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16th World Conference on Earthquake, 16WCEE 2017
Santiago Chile, January 9th to 13th 2017
MODELING SEISMIC HAZARD BY INTEGRATING
HISTORICAL EARTHQUAKE, FAULT, AND STRAIN
RATE DATA
Y. Rong(1), M. Pagani(2), H. Magistrale(3), G. Weatherill(4)
(1) Senior Lead Research Scientist, Center for Property Risk Solutions, FM Global, Research Division, Norwood, Massachusetts,
USA, yufang.rong@fmglobal.com
(2) Senior Seismic Hazard Modeller, Hazard Team Coordinator, GEM Foundation, Pavia, Italy,
marco.pagani@globalquakemodel.org
(3) Principal Research Scientist, Center for Property Risk Solutions, FM Global, Research Division, Norwood, Massachusetts, USA,
harold.magistrale@fmglobal.com
(4) Senior Seismic Hazard Modeller, GEM Foundation, Pavia, Italy, graeme.weatherill@globalquakemodel.org
Abstract
The OpenQuake-engine software developed by the Global Earthquake Model (GEM) is an open-source tool for the
calculation of seismic hazard and risk. It provides the capability to execute complex seismic hazard calculations on a
range of scales, from detailed site-specific analysis to regional or global-scale models. However, users need to construct
earthquake source models (ESMs), which characterize both the magnitude-frequency distribution of the earthquakes
and their potential finite rupture geometries, and feed the ESMs to OpenQuake for hazard calculations.
In this study, we propose a method to construct ESMs by integrating historical earthquake, geological fault, and strain
rate data. The method requires division of the study area into large seismic zones, based on a set of defined
seismotectonic criteria. For each zone, the seismicity rates are defined by a tapered Gutenberg-Richter (TGR) model.
The TGR a- and b-values are calculated using observed earthquake data, while the corner magnitude is constrained
independently using the seismic moment rate inferred from a geodetically-based strain rate model. Then, we model the
spatial distribution of the seismic activity based on characteristics of active faults, and location and magnitude patterns
of historical earthquakes. The rates of large earthquakes accommodated on active faults are estimated based on the
dimension, slip rate, and paleoseismic data of the faults. Remaining seismicity is distributed to the background using a
smoothed seismicity model. Consistency between observed seismic activity rates and those predicted by the model
should be verified in terms of both spatial and magnitude distributions. To achieve this, the OpenQuake-engine’s event-
based seismic hazard tools are used to generate synthetic catalogs of tens or hundreds of thousands of years duration.
We are developing a toolkit to implement this method. The toolkit is built upon the functionalities of GEM’s Hazard
Modeller’s Toolkit. We use southwest China as an example to illustrate the method, workflow, and toolkit. We build
the toolkit in a flexible manner so that users can make different modeling decisions at each step. This approach will
help make the seismic hazard modeling process more transparent, and prompt the development of new methodologies
for seismic hazard assessment.
Keywords: GEM, Probabilistic Seismic Hazard Analysis, Earthquake Source Model
16th World Conference on Earthquake, 16WCEE 2017
Santiago Chile, January 9th to 13th 2017
1. Introduction
The construction of earthquake source models (ESMs) for probabilistic seismic hazard analysis (PSHA) is a
complex procedure involving various types of information that must be reconciled into a comprehensive
interpretation of the earthquake occurrence process. In recent hazard models, epistemic uncertainties
connected with the various steps of this process are organized into a logic tree structure, which contains the
alternative interpretations for each uncertainty potentially able to control part of the overall results’
variability.
