Relating Seismic Design Values to the Richter Scale
Relating Seismic Design Values to the Richter Scale
(OP)
I have a client asking me what the comparable earthquake magnitude would be (Richter Scale) for the design loads that were calculated. I'm in Portland Oregon and the typical Sds is around 0.70 and Sd1 is around 0.40. Is there anything that relates the two together?






RE: Relating Seismic Design Values to the Richter Scale
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In the first chapter there are some charts/equations that roughly relate ground acceleration to Richter Scale magnitude, which may help you.
RE: Relating Seismic Design Values to the Richter Scale
RE: Relating Seismic Design Values to the Richter Scale
RE: Relating Seismic Design Values to the Richter Scale
On that note, JAE is correct. Generally they use moment magnitude, M-sub-w, nowadays, which is more directly related to energy than the Richter magnitude. Richter M is based on the behavior of a specific type of instrument at some specific distance, so it is a very indirect measure of energy. For a client, you could call moment mag an improved Richter scale - not exactly true, but not a lie.
RE: Relating Seismic Design Values to the Richter Scale
As a footnote, the Richter is really only good in California and it is a Wood-Anderson seismograph within a limited distance from the epicenter.
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RE: Relating Seismic Design Values to the Richter Scale
RE: Relating Seismic Design Values to the Richter Scale
Regardless, if your client has no idea about anything to do with seismic design and asks a question like that. Think long and hard about it, and then make something up.
RE: Relating Seismic Design Values to the Richter Scale
RP = T / [r(1+0.5r)]
r = Probability of exceedance.
T = Exposure time
RP = 50 / [10%(1+0.5(10%))]
RP = 475 years (aka 500 year EQ)
Likewise the 2% in 50 years design is known as the 2500 year EQ.
You'll want to check to see which load probabilities were used in your seismic analysis before giving the 2500 year value a shot.
RE: Relating Seismic Design Values to the Richter Scale
Boore, D. M., W. B. Joyner, and T. E. Fumal (1993). Estimation of Response Spectra and Peak Accelerations from Western North American Earthquakes: An Interim Report, U.S. Geological Survey Open-File Report 93-509, 72 pp.
and subsequent work/comments by Boore in:
Seismological Research Letters; May/June 2005; v. 76; no. 3; p. 368-369; DOI: 10.1785/gssrl.76.3.368
RE: Relating Seismic Design Values to the Richter Scale
This is a common misunderstanding that I can't let go by, lest it be propagated further. The term "return period" misleads a lot of people. It's true that SOME faults show identifiable periodic behavior (including some around the island of Hispaniola, in the news recently), but that is not the general rule, and there are often other potential sources of strong motion in addition to that one particular fault that might have moved this morning. Seismologists typically estimate exeedance probability from historic seismicity using a Poisson model, in which each year is essentially considered an independent trial, so occurrence of the so-called "2500-year earthquake" in 2010 doesn't get us off the hook for larger earthquakes in the following 2500 years. By the Poisson model, it's just as likely in 2011 regardless of whether it occurred in 2010. "Return period" is really just the unfortunate shorthand term used for "reciprocal of annual probability of exceedance." It is more correct to say "The probability of exceedance of this level of shaking is 1/2500 in any given year."
The probability of exceeding the so-called 2500-year EQ in 50 years is
1-(1-1/2500)^50 = 0.0198,
or running it backward, the earthquake with 2% prob of exceedence in 50 years has annual probability equal to
Pa = 1 - (1-0.02)^(1/50) = 4.04x10^-4 = 1/2475
The probability of the "2500-year earthquake" being exceeded in the next 2500 years is
1-(1-1/2500)^2500 = 0.63
Exceedance of the 1/2500 earthquake is at least slightly probable for any period exceeding about 1735 years:
1-(1-1/2500)^1735 > 0.5.
I'd like to see "return period" struck from the dictionary, but it's probably too late for that.