Long-Term, Time-Dependent Probabilities for UCERF3
By the 2014 WGCEP
This document is skeletal, but reviewable in terms of methodology and results.
Having the Time Independent Model Report will be handy while reviewing this
document (http://pubs.usgs.gov/of/2013/1165/).
Abstract
Innovations:
 More self-consistent probability calculation
 Support for magnitude-dependent aperiodicity
 Accounting for historic open intervals on all faults
Remaining Issues/Questions:
 More vetting of date-of-last-event data (Ts)?
 Apply currently excluded (because “inadequate”) date-oflast-event data in a separate logic tree branch? Or does
accounting for the historic open interval get us close
enough for now?
 Is 1875 an adequate default historic open interval, and/or
should we apply fault- or region-specific values?
 How much fault-by-fault explanation of U2 to U3 changes
and logic-tree-branch influence is needed here?
 UCERF2 included the empirical model on faults; how
much should we discuss this?
* USGS Peer Review DISCLAIMER: This draft manuscript is distributed solely for purposes of
scientific peer review. Its content is deliberative and predecisional, so it must not be disclosed or
released by reviewers. Because the manuscript has not yet been approved for publication by the U.S.
Geological Survey (USGS), it does not represent any official USGS finding or policy.
Introduction
Methodology
We utilize a new methodology for computing elastic-rebound-motivated
earthquake probabilities, which solves a self-consistency problem with the previous
approach (WGCEP; 2003, 2007) that worsens when segmentation assumptions are
relaxed. Full details are given by Field (2014; Available Here), including a comparison
to the previous approach, an analysis of what current physics-based earthquake
simulators imply with respect to elastic rebound predictability, and Monte Carlo
simulation tests of the new methodology.
The approach, like its predecessor, assumes the availability of a long-term
earthquake-rate model, which gives the frequency of all possible supra-seismogenic
ruptures on a fault or fault system, where the latter is represented by some number of
fault sections (need to add Figure). From this long-term rate model, the frequency of
supra-seismogenic events on each fault section can be computed as
𝑅
𝑓𝑠 = ∑ 𝐺𝑠𝑟 𝑓𝑟
𝑟=1
where 𝑓𝑠 is the frequency of the sth section (or subsection), 𝑓𝑟 is the long-term rate of the
rth rupture, and matrix Gsr indicates which sections are utilized by each rupture (values
are 1 or 0). The mean recurrence interval of each fault section is then computed as
1
𝜇𝑠 = 𝑓 .
𝑠
The previous approach (WGCEP, 2003, 2007) involved computing a conditional
probability for each fault section using this recurrence interval (𝜇𝑠 ), the time since last
event on the section (Ts), and an assumed aperiodicity (). The Brownian Passage Time
(BPT) renewal model (Matthews et al., 2002) was used for the calculation, which gives
results that are similar to applying a Lognormal distribution.
The probability for each
rupture was then computed by aggregating the associated section probabilities
(essentially multiplying the long-term rupture rate by a weighted average of the faultsection probability gains).
Rather than averaging section probabilities, the new approach averages section
recurrence intervals and the dates of last event. We first assume that a given rupture will
be the next event to occur, and then compute the expected recurrence interval as a
weighted average of the long-term recurrence intervals of the sections involve:
𝜇𝑟𝑐𝑜𝑛𝑑 =
∑ 𝜇𝑠 𝐴𝑠
∑ 𝐴𝑠
where the weights are section area (𝐴𝑠 ), and the sums are only over the sections utilized
by the rth rupture (matrix Gsr is implicit here). The superscript “cond” indicates that the
recurrence interval is conditioned on the fact that rupture will be the next event to occur.
Due to the existence of many overlapping rupture possibilities (e.g., with slightly
different endpoints), these conditional recurrence intervals are generally much lower than
that implied by the long-term rate of the rupture (𝜇𝑟 = 1/𝑓𝑟 ). In fact, the recurrence
interval for any given rupture goes to infinity as the fault discretization becomes
infinitesimally small.
We also define an average, normalized time since last event for the rth rupture as
𝜂𝑟 =
∑(𝑇𝑠 /𝜇𝑠 )𝐴𝑠
∑ 𝐴𝑠
where 𝑇𝑠 is the elapsed time on the sth section (which may vary between sections in an
un-segmented model), and the sums are, again, only over the sections utilized by the rth
rupture.
Recall that BPT renewal model probabilities depend on only three parameters: the
time since last event normalized by the mean recurrence interval (𝜂 = 𝑇/𝜇), the meannormalized forecast duration (∆𝑇/𝜇), and the assumed aperiodicity (𝛼). We therefore
have all the information needed to compute the conditional BPT probability for a given
rupture, which we write as 𝑃𝑟𝐵𝑃𝑇 . Note that this probability is “conditional” in both the
traditional sense (that there has been a specified period of time since the last event), and
in the sense that the rth rupture is assumed to be the next event to occur.
