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SPATIOTEMPORAL SEISMIC HAZARD AND RISK ASSESSMENT OF M9.0
MEGATHRUST EARTHQUAKE SEQUENCES OF WOOD-FRAME HOUSES IN
VICTORIA, BRITISH COLUMBIA, CANADA
Lizhong Zhang1, Katsuichiro Goda2,3, Maximilian J. Werner4, and Solomon
Tesfamariam5
1Department of Civil Engineering, University of Bristol, Bristol, United Kingdom
2Department of Earth Sciences, University of Western Ontario, London, Canada
3Department of Statistical & Actuarial Sciences, University of Western Ontario, London, Canada
4School of Earth Sciences and Cabot Institute, University of Bristol, Bristol, United Kingdom
5School of Engineering, The University of British Columbia, Kelowna, British Columbia, Canada
Megathrust earthquake sequences, comprising mainshocks and triggered aftershocks along the subduction
interface and in the overriding crust, can impact multiple buildings and infrastructure in a city. The time between
the mainshocks and aftershocks usually is too short to retrofit the structures; therefore, moderate-size aftershocks
can cause additional damage. To have a better understanding of the impact of aftershocks on city-wide seismic
risk asses sment , a new simulation f ramewor k of sp atio temporal seismic hazard and risk assessment of future M9.0
sequences in the Cascadia subduction zone is developed. The simulation framework consists of an Epidemic Type
Aftershock Sequence (ETAS) model, ground-motion model, and state-dependent seismic fragility model. The
spatiotemporal ETAS model is modified to characterise aftershocks of large and anisotropic M9.0 mainshock
ruptures. To account for damage accumulation of wood-frame houses due to aftershocks in Victoria, British
Columbia, Canada, state-dependent fragility curves are implemented. The new simulation framework can be used
for quasi-real-time aftershock hazard and risk assessments and city-wide post-event risk management.
KEYWORDS
Spatiotemporal ETAS seismicity model; Cascadia subduction earthquakes; Mainshock-aftershock sequences;
State-dependent aftershock fragility curves; Wood-frame houses; City-wide seismic risk; Damage accumulation.
1 INTRODUCTION
Recent M9.0 earthquake sequences, such as the 2004 Aceh-Andaman earthquake, the 2010 Maule earthquake,
and 2011 Tohoku earthquake, triggered large aftershock events (e.g., M≥7.0) on the subduction interface and in
the overriding crust, demonstrating the destructive effects of aftershocks on buildings [1,2]. Because the time to
repair damaged buildings between a mainshock and aftershocks is often short, the cumulative damage effect of
buildings due to aftershocks can have a significant impact on post-earthquake risk assessment [3–5]. A
spatiotemporal seismic risk assessment that considers the cumulative damage effect due to M9.0 earthquake
sequences is necessary to quantify the impact of aftershocks on post-event risk management decision-making,
including resource allocation, evacuation planning, and rapid seismic loss estimation [6,7].
Devastating M9.0 events are not limited to the most active seismic regions mentioned above and could
occur in other subduction zones. For example, according to turbidite records of the past 10,000 years, the Cascadia
subduction zone (CSZ) ruptured 19 times [8]. The current best estimate of the mean recurrence period for M9.0
events in the CSZ is 526 years, and the last event occurred in 1700 [9]. On the other hand, Ventura et al. [10]
estimated that 56% of buildings in British Columbia (BC), Canada, are wood-frame houses, 40% of which were
built before 1970. Since seismic provisions of the National Building Code of Canada were adopted and enforced
in BC after 1973, the seismic resistance of old residential houses is likely to be below the current seismic standard
of the building stock in BC. Consequently, in the urban areas (e.g., Vancouver and Victoria) of BC, a large number
of wood-frame houses [11] may be particularly at risk from M9.0 subduction earthquake sequences.
To conduct a spatiotemporal seismic risk assessment, a model that can describe the time-dependent
seismicity rate in space and time is necessary. An epidemic type aftershock sequence (ETAS) model [12] is such
a spatiotemporal seismicity model. The model has been employed to conduct operational earthquake loss
forecasting in California and Italy [13,14]. All above-mentioned studies, however, focussed on shallow crustal
seismicity, whereas regional spatiotemporal seismic risk assessments in subduction zones are rarely carried out.