Common methods for the construction of ESMs are well established. They typically comprise the
construction of a harmonized earthquake catalog, the pre-processing of the catalog, the definition and the
characterization of distributed seismicity sources using past seismicity, tectonics and geodesy, the
description and characterization of shallow faults using geologic information, and the definition and
characterization of subduction sources using past seismicity and tectonics. Today, the evolution of methods
for building ESMs is relatively slow. The introduction of new procedures is intermittent, and usually of
limited impact, albeit with notable exceptions such as the Uniform California Earthquake Rupture Forecast
Version 3 model [CITATION Fie14 \l 1033 ]. The creation of new PSHA methodologies is limited on the
one hand by the rate at which new information is obtained and on the other hand by a general lack of
transparency and standardization of the model building process – standardization that currently would be
possible for the most common and uncomplicated cases. The lack of standardization and transparency on
basic methodologies is preventing the implementation of an efficient community-based trial-and-error
process, which would help progress towards new innovative and widely recognized methodologies.
The overall goal of this paper is to present a simple but practical method for constructing an onshore
ESM by leveraging the suite of methods incorporated into the GEM OpenQuake Hazard Modeller’s Toolkit
(oq-hmtk) [CITATION Wea14 \l 1033 ], and to discuss the relative advantages and limitations of alternative
approaches for each step. In the next section, we briefly review the overall structure and the main features
available in the oq-hmtk. In Section 3, we demonstrate the method for constructing an ESM and its workflow
using southwest China as an example. In Section 4, we introduce the OpenQuake Earthquake Model
Building Toolkit concept before summarizing the main results and possible directions for future work in
Section 5.
2. The OpenQuake Hazard Modeller’s Toolkit
The oq-hmtk [CITATION Wea14 \l 1040 ] is a software suite for the preparation of various components of
an ESM organized around three main modules. The first module contains the methods necessary to process a
catalog and build sources for PSHA. These include methods for: declustering a catalog, analyzing the
completeness of a catalog through time, computing the parameters characterizing earthquake occurrence, and
assessing the maximum magnitude on a statistical basis. The second module contains methods for the
construction of earthquake sources starting from information provided by geologic observations. The third
module currently comprises one single calculation workflow based on the work of Bird and Liu [ CITATION
Bir071 \l 1033 ]; this workflow uses the strain rate model obtained by the processing of GPS velocities for
the calculation of seismic occurrence. The oq-hmtk source code can be downloaded from a github repository
(https://github.com/GEMScienceTools/hmtk; license GPL Affero v. 3.0).
3. Workflow of constructing an ESM
The workflow we illustrate here can be used for the construction of ESMs in Active Shallow Crust tectonic
environments by integrating a historical earthquake catalog, active faults, and geodetic strain rates. The
required input data include a homogeneous historical and instrumental catalog, geological information of
active faults (fault plane geometries and slip rates), and a strain rate model describing the long-term
deformation process within the study region.
Active faults are primary sources of earthquake generation, however, not all faults are mapped. As a
result, the fault database is not likely to include every fault that could generate earthquakes relevant to the
16th World Conference on Earthquake, 16WCEE 2017
Santiago Chile, January 9th to 13th 2017
seismic hazard analysis. Moreover, historical earthquake catalogs may not be long
enough to include all the large earthquakes that happened in the past. These drawbacks
are addressed in the modeling process by including another set of useful information based on
geodetic (strain) measurements. For example, tectonic moment rate can be calculated from a strain rate
model based on the reasonable assumption that the long-term average rate of elastic strain is negligible in
comparison to the rate of permanent strains accumulated by frictional faulting (and other mechanisms such
as cold-work plasticity, solution transfer, and dislocation creep [ CITATION Bir071 \l 1033 ]). Under these
assumptions, the tectonic moment provides an upper limit for the seismic moment budget.
In the following subsections, we briefly outline the main steps comprising this workflow, from the
initial processing of the catalog to the final combination of faults and distributed seismicity sources. We
describe each step to emphasize the most crucial and controversial aspects and to promote open discussion.
3.1 Catalog pre-processing
For this step, we assume that a homogenized earthquake catalog with magnitudes defined in terms of
moment magnitude (Mw) is available. GEM provides tools for constructing homogenized catalogs from a
heterogeneous set of catalogs. However, the description of those tools and procedures is beyond the scope of
this paper (see [CITATION Wea16 \l 1040 ]).