We now account for the fact that we lack knowledge of which rupture will
actually occur next, and that there are many overlapping possibilities (e.g., more than
60,000 for points on the Mojave section of the San Andreas). We simply use the ratio of
the conditional rupture recurrence interval to the long-term recurrence interval (𝜇𝑟𝑐𝑜𝑛𝑑 /
𝜇𝑟 ) as proxy for probability that the rth rupture is chosen given an occurrence of one of
the overlapping ruptures:
𝑃𝑟𝑈3 = 𝑃𝑟𝐵𝑃𝑇 [
𝜇𝑟𝑐𝑜𝑛𝑑
]
𝜇𝑟
(1)
In words, 𝑃𝑟𝐵𝑃𝑇 is the probability of having the rth rupture in the given timespan,
conditioned on the fact that it will be the next event to occur, and (𝜇𝑟𝑐𝑜𝑛𝑑 /𝜇𝑟 ) represents
the relative likelihood of selecting the rth rupture given an occurrence of one the
overlapping possibilities.
The superscript “U3” indicates that this approach was
developed for UCERF3.
Again, Field (2014) demonstrates that this approach is more self-consistent, less
biased with respect maintaining long-term rates in Monte Carlo simulations, and
generally consistent with the first-order elastic rebound predictability implied by physicsbased earthquake simulators. Such support is more than can be said of previous WGCEP
approaches, although we acknowledge that adequate data for testing any elastic-rebound
model is still lacking.
Unknown Time Since Last Event and Historic Open Intervals
The methodology outlined above assumes knowledge of the date of last event on
each fault section, which at this time is unavailable for most California faults. It also
does not consider the historic open interval, 𝑇𝐻 , defined as the period of time over which
it is known that an event did not occur (i.e., since record keeping began).
To address this, let 𝑓(𝑡) be the probability density function (PDF) of recurrence
intervals for a given renewal model. If the time since last event is known only to be
greater than 𝑇𝐻 , then the probability of having an event over forecast duration (∆𝑇) is
computed as
𝑇 +∆𝑇
∆𝑇 − ∫𝑇 𝐻
∞
𝐻
𝐹(𝑇) 𝑑𝑇
∫𝑇 [1 − 𝐹(𝑇)]𝑑𝑇
𝐻
(Field and Jordan, 2014; Available Here), where 𝐹(𝑇) is the cumulative distribution
𝑇
(𝐹(𝑇) = ∫0 𝑓(𝑡)𝑑𝑡). We use this equation to compute 𝑃𝑟𝐵𝑃𝑇 when the date of last event is
unavailable on all fault sections of the rupture.
The situation is more complicated, however, when we know the date of last event
on some fault sections, but not others. The PDF for the time since last event, 𝑝(𝜏) ,
conditioned on the fact that is greater than 𝑇𝐻 , is given as
𝑝(𝜏|𝜏 ≥ 𝑇𝐻 ) =
1−𝐹(𝜏)
∞
∫𝑇 [1−𝐹(𝑡)]𝑑𝑡
(2)
𝐻
(Field and Jordan, 2014; Available Here). In principle, we could aggregate such PDFs
over all relevant fault sections to get a joint probability for the date of last event.
However, each fault section will have a different 𝑝(𝜏) (e.g., if 𝜇𝑠 varies between them).
Another problem is that the recurrence interval distribution at a point on a fault, or fault
section, does not generally agree with typical renewal models (Field, 2014); for example,
very short recurrence intervals can occur due to overlap among ruptures that occur on
adjacent parts of a fault. We therefore cannot safely assume a general form for 𝑓(𝑡) on
fault sections (at least not as safely as the assumption with respect to conditional ruptures
above; Field, 2014). A final complication is correlation in the date of last event among
fault sections, as the most recent rupture generally involves multiple sections. These
complications necessitate some simplifying assumptions.
The approach taken here is as follows. First, we assume that, for a given rupture,
the date of last event is the same on all the fault sections where currently unknown, which
we write as 𝜏′. For the purpose of defining the probability distribution of 𝜏′, written as
𝑝(𝜏′|𝜏′ ≥ 𝑇𝐻 ) and given by Equation (2), we compute the mean recurrence interval as the
average of section values where the date-of-last-event is unknown (again, weighted by
section areas).
We now have the probability distribution 𝑝(𝜏′|𝜏′ ≥ 𝑇𝐻 ) for candidate
values of 𝜏′. Each of these is then combined with average time since last event where
known, 𝜏 𝑘 , in order to get a total candidate time since last event for the rupture:
𝑇𝑟′ =
𝐴𝑢 𝜏 ′ + 𝐴𝑘 𝜏 𝑘
𝐴𝑢 + 𝐴𝑘
where 𝐴𝑘 and 𝐴𝑢 are the total section areas where known and unknown, respectively. To
ensure full consistency with the 𝜇𝑟𝑐𝑜𝑛𝑑 and 𝜂𝑟 definitions above, 𝜏 𝑘 is computed as the
average normalized time since last event multiplied by average recurrence interval:
𝜏𝑘 = (
∑(𝑇𝑠 /𝜇𝑠 )𝐴𝑠
∑ 𝜇𝑠 𝐴𝑠
)(
)
∑ 𝐴𝑠
∑ 𝐴𝑠
where the averaging here is over sections with known date of last event. Finally, for each
total candidate time since last event, 𝑇𝑟′ , we compute the implied conditional probability
of the rupture, 𝑃𝑟𝐵𝑃𝑇 (𝑇𝑟′ ) , and combine all candidate probabilities using the total
probability theorem:
∞
′
∫ 𝑝(𝜏′|𝜏′ ≥ 𝑇𝐻 )𝑃𝐵𝑃𝑇
𝑟 (𝑇𝑟 )𝑑𝜏′
𝑇𝐻
Conveniently, this formulation reverts to the simpler cases above when either the date of
last event is known on all fault sections, or known on none of them; this is the reason for
using the relatively complicated expression for 𝜏 𝑘 above (as opposed to simply averaging
𝑇𝑠 where known).