Recently, Zhang et al. [15] applied the ETAS model to subduction-zone regions and developed a new simulation
framework to assess spatiotemporal seismic hazard and risk due to aftershocks triggered by M9.0 events. Their
case study of Tohoku-like events has shown that synthetic catalogues from the new simulation framework are in
good agreement with the observed M9.0 Tohoku sequence. Moreover, Zhang et al. [16] investigated the variability
of ETAS parameters across different subduction-zone regions using global earthquake catalogues to derive
preferred ETAS parameters for future M9.0 earthquake sequences. Their outputs allow forecasting spatiotemporal
seismic hazard due to M9.0 sequences in subduction zones using observed catalogues in global subduction zones.
2
For seismic risk assessment, recent studies have investigated the seismic performance of individual
buildings in western Canada when exposed to hypothetical M9.0 events in the CSZ [17–19]. For instance, Koduru
and Haukaas [18] highlighted the significant contribution (up to 75%) of megathrust subduction events to the total
monetary loss for the case of a single 15-storey high-rise building in Vancouver. In terms of the impact of
aftershocks occurring in the CSZ on individual buildings, Salami and Goda [20] showed that mainshock-
aftershock sequences can cause additional 5%-20% damage in comparison with mainshocks alone. On the other
hand, megathrust earthquakes affect many buildings simultaneously. Therefore, city-wide seismic risk
assessments were conducted to make decisions more efficiently for Vancouver and Victoria [11,21,22]. However,
time-dependent seismic risk assessments of multiple buildings within a city subjected to M9.0 earthquake
sequences in the CSZ have not been investigated. In addition, most spatiotemporal seismic risk studies ignore the
cumulative damage effect due to aftershocks. This is because (1) a seismicity model to describe the mainshock-
aftershock sequences in space and time is not available in the CSZ, and (2) state-dependent aftershock fragility
curves are not available for various building typologies, and only mainshock fragility curves that do not account
for the cumulative damage effect of aftershocks have been used. Recently, Zhang et al. [23] have developed state-
dependent fragility curves of wood-frame houses in BC to estimate the damage state (DS) of wood-frame houses
after each event during an earthquake sequence. The new state-dependent fragility curves can be combined with
the quasi-real-time aftershock forecasting hazard assessment to build a simulation framework of city-wide
spatiotemporal seismic hazard and risk due to megathrust subduction earthquake sequences in the CSZ.
This study, for the first time, assesses spatiotemporal seismic hazard and risk due to M9.0 mainshock-
aftershock sequences using a realistic building portfolio of wood-frame houses in Victoria, BC, Canada. The
developed spatiotemporal simulation framework is innovative, and its main novelty is attributed to the integration
of two compatible components. The first component is the ETAS seismicity model for the CSZ. Unlike other
active subduction zones, where many observed events are available to calibrate the ETAS parameters (e.g.,
Tohoku region, Japan), the CSZ lacks direct observations; thus, its ETAS parameters for M9.0 scenarios are
calibrated based on seismicity data from other global subduction zones [16]. Secondly, the state-dependent
aftershock fragility curves of wood-frame houses are used [23] to better estimate the cumulative damage effect of
mainshock-aftershock sequences and to develop a real-time risk forecasting framework for decision-making. In
addition, a realistic building dataset of wood-frame houses in Victoria is employed, aiming at estimating the total
seismic loss for the building portfolio. The objectives of this paper are: 1) to show how the simulation framework
of spatiotemporal seismic hazard and risk assessment, developed for active subduction regions, can be applied to
the CSZ, 2) to quantify the impact of aftershocks on the short-term seismic risk assessment in terms of DS and
seismic loss, and 3) to demonstrate how the outputs of the framework can be used for post-earthquake decision-
making. In the following, Section 2 describes the new framework of the spatiotemporal seismic hazard and risk
assessment for Victoria. Section 3 discusses the impact of mainshocks and aftershocks on the city-wide seismic
risk assessment in Victoria.
2 SPATIOTEMPORAL SEISMIC HAZARD AND RISK ASSESSMENT IN VICTORIA
An overview of the framework of spatiotemporal seismic hazard and risk assessment is given in this section. The
framework consists of a seismicity model (ETAS model), a ground motion model (GMPEs), and a seismic fragility
model (aftershock fragility curves) as shown in Figure 1. Synthetic catalogues are generated from ETAS
simulations. The synthetic catalogues contain the times, magnitudes, and locations of mainshock-aftershock
sequence events. Subsequently, the synthetic catalogues and local soil conditions (Vs30) are used as inputs to
GMPEs to estimate the ground motion intensity measures of the mainshock-aftershock sequences at different
sites. Following that, the intensity measures at multiple sites are applied to the aftershock fragility curves to
estimate the DSs and losses of multiple wood-frame houses at different times after a mainshock.