Two fundamental steps are completed in this phase. The first is the catalog declustering in which
dependent earthquakes are removed. While the declustering is often uniformly applied to the entire study
area, it is certainly possible to use different declustering parameters in different tectonic regions. In the
example of southwest China, we use a single declustering procedure based on the widely known algorithm of
Gardner and Knopoff [ CITATION Gar \l 1040 ]. The second step is the definition of the magnitude-time
windows in which the catalog can be considered complete, i.e., where we can confidently assume that for
each temporal window considered, the catalog contains all the earthquakes with a magnitude equal to or
larger than a threshold magnitude.
The blue dots in Fig. 1 show the epicenters of earthquakes included in the catalog by Weatherill et al.
[CITATION Wea16 \l 1040 ] and classified as independent mainshocks by the Gardner and Knopoff
declustering algorithm [ CITATION Gar \l 1040 ] for a portion of the example study area; the red crosses
show the dependent earthquakes identified as aftershocks or foreshocks. As expected, the largest
concentration of aftershocks is from the 2008 Mw 7.9 Wenchuan earthquake located in the upper right corner
of the map.
3.2 Seismic source zones definition
Many traditional PSHA models are based on small seismic source zones, and the seismicity rate is assumed
to be uniform within each of the source zones. However, small source zones often do not have enough
historical earthquakes to robustly characterize the earthquake magnitude-frequency distribution (MFD). We
use large seismic source zones to mark large tectonic provinces with ‘similar’ geologic and seismotectonic
characteristics; the use of large areas is motivated by the need to include an adequate number of past
earthquakes in order to provide reliable estimates of the parameters characterizing a simple Gutenberg-
Richter (GR) relationship. However, in our method, the seismicity does not need to be uniformly distributed
within each of the large seismic source zones. Instead, we can assign the seismicity to the background using
a smoothed seismicity approach, or onto the active faults, based on the location, size, and frequency of
historical earthquakes and the characteristics of the faults. For each seismic source zone, we define a
seismogenic depth based on seismicity and tectonics. Fig. 2 shows some example seismic source zones for
southwest China; for the demonstration of this workflow, we will look at source zones 3 and 7.
16th World Conference on Earthquake, 16WCEE 2017
Santiago Chile, January 9th to 13th 2017
Fig. 1 – A map showing main shocks (blue dots) and aftershocks (red crosses) in southwest China from the
catalog of Weatherill et al. [CITATION Wea14 \l 1040 ]. Colors indicate elevation (green low, white high).
16th World Conference on Earthquake, 16WCEE 2017
Santiago Chile, January 9th to 13th 2017
Fig. 2 – Exemplary seismic source zones (blue polygons labeled by numbers) and major active faults in
southwest China. Green lines are faults with known slip rates, and gray lines are faults
whose slip rates are unknown.
3.3 Modeling fault sources
Faults are primary sources of earthquake generation. For seismic hazard analysis, seismogenic fault sources
need to be compiled from geologic fault databases. The workflow from fault traces to fault sources is
demonstrated in [ CITATION Lit13 \l 1033 ].
In many seismic hazard analyses (e.g., [CITATION Ear05 \m Pet08 \l 1033 ]), earthquake magnitude
rates on faults are modeled using the characteristic earthquake model, which assumes that large characteristic
earthquakes repeatedly rupture the same fault segments with a similar magnitude and slip distribution
[CITATION Sch84 \m Wes94 \l 1033 ]. Implementing the characteristic model into seismic hazard analysis
is tempting because of its simplicity and clarity dictated by an almost regular rupturing process on the same
fault by almost the same size earthquakes. However, the characteristic model has its limitations and its
validity has been seriously challenged [ CITATION How85 \l 1033 \m Bir10 \m Ron03 \m Kag121 \m
Pag15 \m Kag93]. Moreover, implementing a characteristic model requires the knowledge of fault
segmentation, characteristic magnitude, and recurrence times, which are all very uncertain for most faults.
