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USGS's FAQ Response to :PGA, EPA, PGV, and EPV

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Recently, Mr. Dave Perkins of USGS was kind enough to send me a copy of a
proposed FAQ on the above subject which they may post in their website (
http://geohazards.cr.usgs.gov/eq/faq ).  This is not an attempt to exhaust the
subject but merely to provide some help information to novices like myself.  I
though those on this list may find it interesting.  Also, perhaps, some of you
may share some insights into this very key seismic design parameter, including
some knowledge of its historical development since ATC 3-06.
**********
Ed

Here is the modified draft on Effective peak acceleration. You can use it:


Question: What is the relationship between peak ground acceleration PGA and
"effective peak acceleration," Aa, or between peak ground velocity and
"effective peak velocity," Av, as these parameters appear on building code
maps?

Answer: Aa and Av have no clear physical definition, as such. Rather, they
are building code constructs, adopted by the staff that produced the
Applied Technology Council (1978) (ATC-3) seismic provisions. Maps for Aa
and Av were derived by ATC project staff from a draft of the Algermissen
and Perkins (1976) probabilistic peak acceleration map (and other maps) in
order to provide for design ground motions for use in model building codes.
Many aspects of that ATC-3 report have been adopted by the current (in use
in 1997) national model building codes, except for the new NEHRP
provisions.

This process is explained in the ATC-3 document referenced below, (p
297-302). Here are some excerpts from that document:

p. 297. "At the present time, the best workable tool for describing the
design ground shaking is a smoothed elastic response spectrum for single
degree-of-freedom systems . . .

p. 298. "In developing the design provisions, two parameters were used to
characterize the intensity of design ground shaking. These parameters are
called the Effective Peak Acceleration (EPA), Aa, and the Effective Peak
Velocity (EPV), Av. These parameters do not at present have precise
definitions in physical terms but their significance may be understood from
the following paragraphs.

"To best understand the meaning of EPA and EPV, they should be considered
as normalizing factors for construction of smoothed elastic response
spectra for ground motions of normal duration. The EPA is proportional to
spectral ordinates for periods in the range of 0.1 to 0.5 seconds, while
the EPV is proportional to spectral ordinates at a period of about 1 second
. . . The constant of proportionality (for a 5 percent damping spectrum) is
set at a standard value of 2.5 in both cases.

". . . The EPA and EPV thus obtained are related to peak ground
acceleration and peak ground velocity but are not necessarily the same as
or even proportional to peak acceleration and velocity. When very high
frequencies are present in the ground motion, the EPA may be significantly
less than the peak acceleration. This is consistent with the observation
that chopping off the spectrum computed from that motion, except at periods
much shorter than those of interest in ordinary building practice has very
little effect upon the response spectrum computed from that motion, except
at periods much shorter than those of interest in ordinary building
practice. . . On the other hand, the EPV will generally be greater than the
peak velocity at large distances from a major earthquake . . .

p. 299. "Thus the EPA and EPV for a motion may be either greater or smaller
than the peak acceleration and velocity, although generally the EPA will be
smaller than peak acceleration while the EPV will be larger than the peak
velocity.

". . . For purposes of computing the lateral force coefficient in Sec. 4.2,
EPA and EPV are replaced by dimensionless coefficients Aa and Av
respectively. Aa is numerically equal to EPA when EPA is expressed as a
decimal fraction of the acceleration of gravity . . ."

Now, examination of the tripartite diagram of the response spectrum for the
1940 El Centro earthquake (p. 274, Newmark and Rosenblueth, Fundamentals of
Earthquake Engineering) verifies that taking response acceleration at .05
percent damping, at periods between 0.1 and 0.5 sec, and dividing by a
number between 2 and 3 would approximate peak acceleration for that
earthquake. Thus, in this case, effective peak acceleration in this period
range is nearly numerically _EQUAL_ to actual peak acceleration.

However, since the response acceleration spectrum is asymptotic to peak
acceleration for very short periods, some people have assumed that
effective peak acceleration is 2.5 times _LESS THAN_ true peak
acceleration. This would only be true if one continued to divide response
accelerations by 2.5 for periods much shorter than 0.1 sec. But EPA is only
defined for periods longer than 0.1 sec.

Effective peak acceleration could be some factor lower than peak
acceleration for those earthquakes for which the peak accelerations occur
as short-period spikes. This is precisely what effective peak acceleration
is designed to do.

On the other hand, the ATC-3 report map limits EPA to 0.4 g even where
probabilistic peak accelerations may go to 1.0 g, or larger. THUS EPA IN
THE ATC-3 REPORT MAP may be a factor of 2.5 _LESS THAN_ than probabilistic
peak acceleration for locations where the probabilistic peak acceleration
is around 1.0 g.

The following paragraphs describe how the Aa, and Av maps in the ATC code
were constructed.

The USGS 1976 probabilistic ground motion map was considered. Thirteen
seismologists were invited to smooth the probabilistic peak acceleration
map, taking into account other regional maps and their own regional
knowledge. A final map was drawn based upon those smoothings. Ground
motions were truncated at 40 % g in areas where probabilistic values could
run from 40 to greater than 80 % g. This resulted in an Aa map,
representing a design basis for buildings having short natural periods. Aa
was called "Effective Peak Acceleration."

An attenuation function for peak velocity was "draped" over the Aa map in
order to produce a spatial broadening of the lower values of Aa. The
broadened areas were denominated Av for "Effective Peak Velocity-Related
Acceleration" for design for longer-period buildings, and a separate map
drawn for this parameter.

Note that, in practice, the Aa and Av maps were obtained from a PGA map and
NOT by applying the 2.5 factors to response spectra.

Note also, that if one examines the ratio of the SA(0.2) value to the PGA
value at individual locations in the new USGS national probabilistic hazard
maps, the value of the ratio is generally less than 2.5.

References

Algermissen, S.T., and Perkins, David M., 1976, A probabilistic estimate of
maximum acceleration in rock in the contiguous United States, U.S.
Geological Survey Open-File Report OF 76-416, 45 p.

Applied Technology Council, 1978, Tentative provisions for the development
of seismic regulations for buildings, ATC-3-06 (NBS SP-510) U.S Government
Printing Office, Washington, 505 p.