2.1 Seismicity model
This subsection analyses regional seismicity for the CSZ and introduces suitable ETAS parameters based on
global subduction data. In Section 2.1.1, the Advanced National Seismic System (ANSS)
(https://www.ncedc.org/anss/catalog-search.html) and the Seismic Hazard Earthquake Epicentre File (SHEEF)
catalogues [24] are analysed to investigate the main characteristics of the regional seismicity for the CSZ, while
ETAS simulations for the CSZ are presented in Section 2.1.2.
3
1
Figure 1. Simulation framework of spatiotemporal seismic hazard and risk assessments. 2
4
2.1.1 Analysis of ANSS and SHEEF catalogues in the CSZ 3
Although a small dataset of observed events in the CSZ does not allow calibrating the ETAS parameters reliably, b-4
value estimation is easier and important because the generic ETAS simulation framework assumes b = 1.0 [16]. The 5
local ANSS and SHEEF databases are used to estimate the completeness magnitude Mc and b-value because they 6
include more events than global catalogues (e.g., National Earthquake Information Centre). In addition, the SHEFF 7
catalogue consists of a uniform magnitude type and revised earthquake hypocenters [24]. A shortcoming of the SHEFF 8
catalogue is that only events in the vicinity of Canada until 2010 are available (e.g., seismicity data in Oregon are 9
missing). We therefore search the ANSS catalogue for more events in a larger spatiotemporal window. 10
11
Figure 2. Seismicity of the CSZ in target window (dashed red polygon) listed in the ANSS catalogue during 1981-12
2017 (top) and the SHEEF catalogue during 1981-2010 (bottom): (a, c) epicentral locations and (b, d) latitudinal 13
distribution over time. 14
15
Events are selected from the ANSS and SHEFF catalogues between 1 January 1981 and 31 December 2017 16
with depths less than 100 km. Following the 2014 U.S. national seismic hazard model [25], a spatial window is set as 17
shown in Figure 2(a) by enclosing down-dip rupture limits of the M9.0 mainshock rupture model in the CSZ [26–18
28]; its eastern boundary extends to the western coastline of Vancouver Island. The southern edge of the target window 19
is not extended into northern California (e.g., lower than 43°N), because some M7.0 events took place in the 20
Mendocino Triple Junction rather than within the CSZ (e.g., the 2010 M6.5 Gorda Plate event and the 2014 M6.8 21
Ferndale event) [29]. Figure 2 shows spatiotemporal plots of the observed events with M≥2.0 from the ANSS and 22
SHEFF catalogues. The ANSS catalogue (Figure 2(b)) covers a larger area in the western coast of Washington and 23
Oregon States and includes events after 2010. The SHEEF catalogue contains smaller events near 50° in latitude 24
before 1990 as shown in Figure 2(d). These two sub-catalogues are used to estimate the b-values. 25
In Figure 3, the b-values of the CSZ based on the ANSS and SHEFF catalogues are estimated as 0.53±0.03 26
and 0.82±0.04, respectively. The b-value = 0.82 from the SHEFF catalogue suggests that the northern CSZ has a 27
magnitude-frequency distribution more similar to other regions with b-value ≈ 1. The low b-value from the ANSS 28
catalogue is due to missing events before 2000. Because of the fewer events in the CSZ (less than 100 with Mcut = 4), 29
reliable estimates of the ETAS parameters cannot be obtained solely based on the local catalogues. ETAS estimation 30
5
(a prerequisite for modelling) requires well-recorded sequences [15]. Consequently, the global ETAS parameters (K0 31
= 0.04±0.02, α = 2.3, c = 0.03±0.01, p = 1.21±0.08, γ =1.61±0.29, d = 23.48±18.17, and q = 1.68±0.55) with b-32
value=1.0 from Zhang et al. [16] for future M9.0 sequences are used to generate synthetic catalogues in the CSZ. 33
34
35
Figure 3. Observed magnitude–frequency distributions (MFD) and fitted Gutenberg–Rich ter laws with the max imu m-36
likelihood estimates of the b-values and 5th–95th percentiles from (a) the ANSS and (b) the SHEFF catalogues. 37
38 2.1.2 ETAS simulation 39
The ETAS simulation framework with the anisotropic power-law kernel [15] is employed to generate synthetic 40
catalogues of aftershocks given an M9.0 earthquake. The developed anisotropic power-law kernel combines the 41
simulated 2D rupture rectangular area with a power-law beyond the rupture area, which can distribute the first 42
generation of aftershocks anisotropically in space. However, in comparison with the bilateral rupture area of the 43