Supporting Data
Aperiodicity Values
Another advantage of the new probability calculation is the ability to apply
magnitude-dependent aperiodicity.
As discussed by Field (2014), a decrease in
aperiodicity with magnitude is both implied by current physics-based simulators, and
physically appealing in that smaller events are presumably more influenced by evolving
stress heterogeneities. Table 1 lists three sets of aperiodicity values tested by Field (2014),
which we adopt as alternative logic-tree branches with equal weights (at least for now).
Table 1. Magnitude-dependent aperiodicity options adopted for UCERF3.
Logic Tree Branch
LOW RANGE
MID RANGE
HIGH RANGE
M≤6.7
0.4
0.5
0.6
6.7<M≤7.2 7.2<M≤7.7
0.3
0.2
0.4
0.3
0.5
0.4
M>7.7
0.1
0.2
0.3
Note that these aperiodicity values apply to conditional ruptures, and those
implied for a point on a fault (e.g., from a paleoseismic study) are considerably larger.
For example, the UCERF3 Monte Carlo simulations conducted by Field (2014) imply
average section aperiodicity values of 0.5, 0.6, and 0.7 for the low, mid, and high-range
options listed in Table 1; for comparison, the values assumed for UCERF2 were 0.3, 0.5,
and 0.7 (with weights of 0.2, 0.5, and 0.3, respectively)
Date of Last Event Data
Relaxing segmentation means we can no longer assume that a paleoseismic
constraint on the date-of-last-event applies to an entire segment. In fact, we may have no
information on how such observations extend along a fault. One can imagine various
sophisticated solutions to this problem, including something analogous to the “Stringing
Pearls” analysis of Biasi and Weldon (2009). We limit ourselves here, however, to a
relatively straightforward, more tentative, interpretation of the date.
The entire date-of-last-event dataset, compiled by Tim Dawson, Ray Weldon, and
perhaps others, is available here:
http://www.wgcep.org/sites/wgcep.org/files/UCERF3_OpenIntervals_ver8.xls
Their analysis separates the constraints into three categories:
1. Well Resolved Historical
2. Well Resolved Paleoseismic
3. Inadequately Resolved Paleoseismic.
Here, “well resolved” means that we can confidently identify the lateral extent of the
rupture, and these are the constraints we consequently use in UCERF3. Table 2 lists the
names of fault sections that have such data (on one or more of the associated subsections).
The “inadequately resolved” paleoseismic data, which we exclude in UCERF3, are listed
in
Table 3.
Both tables indicate whether the section was treated as time dependent in
UCERF2 (in an elastic-rebound sense), and Table 4 lists those treated as time dependent in
UCERF2, but that currently lack even inadequate data.
22 fault sections have been elevated to the time-dependent category since
UCERF2 (those in Table 2 without an “X” in column 4). However, 11 have been demoted
to the inadequately resolved category (
Table 3),
including sections of the Hayward, Rodgers Creek, and Calaveras faults. Even
worse, nine that were treated as time dependent in UCERF2 currently lack even an
inadequately resolved constraint (Table 4). These demotions are generally a consequence
of relaxing segmentation assumptions.
The inadequately resolved list (
Table 3)
is sorted according to the normalized time since last event, defined as elapse time
divided by the UCERF3-implied section recurrence interval. Those at the top of the list
imply lower probability gain, relative to long-term rates, while those at the bottom
suggest a relatively high gain. This ordering might help prioritize any attempts to elevate
some of these constraints to the well-resolved category. The inadequately resolved cases
could also be applied in an alternative, lower-weighted logic-tree branch. Doing so,
however, would require someone estimating what the lateral extent of each observation is.
Historic Open Interval
For the preliminary calculations presented here, we use the year of 1875 to define
the open interval (𝑇𝐻 = 2014 - 1875 = 139 years). That is, for faults where we lack a date
of last event, we assume it is prior to 1875. We understand there may be some observed
post-1875 supra-seismogenic events that remain unassociated. To handle these properly,
logic-tree braches with associated weights could be assigned for all the generating fault
possibilities. However, unless the event can be associated with only a few candidates, it
is not likely to have a big impact on the results, and certainly not compared to other
epistemic uncertainties. We explore sensitivity to the choice of historic open interval
below, although the question of whether this should be spatially variable remains.
