[Shake-dev] Re: [Fwd: Re: Solution: regression distances and plotregr?]
Jack Boatwright
boat at usgs.gov
Wed Mar 7 23:34:57 GMT 2007
Pete,
Really, there is only one fault measure used in any of these calculations,
which is the
3D distance from the station to the source. Joyner-Boore calculate this
distance by using a fixed source depth, h, in the equation you quote below.
It's just that when they wrote the 1979 paper, they didn't want to be
bothered with assigning a source depth to each earthquake (centroid,
hypocentral, ...) and solved for a source depth that fit the whole data
set. The Rjb is the closest horizontal distance to the surface projection
of the fault, but Rjb is always Pythag- orithmed to 3D distance in their
attenuation relation. Another reason that Joyner & Boore could get away
with the single depth approximation was that they were looking at large
earthquakes, whose ruptures usually extended from 10 km depth or more to
the surface.
For moderate earthquakes, however, the rupture area is much smaller. A
good rule of thumb is that a M4 event has a rupture length of a kilometer
or less. Thus we expect that for these earthquakes source depth has a
stronger effect on attenuation. Compare, for example, one of the shallow
Geysers events with the high near-field PGAs with one of the deep Livermore
events. Generally, they have much different attenuations.
Remember that when Dave Wald modelled the Nisqually earthquake, he had to
go in and manually adjust the "fixed" source depth in the Joyner-Boore
formula to model the attenuation. I think he ended up using h = 30 km or
so.
So the best approach would be to use the general distance term R =
sqrt(Rjb**2 + h**2).
Then for the Joyner-Boore attenuation relations in, HazusPGV, h is fixed to
whatever depth they have determined fits the data set best. But if we use
Small_Seg for moderate earthquakes, then we use the actual source depth for
h. This doesn't seem to be sufficient grounds for a big fight.
The only further question is how you want to plot the data in plotregr.
Dave Boore was impressed by your use of Rjb as the ordinate for the
Lafayette earthquake. If you want to plot the small_seg attenuation curve,
however, it will not be a fixed function of Rjb, but will also vary in
shape with the source depth. But that's okay.
take care, Jack
At 1:58 PM -0800 3/7/07, Peter Lombard wrote:
>Peggy and Bruce,
>
>Bruce's fix should help us for events with M < 5.5. For larger events, we use
>Large_Seg.pm, another of Jack's regressions. Large_seg has similar problems:
>it uses hypocentral distance for PGA and PGV, distance to the projection of
>the hypocenter to the seismogenic(?) depth for PSA. And the depth is different
>for each of the three PSA periods.
>
>The more I look at ShakeMap codes, the more confused I get about distances
>used by regressions.
>
>Take the Small.pm regression for example. The comments at the top of the file
>say:
>
># Regression form:
># (same as Boore, Joyner and Fumal, 1997, SRL, Volume 68, p. 128.
># log_10 (PGA,PSV) = B1 + B2(M-6) + B3(M-6)**2 - B5*ln(R) - Bv*ln(Vs/Va),
>#
># where R = sqrt(Rjb**2 + h**2)
>
>What does that tell me about which distance measure is used here?
>
>Then in the maximum() function there is this line:
>
> my $Rjb = (defined $dist) ? $dist : dist_rjb($lat,$lon,$this);
>
>In other words, it uses Joiner-Boore distance unless it is given any other
>distance as an argument.
>
>But then it recomputes Rjb into some other distance measure in _psa_formula():
>
> $R = sqrt($Rjb**2 + $c{h}**2);
>
>Here $c{h} = 6.0 for PGA, PGV, PSA. At least this is consistent with the
>comment at the top of the file. But it is really not clear to me that this is
>much better that the case of Small_Seg.pm.
>
>---
>
>It looks like I have opened a horrible can of worms, for which I
>apologise. Hopefully the exports, Bruce and Dave, can correct my confusion.
>
>Pete
>
>
>
>Peggy Hellweg writes:
> > Hi Bruce, Pete
> >
> > your suggestion for fixing it sounds good to me.
> >
> > Pete, may this help plotregr?
> >
> > Peggy
> >
> > -------- Original Message --------
> > Subject: Re: Solution: regression distances and plotregr?
> > Date: Wed, 7 Mar 2007 13:05:41 -0700
> > From: Jack Boatwright <boat at usgs.gov>
> > To: peggy at seismo.berkeley.edu, Peter Lombard <lombard at seismo.berkeley.edu>
> >
> > Fine. NB- it works now.
> >
> >
> > At 12:03 PM -0800 3/7/07, Peggy Hellweg wrote:
> > >Hi Jack,
> > >
> > >is this an OK way to deal with the "regression distance problem" for
> > >Small_Seg?
