relationships is essential for earthquake engineering and for ensuring public safety in seismic regions.
Worked example
Peak Ground Acceleration Attenuation – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Magnitude (M) | 6 |
| Distance (km) | 10 |
| Parameter | Value |
|---|---|
| M | 7.5 |
| Distance | 50 |
Common mistakes
- PGA attenuation: PGA = a × 10^(b·M) / (R+c)^d – empirical ground motion prediction.
- Coefficients a,b,c,d: Region‑specific – use appropriate values from local ground‑motion models.
- Distance R: Usually hypocentral or source‑to‑site distance – in km.
- Magnitude M: Moment magnitude – not all scales are interchangeable.
- Units: PGA in g (acceleration of gravity) or cm/s² – check the model.
Applications
The simplified peak ground acceleration (PGA) attenuation relation, PGA = a · 10^(b·M) / (R+c)^d, estimates the expected ground shaking at a site from an earthquake of magnitude M and distance R. This is essential for seismic hazard analysis and for designing earthquake‑resistant structures. Engineers use attenuation relations to define the design ground motions for buildings, bridges, and infrastructure. The coefficients (a, b, c, d) are derived from empirical data and depend on the region. By predicting PGA, professionals can assess the vulnerability of structures, to plan emergency responses, and to develop building codes. Understanding PGA attenuation is critical for mitigating earthquake risk.
- Seismic hazard analysis and ground motion prediction
- Earthquake‑resistant design of buildings and lifelines
- Land use planning and risk management
- Development of building codes and design spectra
- Retrofit prioritisation of existing structures
Frequently Asked Questions
PGA = a × 10^(b·M) / (R + c)^d. It is an empirical relationship that estimates the PGA (in g) at a site due to an earthquake of magnitude M at distance R. The constants a, b, c, d are region‑specific.
Peak Ground Acceleration is the maximum acceleration experienced by the ground during an earthquake. It is a key parameter for engineering design and seismic hazard analysis.
They are determined by regression analysis of strong‑motion data. For example, the Boore‑Atkinson (2008) model for western North America uses different coefficients than models for Japan or Europe. Regional differences reflect variations in crustal attenuation and earthquake source mechanisms.
PGA increases with magnitude (the term 10^(b·M)). A larger magnitude event produces stronger shaking at a given distance.
PGA decreases with distance following a power law (R + c)^‑d. The constant c accounts for near‑source effects, and d is the attenuation rate (typically ~1–2).
- It is site‑specific; using constants from a different tectonic region can produce large errors.
- It ignores site effects (soil amplification, basin effects).
- It does not account for the directionality or rupture directivity.
It is used to define the design ground motion for buildings, bridges, and other structures. Building codes (e.g., ASCE 7) often use PGA or spectral acceleration to prescribe seismic design criteria.
PGA is the peak of the acceleration time history. Spectral acceleration (SA) is the acceleration response of a single‑degree‑of‑freedom oscillator at a given period. SA is more representative of structural response.
Soft soils can amplify PGA by a factor of 2–3 compared to rock sites, especially at long periods. Modern attenuation relationships include site‑amplification factors.
PSHA integrates over all possible earthquake magnitudes and distances to estimate the probability of exceeding a given PGA level in a specified time period. This forms the basis for seismic zoning maps.