Tohoku mainshock, several studies suggested a longer and narrower shape of the mainshock rupture area for the CSZ 44
[25,30]. The M9.0 rupture dimensions of the CSZ are more similar to the 2004 M9.1 Aceh-Andaman earthquake, 45
which has a greater rupture length-to-width ratio than the Tohoku mainshock [31]. In this study, the shape of the 46
rupture area is developed and modelled by the down-dip edge models [26–28], and the rupture dimensions are 47
simulated from the empirical scaling law [31]. The down-dip edge of the CSZ is critical for the hazard calculation, as 48
it primarily controls the rupture distances from the mainshock to the coastal city (e.g., Victoria). Different down-dip 49
edge models have been developed based on different assumptions of geothermal conditions, episodic tremor, and slip 50
zones [28]. Rupture widths are simulated to capture the locations of different down-dip edge models from the 2014 51
USGS national seismic hazard model. In terms of the aftershock decay outside the CSZ rupture area, the same 52
procedures as in the Tohoku case [15] are applied to build a spatial kernel function using 1D and 2D power laws. 53
Figure 4 shows the probability density distribution of the aftershock spatial distribution outside the rupture area of 54
the M9.0 event with a rupture length of 1,100 km and width of 130 km. 55
Additional features including the depth, earthquake type, and focal mechanism, are assigned to each event in 56
synthetic catalogues based on Zhang et al. [15]. These additional features allow simulating the rupture plane of large 57
crustal and subduction-zone aftershocks (M≥6.5) and evaluating seismic intensity measures (IMs) using GMPEs. 58
Depths for earthquakes with M<8 are sampled from empirical cumulative distribution functions (ECDFs) of depths 59
obtained from past observations in the CSZ. The slab model [32] of the CSZ (Figure 4) is divided into sub-regions 60
with 10 km width from the trench line to the continental crust to estimate the ECDFs of depth in each sub-region. We 61
use past earthquakes M≥2 from the ANSS catalogue within the slab model. Events with depths less than 5 km are 62
eliminated because the majority of these events are remote events, and their depths are poorly estimated with depths 63
of 0 km [33]. 64
All simulated earthquakes with M≥8 are treated as subduction-interface earthquakes, and the depths are 65
assigned directly from the slab model [32] (Figure 4). Earthquake types (continental-crust, subduction plate-boundary, 66
or subduction intra-plate) are defined by the sampled depths and the slab model. Earthquakes more than 20 km above 67
the plate interface are defined as crustal events, earthquakes falling in the layer within ±20km of the plate interface 68
are classified as subduction-interface events (allowing for depth uncertainty), and remaining deep earthquakes are 69
treated as intra-slab events. 70
71
6
72
Figure 4. Probability density distribution of the aftershock spatial distribution outside a simulated rupture area of the 73
M9.0 event (rupture length × rupture width = 1,100 km × 130 km). 74
75
Due to the plate motion of the subduction zone, the crustal and subduction-zone earthquakes tend to have 76
similar strike directions as the subduction plane [15]. Following that, the strike and dip angles of the subduction and 77
crustal aftershock are assumed to be similar to the strike and dip angles of the subduction plane. The ECDFs of strike 78
and dip angles for crustal and subduction earthquakes are evaluated from the global Centroid Moment Tensor (gCMT) 79
catalogue, and the sampled angles are assigned to the large aftershocks with M≥6.5. Specifically, given the target city 80
is Victoria, the strike angle of a nodal plane 1 or 2 that is closer to the target strike angles (320°-350°) of the subduction 81
plane of the northern and central CSZ is selected [32]. 82
In total, 10,000 synthetic mainshock-aftershock catalogues are generated over a one-year period. The 83
magnitude frequency distribution and the daily number of events in a squared root scale are shown in Figure 5. The 84
aftershock seismicity rate with M≥5.5 is high immediately after the mainshock and gradually decays after day 5. 85
86
87
Figure 5. (a) Simulated magnitude-frequency distributions of aftershocks. (b) The daily number of simulated events 88
over a month after the mainshock. 89
7
2.2 Ground motion model 90
