[CEUS-earthquake-hazards] FW: alternative hazard maps

Fri Feb 8 12:20:40 MST 2008

Susan,

You are right that John Anderson and Jim Brune were among the first to
discuss this, "an ergodic assumption is made when PSHA treats that spatial uncertainty of ground motions as an uncertainty over time (temporal uncertainty) at a single point"(Anderson and Brune, 1999). This is what I mean "mixing the temporal and spatial measurements."

I am not suggesting this might bias the hazard maps, but I am saying this is problematic.

Detailed demonstration on how the ground motion uncertainty impact on hazard calculation will take a big space. Any interested person can read the attached paper or other publications.

Let's look at a single M7.7 New Madrid earthquake (500 years recurrence interval) and the hazard in Paducah, Ky. A median PGA and standard deviation of 0.3g and 0.7 (in log) are assumed for Paducah from this earthquake.

>From PSHA, a range of return period, from 500 to millions of years, could be derived (hazard curve). The return periods of 500, 1,000, and 2,500 years are only three points on the hazard curve. The corresponding PGAs will be 0.0, 0.3g, and 0.86g for these return periods. All these ground motions reflect different level of uncertainty, 0.0g with 100% exceeding (sure to occur), 0.3g with 50% exceeding, 0.86g with 20% exceeding. However, these ground motions have been interpreted as that WILL occur in 500, 1,000 and 2,500 years, respectively. These have also been heard over the media, 500 vs. 2,500 events (confusing).

>From PSHA point of view, the ground motion with 500-year return period is equally valid for any users in comparison with other ground motions on the hazard curve (1,000, 2,500, and 1,000,000-year return periods). But I do have concern if the ground motion with 500-year return period is used in this case. And I also think the ground motion with 2,500-year return period is conservative.

Thanks.

Zhenming

-----Original Message-----
From: Susan Hough [mailto:hough at gps.caltech.edu]
Sent: Friday, February 08, 2008 12:13 PM
To: Wang, Zhenming
Cc: ceus-earthquake-hazards at geohazards.usgs.gov
Subject: Re: [CEUS-earthquake-hazards] FW: alternative hazard maps

Okay, I'll confess to confusion here.  Zhenming, you seem to be focusing
on the so-called ergodic assumption, namely that the event-to-event
variability in ground motions will be adequately captured by the
site-to-site variability in recorded ground motions from a limited number
of events.  I believe John Anderson and Jim Brune were among the first to
discuss this.  What I don't understand is, exactly how are you suggesting
this might bias the hazard maps?  Seems to me the real problem in the CEUS
is that we don't have recorded ground motions or instrumental magnitudes
for any large events, so the uncertainties in "attenuation relations"
(really ground motion relations) are a lot more fundamental than any
subtle biases that might be associated with the ergodic assumptions.  But
maybe I'm missing something?

