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Peak Ground Acceleration

  In aseismic (earthquake resistant) design applications peak ground acceleration (PGA) is frequently mentioned. This is because acceleration is considered a measure of  force, and is easy to comprehend. While PGA is said to be the design parameter, other components of ground motion (peak values of ground velocity and acceleration, duration of strong motion, frequency content of the vibration etc.) are equally important For a future earthquake (the design basis earthquake) the PGA value at a specified location is estimated from its magnitude and source location parameters (latitude, longitude and depth of focus). Using recorded data from past earthquakes empirical relationships have been developed relating these parameters. Several empirical relationships of this type exist concurrently. Each one of these is based on a chosen data set, and hence is more applicable for the source-site combinations characterized by the data set.  One of such empirical relationships is selected for estimating the PGA for a site, and from a specified earthquake.

An empirical relationship, normally, consists of three basic components, namely:

The PGA value in the epicentral zone,

Attenuation of the ground motion parameter (PGA) during its traverse from the earthquake source to the site, and

Modification of the base level ground motion at the site by the local site conditions.

 Empirical methods are used because of the very complex nature of the seismic signal, the attenuation path and the seismic signal modification properties of the site geology, which make it difficult to deal with the problem analytically. Availability of recorded accelerograms of strong earthquakes has made it possible to derive empirical expression to relate them.  These expressions are derived using one or the other of the two forms given below:

      Log_e a = C₁ +C₂ M + C₃ Log_e(R+C₄)

or   Log_e  a=C1 + C₂ M +C₃ Log _e(R+r₀) + C₄ (R+r₀)

Here a is the peak ground acceleration, R is the distance of the earthquake source from the site, C₁, C₂, C₃ and r₀ are empirically determined constants. Similar relations exist for ground velocity and displacement[1]. Isoseismals (see Earthquake intensity ^4.1 ) and accelerograms of strong earthquakes are useful in determining signal attenuation characteristics of the seismic signal transmission path[2]^,[3],[4]. It has been observed that isoseismals are, often, not circular in shape. This is because there are directional variations in regional geology and orientation of the causative fault and dynamics of the rupture propagation favor certain directions over others. Values of PGA estimated from different empirical relationships (which are, in turn, based on different data sets) exhibit a large variation.  Several empirical relations are, therefore, in use, concurrently. Apart from being based on different data sets (drawn from different regions) they differ in use of the magnitude scale (Richter scale, local, body wave, surface wave a magnitudes etc.) and in the definition of the term distance of the earthquake source from the site. Some are based on epicentral distance, others on hypocentral distance and still some others on distance from the causative fault of the earthquake. Depth of focus is an important parameter in determining the earthquake ground motion parameters, though role of depth in modifying the ground motion is not well understood, its influence cannot be denied. In selecting a particular empirical relationship for use in a particular situation, the following factors need to be constrained:

§         The magnitude scale used,

§         Definition of the term distance,

§         Depth of focus

§         Site geology, and

§         The scatter of the observed data.

Most of the relationships use the earthquake magnitude on the Richter scale, but use of the body wave magnitude m_b or surface wave magnitude M_s   is not uncommon. These constraints limit the number of the available empirical relationships to choose from.. Estimates of the hypocentral distance are based on the first seismic arrivals, whereas the maximum seismic energy release, often, occurs else where on the fault. Observed elongation of isoseismals parallel to the fault favors use of the distance from the causative fault [5].   As far as possible the empirical relationship used for estimating the PGA value at a specific site must be based on a homogeneous data set representing the site source conditions.  

PGA Empirical Relationships

PGA Empirical Relationship Codes

PGA Empirical Code Relationships References

This page was updated on10-12-10