To compute scenario-based shake maps of M9.0 earthquake sequences for the City of Victoria, the following GMPEs 91
and Vs30 information are used. PGV is adopted as IM in the risk analysis because PGV shows a better performance in 92
capturing the cumulative damage effects of wood-frame houses [23]. Accordingly, the GMPEs by Ghofrani and 93
Atkinson [34] and Boore et al. [35] are used to compute the PGV for subduction-zone and crustal earthquakes, 94
respectively. 95
Ground motion models for the CSZ should reflect seismological findings from recent major subduction and 96
crustal events. Although other global subduction-zone GMPEs are available (e.g., [36,37]), they do not include the 97
ground motion from the 2011 Tohoku sequences, and thus the equations need to be extrapolated beyond the range of 98
the underlying ground motion data. On the other hand, PGV is not always included as the output variable of the newest 99
subduction-zone GMPEs [38,39]. Therefore, we use the GMPEs from Ghofrani and Atkinson [34], which includes 100
the ground motion records from the 2011 Tohoku event together with adjustment factors for the CSZ to account for 101
its deeper soil profile compared with Japan. In comparison with other cru stal GMP Es fr om the NGA-West2, the GMPE 102
by Boore et al. [35] requires less input information (e.g., unknown options for fault type and hanging wall effect). 103
This is more suitable for southwestern BC, since a complete inventory of active faults and their geometry is not 104
available, except for a few fault systems, such as the Leech River Valley fault [40]. 105
The synthetic catalogues with times, magnitudes, locations, and earthquake types are applied to the GMPEs 106
to calculate the median values of PGV. Source models for M≥6.5 crustal and subduction-zone aftershocks are 107
generated from empirical scaling laws [31] and the ECDFs of strike and dip angles. This allows calculating the shortest 108
rupture distances from the simulated rupture dimension to target sites. 109
The Vs30 map of the City of Victoria is taken from Wald and Allen [41], and is generally consistent with the 110
observations from Monahan and Levson [42]. The soil conditions in Victoria correspond to the National Earthquake 111
Hazard Reduction Program site classes C to E (e.g., Vs30 < 760 m/s). We use a grid size of 500 m × 500 m for the City 112
of Victoria to produce the mainshock and aftershock shaking maps. We consider the spatial correlation models from 113
Goda and Hong (2008) [43] and Goda and Atkinson (2010) [44] for crustal and subduction-zone events, respectively. 114
The error terms are sampled from the inter-event sigma and the intra-event sigma with the spatial correlation models. 115
116
117
Figure 6. Spatial distribution of wood-frame houses in Victoria (6,711 in total with House 1 #387, House 2 #197, 118
House 3 #257, and House 4 #5,870). 119
120
8
2.3 Seismic risk model 121
The state-dependent fragility curves of wood-frame houses [23] are used to assess the performance of the wood-frame 122
houses under an M9.0 megathrust subduction earthquake sequence. To develop the state-dependent fragility curves, 123
Zhang et al. [23] used structural responses before and after each event of real mainshock-aftershock records to obtain 124
statistical relationships among the engineering demand parameter (EDP) prior to the seismic event, the intensity 125
measure (IM) of the seismic event, and the EDP after the seismic event. The 3D dataset (pre-EDP-IM-post-EDP) is 126
binned according to the same pre-DS. For each IM-post-EDP dataset that is classified by the same pre-DS, IM values 127
corresponding to specific post-EDP intervals are then fitted to produce the state-dependent fragility curves. The 128
developed fragility curves account for damage accumulation, providing the exceeding probability of DS given the IM 129
of the event and the DS of the structure prior to the seismic excitation. 130
Due to different shear-wall configurations, four types of two-storey wood-frame houses are defined: (1) 131
House 1 with stucco/engineered oriented strand board (OSB)/gypsum wallboard (GWB), (2) House 2 with engineered 132
OSB/GWB, (3) House 3 with non-engineered OSB/GWB, and (4) House 4 with horizontal boards (shiplap)/GWB. 133
The term ‘engineered’ for Houses 1 and 2 i ndi cates that hold-downs and blocking of the wall panel are used to increase 134
their seismic resistance and to meet the seismic code requirements [45]. By considering post-earthquake building 135