Table 2. Fault sections for which the date of last event is well resolved on one or more of its subsections,
together this the associated time since last event. An “X” in the “Used In UCERF2” column indicates that
the fault section was treated as time dependent in UCERF2 (in an elastic-rebound sense).
Fault Section Name
Years Since
Last Event
(as of 2014)
Burnt Mtn
Camp Rock 2011
Cerro Prieto
Elmore Ranch
Elsinore (Glen Ivy)
Emerson-Copper Mtn 2011
Eureka Peak
Greenville (No) 2011 CFM
Hayward (South) 2011 CFM
Hector Mine
Hilton Creek 2011 CFM
Homestead-Valley-2011
Imperial
Johnson-Valley-(No)-2011-rev
Kickapoo
Laguna Salada
Northridge
Owens Valley
Pisgah-Bullion-Mtn-Mesquite-Lk
San Andreas (Big Bend)
San Andreas (Carrizo) rev
San Andreas (Cholame) rev
San Andreas (Mojave N)
San Andreas (Mojave S)
San Andreas (North Coast) 2011 CFM
San Andreas (Offshore) 2011 CFM
San Andreas (Parkfield)
San Andreas (Peninsula) 2011 CFM
San Andreas (San Bernardino N)
San Andreas (Santa Cruz Mts) 2011 CFM
San Jacinto (Anza) rev
San Jacinto (Borrego)
Sierra Madre (San Fernando)
Superstition Hills
White Wolf
San Jacinto (Anza) rev
San Jacinto (Clark) rev
San Andreas (North Branch Mill Creek)
San Andreas (Coachella) rev
San Jacinto (Stepovers Combined)
Rose Canyon
21
21
79
26
103
21
21
33
145
14
33
21
73
21
21
121
19
141
14
156
156
156
156
156
107
107
9
107
201
107
95
45
42
26
61
213
213
333
333
213
360
Calendar
Year
1992
1992
1934
1987
1910
1992
1992
1980
1868
1999
1980
1992
1940
1992
1992
1892
1994
1872
1999
1857
1857
1857
1857
1857
1906
1906
2004
1906
1812
1906
1918
1968
1971
1987
1952
1800
1800
1680
1680
1800
1653
Used In
UCERF2
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Data Type
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Historical
Paleoseismic
Paleoseismic
Paleoseismic
Paleoseismic
Paleoseismic
Paleoseismic
Table 3. Names of fault sections that have an inadequately resolved paleoseismic constraint on the date of
last event (in terms of being able to infer the lateral extent of rupture along the fault). “Normalized Time
Since” is the time since last event divided by the UCERF3-implied average recurrence interval for the
associated section; the table is sorted in ascending order, meaning those listed at the top have a lower
probability of occurrence, and vise versa with respect to those at the bottom. An “X” in the “Used In
UCERF2” column indicates that the fault section was treated as time dependent in UCERF2 (in an elasticrebound sense).
Fault Section Name
Puente Hills
Incline Village 2011 CFM
Compton
Elsinore (Temecula) rev
San Cayetano
Garlock (Central)
Panamint Valley
Garlock (West)
Elsinore (Julian)
San Gregorio (North) 2011 CFM
Little Salmon (Onshore)
Lenwood-Lockhart-Old Woman Springs
Lenwood-Lockhart-Old Woman Springs
Garlock (Central)
Lenwood-Lockhart-Old Woman Springs
Calico-Hidalgo
Green Valley 2011 CFM
Calico-Hidalgo
Rodgers Creek - Healdsburg 2011 CFM
Hayward (No) 2011 CFM
San Jacinto (Superstition Mtn)
Garlock (East)
Whittier alt 1
Calaveras (No) 2011 CFM
Green Valley 2011 CFM
Chino alt 1
Years Since
Last Event
(as of 2014)
Normalized
Time Since
313
642
1288
281
353
468
563
563
1225
491
357
1863
1863
468
1863
1363
398
1363
323
300
473
1600
1863
721
398
14263
0.09
0.11
0.26
0.26
0.28
0.38
0.43
0.46
0.49
0.51
0.56
0.56
0.56
0.59
0.60
0.82
0.83
0.83
0.91
0.92
0.94
1.06
1.16
1.18
1.18
6.16
Used In
UCERF2
X
X
X
X
X
X
X
X
X
X
X
Table 4. Fault sections that were treated as time dependent
in UCERF2 (in an elastic-rebound sense), but that currently
lack any type of date-of-last-event constraint.
UCERF2 Fault Section Name
Calaveras (Central)
Calaveras (So)
Elsinore (Coyote Mountain)
Elsinore (Glen Ivy stepover)
San Andreas (San Bernardino S)
San Andreas (San Gorgonio Pass-Garnet Hill)
San Jacinto (Coyote Creek)
San Jacinto (San Bernardino)
San Jacinto (San Jacinto Valley) rev
Results
UCERF3 has over 2,000 fault subsections in the model (the exact number
depending on which fault is utilized). We show the probability of one or more events for
each subsection in our map-based plots, but aggregate subsection probabilities back onto
the main “parent” fault sections when listing values.