> > >
> > >Peggy
> > >
> > >-------- Original Message --------
> > >Subject: Re: regression distances and plotregr
> > >Date: Wed, 7 Mar 2007 10:47:58 -0800
> > >From: Bruce Worden <bruce at gps.caltech.edu>
> > >To: Pete Lombard <lombard at seismo.berkeley.edu>, Howard G Bundock
> > ><bundock at usgs.gov>
> > >CC: shake_dev at seismo.berkeley.edu, Peggy Hellweg
><peggy at seismo.berkeley.edu>
> > >References: <17898.2102.936430.691029 at gargle.gargle.HOWL>
> > >
> > >Pete/Howard,
> > >
> > >I think I can fix Small_Seg to work for PGA and PGV (which means MMI,
> > >too) without much trouble. The PSAs are the issue, but since this is
> > >a regression for small events, you probably don't need those. For
> > >any event you wanted to run with -psa, you could use HazusPGV.
> > >
> > >Would that work for you?
> > >
> > >Bruce
> > >
> > >On Mar 3, 2007, at 3:43 PM, Peter Lombard wrote:
> > >
> > >> Bruce,
> > >>
> > >> I have found a problem in plotregr that I really don't know how to
> > >> solve. It
> > >> may also be a problem in grind; you will have to evaluate that!
> > >>
> > >> When I wrote plotregr, I intended it to plot the data values so
> > >> that they
> > >> could be directly compared with the regression for the event
> > >> magnitude. That
> > >> means that the event data should be plotted at the distance that the
> > >> regression module uses when it computes the regression values.
> > >>
> > >> Actual event data shows I have not achieved my goal. In NC, we use the
> > >> Small_Seg regression, which uses hypocentral distance for PGA and
> > >> PGV. A
> > >> recent event here had a hypocentral depth of 16.6 Km. A regression
> > >> plot
> > >> (attached) shows one station plotted at less than 4 km distance.
> > >> That's not
> > >> what I want.
> > >>
> > >> <pga_regr.gif>
> > >>
> > >> In plotregr, I try to use the distance function used by the
> > >> regression, using
> > >> the following code (borrowed from grind):
> > >>
> > >> #---------------------------------------------------------------------
> > >> --
> > >> # Determine which regression to use, load it and create an object
> > >> # Get functions for $DIST and $CUSTOM_SITECORR (custom distance
> > >> and
> > >> # site correction functions)
> > >>
> > >> #---------------------------------------------------------------------
> > >> --
> > >> my $regress = get_regression($src,$faultcoords);
> > >> %amp_sd = $regress->sd();
> > >>
> > >> $DIST = \&dist_rjb;
> > >> $CUSTOM_SITECORR = undef;
> > >>
> > >> if (defined $regress->{dist}) {
> > >> print "Using custom distance formula\n";
> > >> $DIST = $regress->{dist};
> > >> }
> > >>
> > >> The problem is that most regressions don't provide access to the
> > >> function that
> > >> is used by the regression to compute distance. Some regression
> > >> modules use
> > >> different distance measures for the different PGA, PGV, PSA values.
> > >> Thus the
> > >> regressions' distance function needs an argument to specify for which
> > >> regression variable the distance is to be calculated.
> > >>
> > >> For the plotregr program, this leads to misleading plots at near
> > >> distances.
> > >>
> > >> Is this a problem for grind? Does it mean that the "wrong" distance
> > >> is being
> > >> used when comparing station data against the regression for the bias
> > >> computation?
> > >>
> > >> Or is am I mistaken in my understanding of how ShakeMap works?
> > >>
> > >> Pete
> > >
> > >
> > >--
> > >
> > >------------------------------------------------------------------
> > >Dr. Peggy Hellweg University of California, Berkeley
> > >peggy at seismo.berkeley.edu Berkeley Seismological Laboratory
> > >Phone: 510-643-9449 213 McCone Hall # 4760
> > >Fax: 510-643-5811 Berkeley, CA 94720-4760
> > >
> > >There is no problem so great or grave that it cannot be much
> > > diminished by a nice cup of tea. -- Bernard-Paul Heroux
> >
> >
> >
> >
> > --
> >
> > ------------------------------------------------------------------
> > Dr. Peggy Hellweg University of California, Berkeley
> > peggy at seismo.berkeley.edu Berkeley Seismological Laboratory
> > Phone: 510-643-9449 213 McCone Hall # 4760
> > Fax: 510-643-5811 Berkeley, CA 94720-4760
> >
> > There is no problem so great or grave that it cannot be much
> > diminished by a nice cup of tea. -- Bernard-Paul Heroux
> >
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