inspections, three performance thresholds corresponding to Green, Yellow, and Red tags (hereafter referred to as DS1, 136
DS2, and DS3) are defined. Green tag (DS1) represents a case where the house is inspected by a structural engineer 137
and can be immediately occupied, Yellow tag (DS2) indicates that access is limited except for professional 138
maintenance, and Red tag (DS3) means that the house is unsafe to occupy and requires retrofitting or rebuilding [46]. 139
In total, 6,711 houses are considered for the seismic risk assessment in the City of Victoria. The building 140
database is from BC assessment (https://www.bcassessment.ca/). From the building database, the following
141
information was extracted: (1) location, (2) built year, (3) Actual Use by Category (AUC), and (4) building assessment 142
value (Canadian dollars). We removed non-residual buildings and only considered single-family dwellings that are 143
defined by AUC. To link the fragility curves of Houses 1-4 with individual houses in the building data, the wood-144
frame houses are classified into Houses 1-4 according to the construction years, which reflects expected seismic 145
performances of the houses. The four different house types considered are: (1) House 1 - after 1991, (2) House 2 - 146
from 1981 to 1990, (3) House 3 - from 1971-1980, and (4) House 4 - before 1970. The numbers of Houses 1-4 are 147
387, 197, 257, and 5,870, respectively. This is consistent with the descriptions from White and Ventura [45] that the 148
majority of the wood-frame houses were built before 1973 and thus may be deficient in seismic capacity compared 149
with the current seismic design standard in BC. Figure 6 shows a plot of spatially distributed Houses 1-4 in Victoria. 150
To evaluate the seismic damage to each house, we interpolate the simulated PGVs of mainshock-aftershock 151
shaking maps with 500 m × 500 m grid size linearly at each house location and apply the fragility curves. The total 152
asset of the 6,711 houses is approximately $930 million Canadian dollars (CAD$). The seismic loss of the wood-153
frame houses is calculated based on the approach from Onur et al. [11]. Mean damage ratios of 5%, 40%, and 80% 154
(slight, heavy, and major) are considered for Green (DS1), Yellow (DS2), and Red (DS3) tags, respectively. 155
156
3 RESULTS AND DISCUSSION 157
This section discusses the impact of mainshocks and aftershocks from the CSZ on the municipality-wide seismic risk 158
assessment in Victoria. 159
160
Figure 7. (a) Damage probability of Houses 1-4 after mainshocks based on 6,711 houses in Victoria. (b) Loss 161
exceedance curves of mainshocks. 10th, 50th, and 90th percentiles of aggregated losses by mainshocks are 14, 66, and 162
194 million CAD$, respectively. 163
9
3.1 Impact of mainshocks on DS and seismic loss 164
The effects of the CSZ mainshocks on DS distributions and estimated seismic losses of the wood-frame houses are 165
investigated in this subsection. Figure 7 shows the damage probability of Houses 1-4 due to mainshocks only for the 166
building portfolio of wood-frame houses (6,711 houses in total) in Victoria. House 4 makes up almost 90% of the 167
wood-frame houses and is susceptible to significant damage. Figure 7(a) shows that the probabilities of DS1, DS2, 168
and DS3 right after the mainshocks are 51.3%, 9.2%, and 4.5%, respectively. Considering the total number of House 169
4 is 5,870, on average, 265 House 4 could change from DS0 to DS3 after the mainshocks. In Figure 7(b), the 10th, 50th, 170
and 90th percentiles of total aggregated losses by the mainshocks are 14, 66, and 194 million CAD$, respectively. 171
High estimated seismic losses (e.g., 500 million CAD$ with 0.001 exceedance probability) in the right tail in Figure 172
7(b) represent the effects of extreme IMs from the mainshocks. The large variability of PGV values of the mainshocks 173
is due to two sources. The first source is the uncertainty of PGV from the GMPE [34]. The second source is the shortest 174
distance from the mainshock rupture plane to Victoria, which depends on the down-dip edge models of the CSZ. 175
To visualise the uncertainty of the mainshocks from magnitude and rupture area on hazard analysis and 176
quantify the impact of the mainshocks on risk assessment, single simulations of mainshock shaking maps, and DS and 177
loss distributions corresponding to the 10th, 50th, and 90th percentiles of the total loss are examined closely. Figure 8 178