Probabilities for each of the
>200,000 ruptures are not tabulated here, but are available upon request, and will
eventually be posted for those wishing to implement the model.
We compute both 5- and 30-year forecasts (starting at 2014), and present
probabilities for all supra-seismogenic ruptures, and for M≥6.7 and M≥7.7 thresholds.
We also tabulate minimum and maximum values among the logic tree branches, implied
probability gains (relative to Poisson), and UCERF2 results for comparison where
possible. In addition, we have explored sensitivity to logic tree branches, and to various
calculation options (section averaging techniques, historic open interval assumptions,
various logic-tree branch averaging approximations). A representative subset of the
analyses is presented below.
The UCERF3 time-independent model has 1,440 logic-tree branches. Adding the
three aperiodicity options (Table 1) leads to 4,320 branches for the time-dependent model.
Unless otherwise noted, results represent an average over all these branches (weighted by
the relative probability of each). All results are posted (with explanations/legends) at the
following web site:
http://opensha.usc.edu/ftp/kmilner/ucerf3/TimeDependent_AVE_RI_AVE_NORM_TIME_SINCE/
Below, we summarize results for M≥6.7 probabilities for a 30-year forecast.
Subsection Probabilities
Figure 1a shows 30-year, M≥6.7, branch-averaged probabilities for each
UCERF3 fault subsection, together with the implied probability gain (Figure 1b), and
the ratio with respect to UCERF2 for the faults used in both studies (Figure 1c).
It’s important to understand that the probability gains in Figure 1b represent an
average over all ruptures, essentially weighted by the relative rate of each. Figure 1d
shows the probability gains implied by using the average, long-term recurrence interval
of each subsection (𝜇𝑠 , including all supra-seismogenic ruptures), together with the time
since last event where known (Ts) and an assumed aperiodicity () of 0.3; this represents
the result that would be obtained if each subsection ruptured only by itself. Figure 1d
exhibits both more extreme values and more spatial viability along faults, highlighting
the strong influence of averaging in Figure 1b. The probability gain for any one rupture
in UCERF3, however, is more like the along-fault average of those in Figure 1d. Indeed,
if we limit ourselves to smaller events, the probability gain maps look more like Figure
1d.
Figure 1c implies that, for most faults, the differences between UCERF2 and
UCERF3 are greater than the UCERF3-implied probability gains (Figure 1b). There are
many potential sources for the UCERF2 to UCERF3 differences, including: 1) the many
differences in the underlying long-term models (e.g., deformation models, scaling
relationships, degree of segmentation); 2) change in the elastic-rebound probability
calculation (e.g., methodological
differences, magnitude-dependent
aperiodicity,
consideration of historic open interval); and 3) the fact that UCERF2 includes an
“Empirical” model component, which has been dropped in UCERF3 for reasons
discussed in the introduction. Although a complete accounting of the influence of each
of these is beyond present scope, general influences are revealed in the branch sensitivity
tests below.
Figure 1. a) Average M≥6.7, 30-year subsection probabilities for all UCERF3 timedependent model branches. b) UCERF3 subsection probability gains (average time
dependent result divided by average of all time-independent/Poisson model branches).
c) Ratio of UCERF3 to UCERF2 probabilities for faults used in both studies, where
UCERF3 subsection probabilities have been aggregated onto parent sections before
taking the ratio. d) 30-year subsection probabilities computed using average UCERF3
recurrence interval (including all supra-seismogenic ruptures), time since last event
(where known), and an assumed aperiodicity of 0.3; the historic open interval is ignored
(zero) in this plot.
Parent Section Probabilities
M≥6.7 event probabilities have also been aggregated onto the 350 parent fault
sections (the total number between the two fault models). Here, values represent the
likelihood of an event occurring on any part the parent fault section, even if the majority
of the rupture surface is elsewhere. All results are available in the following file:
http://www.wgcep.org/sites/wgcep.org/files/ParentSectProbs_02.xlsx
(and sheets for other magnitude thresholds and a duration of 5 years as well; see the
README sheet).
Table 5 lists the parent fault sections that have the 10 highest and 10 lowest
probability gains (for 30-year, M≥6.7 events). All but three of the lowest gains are due to
recent events, with the exceptions representing faults that mostly rupture with sections
that have recently ruptured: Owens Valley Keough Hot Springs with Owens Valley; White
Wolf (Extension) with White Wolf; and Sargent 2011 CFM with San Andreas (Peninsula)
2011 CFM (plots of the participation of each parent section with neighboring faults are
available at: http://opensha.usc.edu/ftp/UCERF3.3/Model/FaultParticipation/).
That
Sargent 2011 CFM has a lower gain than San Andreas (Peninsula) 2011 CFM (because the
latter is not on the list) results from each participating in a different set of events and
magnitudes, with the latter dictating the applied aperiodicity. If San Andreas (Peninsula)
2011 CFM only ruptured by itself, it would have an even lower gain than listed for
Sargent 2011 CFM (this can be inferred from Figure 1d).
