[Shake-dev] Re: [Fwd: Re: Solution: regression distances and plotregr?]
Jack Boatwright
boat at usgs.gov
Fri Mar 9 17:02:34 GMT 2007
Pete,
Nice plots and an interesting suggestion. I was off talking about
earthquakes to a high school yesterday (the sound of many students
sleeping). Yes, an earthquake with an updip rupture direction might be
better fit just using a shallower depth for the attenuation curve. The
updip rupturing events have a tendency to produce wild shakemaps (some of
the Geysers events, the Simi Valley event, ...). My preference would be to
solve the wider directivity/attenuation problem, rather than just the updip
part, but it deserves talking about.
take care, Jack
At 5:54 PM -0800 3/7/07, Peter Lombard wrote:
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>Jack,
>
>Your explanation help clarify things for me; thanks.
>
>I tried an experiment. I ran the plotregr program on the original station data
>but with the depth set to 166.6, ten times the actual depth. I expected to see
>that the shape of the regression curve woould change at this depth, but that
>the data would not move on the plot. That would convince me that the
>regression depends on depth, but that the distance value returned by the
>Small_seg regression module is independent of source depth. And that is what
>you see in the "pga_regr_deep" deep plot, attached.
>
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>
>Also attached is the regression plot for the depth as resported, 16.6 Km.
>
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>
>The shape of the "pga_regr_deep" plot got me thinking: if the regression drops
>so low at close plotted distances compared to the data, what if I do the above
>experiment at a depth shallowere than 166 km? So I tried it at 1.66 km; see
>the attached "pga_regr_shallow" plot.
>
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>
>This has the regression following the data more closely than for deeper
>depths. What do seismologists think of this?
>
>Note that I did not recompute the bias in any of these experiments. All I did
>was to tell plotreg that the source depth was 1.66 or 166.6 (by editting the
><evid>/output/stationlist.xml file.)
>
>
>---
>
>I think I am convinced that plotreg is plotting both data and regression
>values against the Joiner-Boore depth. That is good because it means the data
>and regressions are being compared on an "equal basis", apples to apples. And
>I think that means that when grind does its bias calculation, it is also
>comparing station data and regression values using the same depth measure.
>
>For people who expect to see the regression plotted in terms of its defined
>distance measure (hypocentral distance for Small_Seg) it is confusing to see
>the plot using a different distance measure.
>
>The difficulty, as Bruce pointed out, is that the regression modules don't
>always make their "defining" distance measure available to external code. As
>long as grind can compare data and regression values on an equal basis,
>perhaps we should live with that limitiation. The reqression plots from
>plotregr are not intendend to be published; thay are a tool to assisit in
>evaluating ShakeMaps.
>
>Pete
>
>
>Jack Boatwright writes:
> > 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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