Therefore, we prefer to characterize seismicity on the faults using fault dimensions and slip rates,
using methods similar to the ones proposed by [CITATION And83 \m You85 \l 1033 ]. In these methods,
we assume that the occurrence of earthquakes on a fault follows a truncated GR or a Tapered GR (TGR)
distribution and the total seismic moment rate from the magnitude distribution equals the geological moment
rate derived from the fault dimension and slip rate. We assume the TGR b-value of earthquakes on the fault
16th World Conference on Earthquake, 16WCEE 2017
Santiago Chile, January 9th to 13th 2017
is the same as the b-value of the seismic source zone containing the fault. For a
truncated GR distribution, we assign lower- and upper-bound magnitudes for each of
the faults. The upper-bound magnitude should not be larger than that inferred from fault length
or area scaling relationships. For TGR, we assign a corner magnitude for each of the faults. The corner
magnitude of the seismic source zone may be used. When we simulate earthquakes on a fault, we use
appropriate earthquake magnitude-area scaling relationships, and allow earthquakes to float along the fault
plane [ CITATION MPa14 \l 1040 ].
3.4 Characterizing earthquake occurrence for a seismic source zone
We use a TGR distribution to define earthquake MFD for each source zone. The TGR distribution has an
exponential taper applied to the number of events of large seismic moment, which ensures a finite moment
flux for a region. It is most conveniently expressed in terms of seismic moment, M, instead of magnitude
(Mw) [ CITATION Kag02 \l 1033 ]:
F
(
M
)
=αt
(
Mt
M
)
β
exp
(
Mt−M
Mc
)
for
Mt≤ M <∞
(1)
where M is in N·m, and
M=101.5 Mw+9.05
[ CITATION Han79 \l 1033 ]. Here, F(M) is the rate of earthquakes
with moment larger than M, and β equals 2/3 of the GR b-value. Mc is called corner moment (the
corresponding magnitude is called corner magnitude, mc), which controls the distribution in the upper ranges
of M. Mt is a threshold moment (the corresponding magnitude is threshold magnitude, mt) above which the
catalog is assumed to be complete, and αt is the seismicity rate for earthquakes with moment Mt and greater.
To construct a TGR MFD, three parameters need to be determined: αt, β, and Mc (or mc).
We estimate the TGR b-value and a-value (and therefore β and αt) using the Weichert method
[CITATION Wei80 \l 1033 ]; catalog completeness is obtained using an automated version of the Stepp
methodology [ CITATION Ste72 \l 1040 ] implemented in the oq-hmtk. For a large region, the b-value is
usually close to 1.0 [CITATION Kag99 \m God00 \l 1033 ]. After αt and β have been determined, Mc can
be estimated using the seismic moment conservation principle[ CITATION Kag021 \l 1033 ]:
M
c
⋍
[
χ´
M
T0
(1−β)
α
t
M
t
β
Γ(2−β)
]
1/(1−β)
(2)
where
´
MT0
is the total tectonic moment rate determined from geodetic or geologic measurements (without
considering the seismic coupling,
χ¿
, and Γ is the gamma function. We estimate
´
MT0
from the geodetic
strain rate model using the method described in [CITATION Bir071 \m Bir10 \m Biron \l 1033 ].
The obtained TGR relationship defines the total MFD for a large seismic source zone. We will split
the total MFD in two parts: one part is attributed to the earthquakes on active faults, and the rest to the
background seismicity. Figure 3 demonstrates the cumulative MFDs for source zones 3 and 7. For
demonstration purposes, we assume that the earthquakes on the active faults span a magnitude range of 6.5 to
8.5. In practical applications, the magnitude range of earthquakes on each fault should be determined based
on characteristics of the fault, regional tectonics, and earthquake history.
In the case of area source 7, it is worth noting that the MFD shows a tapering only at very large
magnitudes. This means that the seismic moment rate derived from strain rate is very high compared to the
moment rate from earthquake history. This is a trend that we observe in some of the zones so far considered;
clearly this is an aspect that will require further investigation.