The 10 highest probability gains in
Table 5 are due to a relatively high normalized time since last event and/or the
historic open interval. The highest gain of 2.33 is for San Andreas (San Gorgonio PassGarnet Hill), which does not have date of last event; the high gain is due to the open
interval and its high rate of participation with San Andreas (Coachella) rev (the latter of
which has the highest gain among faults with known date of last event). The exact same
explanation (open interval and participation with San Andreas (Coachella)) applies to all
other parent sections on the list that lack a date of last event, except for Calaveras (So)
2011 CFM, which is due entirely to the historic open interval. The high gains for Imperial
and Eureka Peak, both of which have a date of last event, also result from high
participation with San Andreas (Coachella). Finally, San Andreas (San Bernardino S) has
a high gain (2.07) due to a high normalized time since last event.
Two of the high-gain cases in
Table 5 warrant further discussion, both because they recently ruptured. Joshua
Tree (Seismicity) does not have a date of last event, which could be an error given the M
6.1 1992 Joshua Tree earthquake (WE NEED TO DISCUSS THIS).
Eureka Peak did
recently rupture as part of the 1992 Landers earthquake, but has a high gain due to it
mostly participating with San Andreas (Coachella). Furthermore, Eureka Peak cannot
rupture with Johnson Valley (No) 2011 rev to the north (as it did in the Landers
earthquake) because the two are separated by more than 5 km.
The latter is an
unfortunate limitation of the model, and in retrospect should have been treated as a
special exception the plausibility filter (WE NEED TO DISCUSS THIS TOO).
Table 6 lists the top 10 parent fault sections in terms of total M≥6.7, 30-year
probabilities for both UCERF2 and UCERF3. Those ranked as 1st, 2nd, 4th, and 5th for
UCERF3 were not included in UCERF2. That San Andreas (Creeping Section) 2011 CFM
makes the UCERF3 list might come as a surprise given the fault is dominated by
microseismicity. However, most of these events only slightly penetrate the creeping
section from either the north or south.
Table 5. 30-year, M≥6.7 UCERF3 probabilities aggregated by parent fault section, where the list here
represents sections that have the 10 lowest and 10 highest probability gains. “U3 Mean” is the branchaveraged probability, “U3 Min” and “U3 Max” are the minimum and maximum among branches, “U3 Mean
Poisson” is the branch average time-independent result, and “Prob Gain” is the ratio of “U3 Mean” to “U3
Mean Poisson”. “Fraction with Years-Since Data” represents the percentage of subsections that have a
useable date of last event, “Ave Years Since” is the average where known, and “Ave Norm Time Since Last”
is the latter divided the long-term recurrence interval (for all supra-seismogenic events).
These
probabilities are computed as one minus the total probability that no M≥6.7 ruptures touch any part of
the parent fault section.
Fraction
with
YearsSince
Data
Ave
Years
Since
Ave
Norm
Time
Since
Last
U3
Mean
U3
Min
U3
Max
U3
Mean
Poisson
Prob
Gain
Kickapoo
1.00
22
0.03
1.07E-04
4.82E-07
1.23E-03
4.02E-03
0.02
Owens Valley
1.00
142
0.31
3.99E-03
1.19E-03
1.79E-02
3.92E-02
0.10
White Wolf
1.00
62
0.06
1.66E-03
1.58E-04
1.57E-02
1.22E-02
0.12
Homestead Valley 2011
0.67
22
0.02
1.29E-03
2.45E-05
5.43E-03
9.40E-03
0.12
Owens Valley Keough Hot Springs
0.00
NA
NA
2.89E-03
4.86E-04
1.26E-02
1.82E-02
0.20
Hector Mine
1.00
15
0.01
5.70E-03
1.65E-04
4.07E-02
1.36E-02
0.23
Hilton Creek 2011 CFM
0.75
34
0.05
6.99E-03
3.10E-03
2.01E-02
3.14E-02
0.23
Johnson Valley (No) 2011 rev
0.43
22
0.03
5.64E-03
1.83E-04
2.73E-02
1.37E-02
0.38
White Wolf (Extension)
0.00
NA
NA
2.55E-03
3.18E-05
2.39E-02
5.82E-03
0.40
Sargent 2011 CFM
0.00
NA
NA
8.22E-03
2.37E-04
4.69E-02
1.74E-02
0.42
San Gorgonio Pass
0.00
NA
NA
1.76E-02
3.28E-03
5.43E-02
9.67E-03
1.80
Calaveras (So) 2011 CFM
0.00
NA
NA
2.12E-01
8.85E-02
4.00E-01
1.16E-01
1.81
Brawley (Seismic Zone) alt 1
0.00
NA
NA
3.16E-01
1.23E-01
4.98E-01
1.73E-01
1.84
Imperial
1.00
48
0.96
2.97E-01
4.91E-02
4.98E-01
1.56E-01
1.94
Eureka Peak
0.67
22
0.03
2.55E-04
2.62E-05
1.32E-03
1.31E-04
2.02
San Andreas (San Bernardino S)
1.00
202
1.23
2.54E-01
7.44E-02
4.00E-01
1.22E-01
2.07
San Andreas (Coachella) rev
1.00
334
1.97
3.12E-01
9.23E-02
4.93E-01
1.43E-01
2.16
Brawley (Seismic Zone) alt 2
0.00
NA
NA
3.02E-01
6.16E-02
4.84E-01
1.36E-01
2.21
Joshua Tree (Seismicity)
0.00
NA
NA
1.78E-03
1.64E-04
1.03E-02
7.68E-04
2.31
San Andreas (San Gorgonio PassGarnet Hill)
0.00
NA
NA
2.49E-01
8.89E-02
4.07E-01
1.06E-01
2.33
Parent Section Name
Table 6. The parent fault sections with the top 10 highest M≥6.7, 30-year probabilities,
where “Mean” is the mean probability and “Gain” is the mean divided by the Poissonmodel mean. UCERF2 results are listed at the bottom for comparison. Names marked
with and asterisk in the UCERF3 list were not included in the UCERF2 model.