Susan

Susan Hough
Scientist-in-Charge
USGS, Pasadena
hough at gps.caltech.edu

>
> The main point is that "The temporal and spatial measurements are two
> fundamental and critical elements for quantifying earthquake and seismic
> hazard. The temporal and spatial measurements are also two basic elements
> of our society. Mixing these two measurements one way or the other will
> cause problem."
>
> Your probability estimates for a 1811-12 type New Madrid earthquake and
> the ground motions at a site from this 1811-12 type New Madrid earthquake
> demonstrates the problem. Under the assumption that earthquake occurrence
> follow Poisson distribution, you have calculated 10% probability of having
> a 1811-12 type New Madrid earthquake in the next 50 years, derived from
> considering a 500 year AVERAGE recurrence time.  As demonstrated in your
> paper (Frankel, 2004), you can provided a range of probability, 10, 5, 2,
> 1, ..., percents, of having the ground motions for this 1811-12 type New
> Madrid earthquake in the next 50 years (hazard curve), by mixing temporal
> measurement (500-year recurrence interval) and spatial measurement (ground
> motion uncertainty).  These probability estimates are contradictory.
>
> "the seismic hazard maps also include the possibility of magnitude 6
> earthquakes, which will be more frequent than the 1811-12 events."  This
> hazard calculation could only be done by mixing the temporal and spatial
> measurements.
>
> Thanks.
>
> Zhenming
>
>
> ________________________________
> From: ceus-earthquake-hazards-bounces at geohazards.usgs.gov
> [mailto:ceus-earthquake-hazards-bounces at geohazards.usgs.gov] On Behalf Of
> Arthur D Frankel
> Sent: Thursday, February 07, 2008 2:56 PM
> To: ceus-earthquake-hazards at geohazards.usgs.gov;
> ceus-earthquake-hazards-bounces at geohazards.usgs.gov
> Subject: Re: [CEUS-earthquake-hazards] alternative hazard maps
>
>
> Zhenming,
>
>   I would like to amplify some of the points that Buddy Schweig made in
> his excellent response to you.
>
>   When deciding on measures for public safety, such as building codes, it
> is critical to consider the random variability that occurs in natural
> processes, such as the timing of earthquakes and the severity of ground
> motions produced by rupture on a fault.
>
>   The 7-10% probability of having a 1811-12 type New Madrid earthquake in
> the next  50 years is derived from considering a 500 year AVERAGE
> recurrence time, along with an assumption on the probability
> distribution around that average recurrence time.  Unfortunately, there
> is randomness to earthquake occurrence and there is a significant
> probability that we will have an 1811-12 type earthquake in the next 50
> years, well before the 500 year average interval has elapsed.
>
> Take the example of great earthquakes on the Cascadia subduction zone
> (CSZ) of the Pacific Northwest.  There is good paleoseismic evidence
> stretching back at least 5000 years that great earthquakes occur along the
> entire CSZ with an average recurrence time of about 500 years (see Atwater
> and Hemphill-Haley, 1997, USGS Professional Paper 1576; Nelson et al.,
> 2006 in Quaternary Research).   Of course, there is uncertainty in our
> dating of these past earthquakes.  Furthermore, there is natural
> variability in the occurrence of these earthquakes. For example, two great
> earthquakes (the U and W events described in Atwater and Hemphill-Haley)
> may have occurred as little as 100 years apart, given   the closeness in
> time of the central estimates of their dates and the uncertainites in the
> dating.
>
> The variability in earthquake recurrence times is understandable: we know
> that slip on a fault during an earthquake is usually very heterogeneous,
> with some patches on a fault slipping a great deal and other areas of the
> fault hardly slipping at all.  Slip on these other areas is sometimes
> observed to be taken up by the next earthquake (see the 1940 and 1979
> Imperial Valley earthquakes for example).    It is also likely that the
> rate of loading of faults is not constant in time or space.  As I said in
> my previous email, the occurrence of a large earthquake can increase
> stress in some areas and affect the timing of other earthquakes in a
> region, adding to the randomness of earthquake occurrence.
>
>    Buddy is also correct in noting that the seismic hazard maps also
> include the possibility of magnitude 6 earthquakes, which will be more
> frequent than the 1811-12 events.
>
>     When an 1811-12 type New Madrid earthquake occurs again, it will
> produce a range of ground motions, even for locations at similar
> distances from the earthquake fault.  Of course, there are differences
> in soil conditions that will affect the ground shaking and we can
> predict that areas of soft soils will have stronger shaking on
> average.   Even considering sites with similar soils at similar
> distances from the earthquake, there will be substantial variation of
> ground shaking.  For example, if a large earthquake on the Reelfoot
> fault ruptures from northwest to southeast, it will produce higher
> ground motions than average for some locations in northwest Tennessee
> because of the strong pulse of velocity produced by rupture
> directivity.  Areas of the fault where there is larger slip during the
> earthquake will likely produce larger ground velocities at nearby
> sites.   These areas of larger slip will vary from earthquake to
> earthquake, as could the direction of rupture.  Thus, we can't predict
> in advance (at least at our present stage of knowledge) where the
> areas of higher (and lower) than average ground motions will occur.
> But we can account for this variability in our seismic hazard
> calculations and in our building codes.  That is the essence of
> probabilistic seismic hazard assessment.
>
>
> Art Frankel
> U.S. Geological Survey
> MS 966, Box 25046
> DFC
> Denver, CO 80225
> phone: 303-273-8556
> fax: 303-273-8600
> email: afrankel at usgs.gov
> _______________________________________________
> CEUS-Earthquake-Hazards mailing list
> CEUS-Earthquake-Hazards at geohazards.usgs.gov
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>

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