shows the mainshock shaking maps corresponding to the 10th, 50th, and 90th percentil es of t he total l oss. T he max imum 179
and average PGV values of each shaking map are also indicated in Figure 8. The average PGV values of the 10th, 180
50th, and 90th percentile scenarios are 14, 25, and 44 cm/s, respectively, whereas the maximum PGV values of Figure 181
8(a)-(c) are 30, 52, and 90 cm/s, respectively. 182
183
Figure 8. Mainshock shaking maps corresponding to (a) 10th, (b) 50th, and (c) 90th percentiles of the total loss. 184
185
The hazard results from Figure 8 can be further applied to seismic risk analysis to estimate the DS of each 186
house and the total seismic loss for the portfolio. Figure 9(a) shows the number of houses with DS0, DS1, DS2, and 187
DS3 for different scenarios. The 10th percentile scenario only has 992 and 4 houses with DS1 and DS2, respectively, 188
which suggest most of the houses can be immediately occupied if no major aftershocks are triggered in a short-time 189
period. Figure 9(c) shows the number of houses with DS0, DS1, DS2 and DS3 for the 50th percentile scenario is 2,106, 190
4,394, 207, and 4, respectively. The 90th percentile scenario has a greater number of houses with DS2 and DS3, which 191
10
are 2,183 and 726, respectively, as indicated in Figure 9(e). The significantly increased number of houses with DS3 192
is a result of the large PGV values with 44 cm/s on average in the 90th percentile scenario. On the other hand, Figure 193
9(b), (d), and (f) show the block maps of loss distributions corresponding to the different scenarios, which are 14, 66, 194
and 194 million CAD$, respectively. 195
196
Figure 9. Simulated DS distributions of wood-frame houses for (a) 10th, (c) 50th, and (e) 90th percentiles of total losses 197
(m CAD$) by mainshocks. The block map of seismic loss distribution of wood-frame houses for (b) 10th, (d) 50th, and 198
(f) 90th percentile scenarios. 199
200
In the post-earthquake risk management of an M9.0 event in the CSZ, if a mainshock source model (e.g., 201
magnitude, rupture dimensions, and strike angle) is available right after the mainshock, quasi-real-time aftershock 202
hazard and risk assessments can be performed using the developed framework. For instance, if the 90th percentile 203
scenario is applicable (see Figure 8), the aftershock forecasting can be useful to evaluate the seismic risk of critical 204
infrastructures on day 1 (e.g., transportation system, electricity, and water supply), and ensure that the service would 205
11
be available in case of future destructive aftershocks. In addition, for the purpose of accurate building tagging, the 206
uncertainty of the mainshock PGV can be constrained by the observed values, which is usually available right after 207
the mainshock (e.g., USGS’s ShakeMap system). This would allow reducing the uncertainty of the IM from GMPEs, 208
and more accurate DSs of buildings can be estimated. 209
210
3.2 Impact of aftershocks on DS and loss estimation 211
This subsection explores the impact of aftershocks on damage probability and loss estimation of the wood-frame 212
houses. To demonstrate the impact of aftershocks on seismic hazard and risk assessments, three single simulations 213
within 7 days after the mainshocks corresponding to 10th, 50th, and 90th percentiles of the total loss are presented. The 214
three cases represent different scenarios of large aftershocks for the City of Victoria: (1) distant large aftershock (10th 215
percentile), (2) moderate-distance large aftershock (50th percentile), and (3) close large aftershock (90th percentile). 216
Due to the large variability of mainshock PGVs from the GMPE, the mainshock PGVs for the 10th, 50th, and 90th 217
percentiles of total losses by day 7 are selected with the similar PGVs as in Figure 8. This is to ensure the impact of 218
aftershocks on risk analysis is not overestimated or underestimated due to the variability of mainshock PGVs. 219
Figure 10(a) shows the average damage probability of Houses 1-4 in Victoria (i.e., 6,711 buildings) for 220
mainshocks only, and durations of 1 day, 1 week, 1 month, and 1 year after the mainshock. The impact of aftershocks 221
on the DS o f Ho uses 1- 4 is diff erent, noting that Hou se 4 has a higher probability of resulting in DS1 by the mainshocks 222
than Houses 1-3. In comparison with the damage probability of Houses 1-4 by the mainshocks, the probabilities that 223