Rank
UCERF3:
1
2
3
4
5
6
7
8
9
10
UCERF2
1
2
3
4
5
6
7
8
9
10
Parent Section Name
Mean
Gain
Cerro Prieto *
Brawley (Seismic Zone) alt 1 *
San Andreas (Coachella) rev
Mendocino *
Brawley (Seismic Zone) alt 2 *
Imperial
Hayward (So) 2011 CFM
San Andreas (Creeping Section) 2011 CFM
San Andreas (San Bernardino N)
Maacama 2011 CFM
0.32
0.32
0.31
0.30
0.30
0.30
0.29
0.28
0.26
0.26
1.08
1.84
2.16
1.43
2.21
1.94
1.76
1.27
1.70
1.70
San Andreas (Cholame) rev
San Andreas (Coachella) rev
Imperial
San Andreas (Parkfield)
San Andreas (Mojave S)
San Andreas (Carrizo) rev
San Andreas (Big Bend)
San Andreas (Mojave N)
San Andreas (San Bernardino N)
Rodgers Creek - Healdsburg 2011 CFM
0.29
0.28
0.28
0.26
0.24
0.21
0.21
0.20
0.20
0.20
1.29
1.44
1.00
1.30
1.30
1.31
1.31
1.31
1.31
1.40
Aggregate Probabilities for Main Faults:
Table 7 lists aggregate 30-year, M≥6.7 probabilities for several “main” faults,
each of which was treated as time dependent in UCERF2 (in an elastic-rebound sense).
The S. San Andreas exhibits the highest UCERF3 probability (0.58), virtually unchanged
from UCERF2 (0.59) in spite of a gain increase from 1.23 to 1.58.
The biggest
probability increase is on the Calaveras fault, going from 0.07 in UCERF2 to 0.30 in
UCERF3, about a factor of 4. Some of this can be attributed to the gain increase from
0.98 to 1.72, due entirely to the historic open interval (no usable date of last event data
exists for this fault). However, most of the Calaveras increase comes from differences in
the UCERF2 and UCERF3 long-term models.
Note that the UCERF2 Calaveras
probability is not even within the range of UCERF3 values (it is below the minimum in
Table 7).
The biggest probability decrease between UCERF2 and UCERF3 is on the San
Jacinto fault, going from 0.31 to 0.07 (about factor of 0.2). Again, some of this can be
attributed to a gain reduction, from 1.02 to 0.62, but most is due to differences in the
long-term models (e.g., moment rate reduction, as evident in Figure 27b of the timeindependent model report: http://pubs.usgs.gov/of/2013/1165/pdf/ofr2013-1165.pdf).
Again, the UCERF2 value is outside the range of UCERF3 values. Other faults in Table
7 exhibit changes of up to ~60% (N. San Andreas), but results are generally consistent
given the uncertainties.
Table 7. Aggregate 30-year, M≥6.7 probabilities for some “main” faults considered by previous WGCEPs.
All probabilities have been rounded to the nearest percent, and UCERF2 results are listed for
comparison. “Min” and “Max” values represent the minimum and maximum among all logic-tree
branches.
UCERF3, from 2014
Main Fault Name
UCERF2, from 2007
Mean
Min
Max
Gain
Mean
Min
Max
Gain
Calaveras
0.30
0.16
0.52
1.72
0.07
0.01
0.22
0.98
Garlock
0.08
0.02
0.20
1.22
0.06
0.03
0.12
1.06
Hayward-Rodgers Cr
0.35
0.20
0.48
1.66
0.31
0.12
0.67
1.34
N. San Andreas
0.33
0.03
0.68
0.94
0.21
0.06
0.39
0.87
S. San Andreas
0.58
0.20
0.85
1.58
0.59
0.22
0.94
1.23
San Jacinto
0.07
0.01
0.29
0.62
0.31
0.14
0.54
1.02
Elsinore
0.06
0.02
0.17
1.16
0.11
0.05
0.25
0.90
At some point we will add magnitude-probability-distribution plots for these faults (like
Figure 31 in the UCERF2 report).
Magnitude-Probability Distribution (MPD) for regions:
These are like MFDs, but with probability on the y-axis (as shown in the
UCERF2 report). These will be added after at least a preliminary review of fault-based
results, and the following regions will be examined: RELM, NCal, SoCal, LA, SF.