3.5 Characterizing background seismicity
After we characterize earthquake occurrence for a source zone and for faults within that source zone, we
attribute the difference between earthquake occurrences in a source zone and on faults to background
seismicity. We use a smoothed seismicity method to distribute the background seismicity, that is, the
distribution of background seismicity is based on the MFD and spatial distribution of historical earthquakes.
16th World Conference on Earthquake, 16WCEE 2017
Santiago Chile, January 9th to 13th 2017
Distributed seismicity is modeled on a regular grid of point sources covering the extent
of the source zone. The total MFD for each zone is scaled proportionally to the rate of
occurrence computed on each node using a smoothed seismicity process. In order to avoid
double counting contributions, the MFD of point sources within a buffer around each fault source is
truncated at the magnitude value which corresponds to the minimum magnitude of the MFD of the
corresponding fault.
16th World Conference on Earthquake, 16WCEE 2017
Santiago Chile, January 9th to 13th 2017
Fig. 3 – Cumulative magnitude-frequency distributions of source zones 3 (upper panel) and 7 (lower panel)
considered in this demonstrative example. The red dashed lines show the TGR distribution obtained using
the information contained in the historical seismicity catalog (for the calculation of αt, and β), and the GEM
strain rate model version 2.1 [CITATION Kre14 \l 1040 ] (for the calculation of the corner magnitude). The red
dots show the MFD obtained using historical seismicity. Yellow lines are the MFDs obtained for the
individual faults (fault IDs are labeled in the plots) inside each zone; the blue curve shows the MFD obtained
by summing the individual fault MFDs.
16th World Conference on Earthquake, 16WCEE 2017
Santiago Chile, January 9th to 13th 2017
3.6 Consistency checks and handling exceptions
To ensure the workflow operates properly, the following consistency checks are
performed for each of the source zones during the modeling process:
1) Comparing moment rates based on strain rate, fault sources, and seismicity (including historical
earthquakes and TGR distribution of the zone);
2) Comparing the MFDs of fault sources with the TGR of the zone.
The first check ensures the consistency of different datasets. The scalar seismic moment rates from
strain and scalar seismic moments from the MFDs (examples of MFDs used for determining scalar seismic
moment are the red dashed lines in Fig. 3) should be consistent. However, the seismic moment rate directly
calculated from historical earthquakes may not be consistent with moment rates from strain and from the
MFDs. This is because the historical catalog-based moment rates are usually dominated by the few large
earthquakes. If those large earthquakes happened within the catalog completeness times, the estimated
seismic moment rates may be larger than those from MFDs; otherwise, the estimated moment rates may be
smaller than those from MFDs.
The workflow described above assumes that the zone TGR distribution based on strain-rate and the
historical earthquake catalog is higher than the total MFD from the faults, so that the leftover seismicity rates
can go to the background seismicity. However, this assumption does not always hold, due mainly to the large
uncertainties in the strain-rate model and fault parameters. For this case, scientific judgment on the fault
coupling coefficients or on the use of the uncertainties in the strain-rate based seismic moment rate is
needed.
3.7 Modeling finite ruptures
The final step of our modeling process is the construction of the input model for the OpenQuake-engine
[ CITATION MPa14 \l 1040 ]. To calculate seismic hazard, earthquake ruptures must be specified. The
OpenQuake-engine can take the sources in the ESM and generate ruptures using its standard hazard
calculation module. It can also generate a synthetic catalog in which each synthetic event is modeled by a
finite rupture. For the ruptures modeled on faults, their geometry is constrained by the characteristics of the
corresponding faults. For the events belonging to background seismicity, we use the prevalent nodal planes
determined from earthquake focal mechanisms and the strain rate model for each area source to define the
geometry and style of their finite ruptures. The scaling relationships between magnitude and rupture area (or
length) are used to define the extent of the finite ruptures.
Fig. 4 shows an example of seismic hazard map computed using a classical PSHA methodology for
the area around source zone 3. The ESMs are constructed using the methodology discussed in this paper. The
ground motion prediction equations by Boore and Atkinson [ CITATION Boo08 \l 1033 ] are used in the
calculation. The OpenQuake-engine is used for hazard calculation. The figure displays the seismic hazard
(peak ground acceleration, PGA, with 10% probability of exceedance in 50 years) obtained by considering
both faults and background seismicity sources.