Participation Prob Maps
These will be added later as well. Only needed to add the influence of gridded
seismicity, which has no time dependence in UCERF3.
Hazard Curves and/or Maps
We’re under no contractual obligation to do this for CEA, but we could compare
mean BPT/Poisson and/or mean U3/U2 hazard values, either in map form or a table for
the BSSC test sites.
Branch Sensitivity Tests
The following links are plots showing the influence of each logic-tree branch on
M≥6.7, 30-year, subsection probabilities (please paste the links in your browser if they
don’t load properly, or click the file links that are also listed under “Attachment“ on
this page - http://www.wgcep.org/U3_TimeDepPreview):
1)
2)
3)
4)
5)
6)
7)
8)
http://www.wgcep.org/sites/wgcep.org/files/FaultModels_combined.pdf
http://www.wgcep.org/sites/wgcep.org/files/DeformationModels_combined.pdf
http://www.wgcep.org/sites/wgcep.org/files/ScalingRelationships_combined.pdf
http://www.wgcep.org/sites/wgcep.org/files/SlipAlongRuptureModels_combined.pdf
http://www.wgcep.org/sites/wgcep.org/files/TotalMag5Rate_combined.pdf
http://www.wgcep.org/sites/wgcep.org/files/MaxMagOffFault_combined.pdf
http://www.wgcep.org/sites/wgcep.org/files/SpatialSeisPDF_combined.pdf
http://www.wgcep.org/sites/wgcep.org/files/MagDepAperiodicity_combined.pdf
Results for 5-year durations and the other magnitude thresholds can be found in the
“BranchSensitivityMaps” subdirectories of
http://opensha.usc.edu/ftp/kmilner/ucerf3/TimeDependent_AVE_RI_AVE_NORM_TIME_SINCE/
Each plot in the above files represents the average for a branch subset (e.g., all branches
for Fault Model 3.1) divided by the total branch-averaged result.
In other words,
summing the maps over all options of a given branch (images within each plot above)
produces a value of 1.0 on each fault section. This comparison therefore quantifies the
relative influence of each branch on each fault section.
The main conclusion here is that deformation models generally have the strongest
influence on fault section probabilities, with scaling relationships coming in second, and
the fault models being important in some isolated areas. The influence of other branches,
including aperiodicity, is relatively small (in general). The overall influence of the timedependent probability model (i.e., the gain shown in Figure 1b) is generally moderate, at
least compared to the influence of deformation models and scaling relationships.
Influence of Historic Open Interval Test
The above analysis assumed a historic open interval based on 1875.
Figure 2
shows the relative probabilities for three alternative values: 1850, 1900, and 2014 (the
latter representing zero open interval). Probabilities obtained for 1850 and 1900 show
negligible differences compared to the epistemic uncertainties discussed above. The
difference between 1875 and 2014 is more significant, especially for the higher event-rate
fault sections. A potential improvement would be to have fault-specific or regionally
varying historic open intervals (ANYONE WILLING TO DO THIS VERY QUICKLY?).
Figure 2. Ratio of fault section probabilities obtained for alternative historic open
intervals, divided by those obtained for 1875 (the value assumed in this report). a) 1850;
b) 1900; and c) 2014 (zero historic open interval since the forecast starts at 2014).
Influence of Different Averaging Approaches
As discussed in Field (2014), there are different ways of averaging over
subsections in computing both the conditional recurrence interval (𝜇𝑟𝑐𝑜𝑛𝑑 ) and average
time since last event for each rupture. The formulation presented above averages section
recurrence intervals in computing 𝜇𝑟𝑐𝑜𝑛𝑑 , whereas one could alternatively compute this as
one over the average of section rates. Likewise, one could average the date of last event
on each subsection, rather than averaging the normalized time since last event as
specified above. Extensive testing has been conducted to evaluate the viability and
influence of each option, a full presentation of which is beyond present scope. Suffice it
to say that the formulation presented here represents our current preference, although one
and possibly two alternatives remain viable alternatives. For UCERF3, the differences
are negligible when the date of last event is known on all fault sections, with some
marginally important difference appearing when accounting for unknown last event dates.
The approach here gives probabilities that are in between the two viable alternatives
(meaning adding a logic tree branch would have relatively little influence on average
hazard), and the differences are generally small compared to the influence of the other
epistemic uncertainties anyway. Field (2014) has more discussion of this issue (AND
ANALYSIS RESULTS FOR THIS CAN BE PROVIDED UPON REQUEST).
Remaining Issues/Questions
(repeated from abstract)

More vetting of date-of-last-event data (Ts)?




Apply currently excluded (because “inadequate”) date-of-last-event data
in a separate logic tree branch? Or does accounting for the historic open
interval get us close enough for now?
Is 1875 an adequate default historic open interval, and/or should we
apply fault- or region-specific values?
How much fault-by-fault explanation of U2 to U3 changes and logictree-branch influence is needed here?
UCERF2 included the empirical model on faults; how much should we
discuss this?
Discussion and Conclusions
References
Data and Resources
Acknowledgements