4. Exploring the feasibility of an OpenQuake Earthquake Model Building Toolkit
It is desirable to create a repository where workflows similar to the one proposed here can be collected and
shared for a wider application in various tectonic regions and seismotectonic contexts around the world.
Thus, GEM plans to create a repository with the provisional name OpenQuake Earthquake Model Toolkit
(oq-emtk). The oq-emtk will be created to formalize the various approaches for the construction of
components of an ESM, and to collect methods assisting hazard modelers to build ESMs. For the
construction of this repository, GEM will follow the approach used for the compilation of the OpenQuake-
engine [ CITATION MPa14 \l 1033 ] [ CITATION VSi14 \l 1033 ] and the hazard toolkits of the OpenQuake
suite [CITATION Wea14 \l 1033 ].
The toolkit architecture will be flexible to accommodate various approaches and to prevent the need to
strictly follow one specific workflow or particular modeling choices (such as the ones described above). For
example, other types of magnitude-frequency distributions (such as the truncated GR or characteristic
16th World Conference on Earthquake, 16WCEE 2017
Santiago Chile, January 9th to 13th 2017
earthquake model) might be used. For the regions that do not have a strain rate model,
a TGR corner magnitude or a truncated GR maximum magnitude can be determined
by other methods, and input as a parameter. For the fault sources, users can choose to use slip
rate or recurrence times of characteristic earthquake magnitude to model earthquake rates. The scaling
relationships of earthquake magnitude and rupture length or area can also be specified by users, offering a
configurable environment for earthquake source model development.
Fig. 4 – Exemplary seismic hazard map (PGA, in g, with 10% probability of exceedance in 50 years) of
southwest China.
5. Conclusions
We developed a new method to construct ESMs for seismic hazard calculations. In the new method, we
defined large seismic source zones, and used TGR distribution to describe the earthquake magnitude-
16th World Conference on Earthquake, 16WCEE 2017
Santiago Chile, January 9th to 13th 2017
frequency distribution for each zone. Then, we distributed the earthquakes rates
defined by the TGR to fault sources and background seismicity. The new method
integrates historical earthquake catalogs, geodetic strain rates, and geological faults. Historical
earthquake catalogs were used to determine GR a- and b-values. Geodetic strain rates define the upper bound
of seismic moment rates and thus were used to constrain the corner magnitude of TGR distributions for
source zones. Earthquake activity on the faults were modeled based on fault parameters such as their length
and slip rate. Background seismicity was captured by the smoothed seismicity method. The traditional way
of constructing ESMs usually requires the knowledge of all the active faults in a study region. Using the
method presented herein, we can construct ESMs for the regions where we only have parameters for some of
the active faults, such as China. We illustrated the workflow using southwest China as an example.
Hazard Modeller's Toolkit
Basic Methods for building the Earthquake
Source Model
Earthquake Model Building Toolkit
Workflows for the construction of the
Earthquake Source Model
Earthquake
Source
Model
Ground
Motion
Model
OpenQuak
e-engine
Fig. 5 – Schematic showing the relationship between the OpenQuake Hazard Modeller's Toolkit, the
OpenQuake Earthquake Model Building Toolkit, and the OpenQuake-engine.
We proposed the development of an open-source toolkit for constructing such source models. The
toolkit will be built on top of the oq-hmtk, and its output will serves as the input for OpenQuake to perform
seismic hazard calculations (Fig. 5). The goal of developing this suite of tools is to make the seismic hazard
modeling process more transparent, and to promote the development of new methodologies for seismic
hazard assessment.
6. Acknowledgements
This work was supported by FM Global. We thank Guihua Chen and Jia Cheng from the China Earthquake
Administration for data compilation. We are grateful to Hosam Ali from FM Global for discussions,
suggestions, and reviews of the manuscript. We also thank Franco Tamanini and Lou Gritzo from FM Global
for reviews and comments.
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