damage conditions of Houses 1-4 are changed from DS0 to DS1 by aftershocks are 4.0%, 2.5%, 3.6%, and 2.0%, 224
respectively. Since Houses 1-3 have higher probabilities of sustaining no damage after the mainshocks than House 4, 225
Houses 1-3 have higher probabilities of changing from DS0 to DS1 due to aftershocks. Compared with the damage 226
probability of the mainshock, additional 1.7%, 3.1%, 2.6%, and 3.8% of Houses 1-4 could change to DS2 due to 227
aftershocks, whereas the probabilities that aftershocks cause further damage to DS3 are 0.3%, 0.9%, 0.7%, and 1.4%, 228
respectively. This indicates that House 4 damaged by the mainshocks tends to have further damage to change to DS2 229
and DS3. The higher damage probability of DS3 for House 4 suggests that the retrofitting of House 4 to meet the 230
seismic provisions of the National Building Code of Canada (Houses 1 or 2) might be necessary to reduce the 231
probability of demolition and reconstruction of House 4 after M9.0 sequences. 232
The loss exceedance curves of mainshock-aftershock sequences for mainshocks only, and durations of 1 day, 233
1 week, 1 month, and 1 year are shown in Figure 10(b). The 10th, 50th, and 90th percentiles of total aggregated losses 234
by day 7 are 20, 71, and 224 million CAD$, respectively. On average, aftershocks could cause additional 10% and 235
20% losses after 1 week and 1 year of the mainshock, respectively, in comparison with the loss exceedance curves of 236
the mainshocks. The effects of aftershocks on seismic loss estimation are consistent with other studies (e.g., [20]). 237
238
239
Figure 10. (a) Damage probability of Houses 1-4 and (b) loss exceedance curves of mainshock-aftershock sequences 240
at durations of 1 day, 1 week, 1 month, and 1 year based on 6,711 houses in Victoria. 10th, 50th, and 90th percentiles 241
of aggregated losses by mainshock-aftershocks within 1 week are 20, 77, and 224 million CAD$, respectively. 242
243
To illustrate different scenarios for risk management decisions, the seismic hazard and risk results within 7 244
days after the mainshocks corresponding to 10th, 50th, and 90th percentiles of the total loss are examined. Figure 11 245
shows plots of three single simulations of aftershock epicentres and latitudinal distribution of aftershocks up to day 7 246
after the mainshock corresponding to the 10th, 50th, and 90th percentiles of total losses from 10,000 simulations. These 247
12
three scenarios represent (1) a distant large aftershock (10th percentile in Figure 11(a) and (b)), (2) a moderate-distance 248
large aftershock (50th percentile in Figure 11(c) and (d)), and (3) a closer large aftershock (90th percentile in Figure 249
11(e) and (f)) of M7.0-class aftershocks. In comparison with the distant M7.0-class aftershocks from 10th and 50th 250
percentile scenarios, the M7.2 subduction aftershock (48.49°N, 124.69°W) in the 90th percentile scenario in Figure 251
11(e) is much closer to Victoria and may cause higher seismic losses. 252
253
Figure 11. Aftershock epicentres and latitudinal distribution of aftershocks with time on day 7 after the mainshock 254
corresponding to (a, b) 10th percentiles, (c, d) 50th percentiles, and (e, f) 90th percentiles of the total loss. 255
256
Figure 12 shows three single simulations of the mainshock PGV maps and the maximum aftershock PGV 257
maps corresponding to the seismicity plots in Figure 11. The same ranges of the maximum and average mainshock 258
PGVs are selected in Figure 12(a), (c), and (e) as in Figure 8 to facilitate the visual comparison. Although two M7-259
class events from the 10th percentile scenario are triggered in the offshore region as shown in Figure 11(a), their 260
impacts on the ground motion hazard are limited due to the long rupture distances. No large aftershocks are triggered 261
13
near Victoria (e.g., within 50 km); therefore, only a few patches in the maximum aftershock PGV map by day 7 have 262
PGV values larger than 10 cm/s in Figure 12(b). Although the epicentre of the M7.8 aftershock (47.74°N, 125,27°W) 263
from the 50th percentile scenario is 200 km away from Victoria, the rupture distance is 110 km when a large finite 264
fault plane is accounted for based on the scaling law of fault dimensions [31] and some sites in the east of Victoria 265
have PGV values larger than 10 cm/s in Figure 12(d). The impact of the M7.2 event from the 90th percentile scenario 266
on the hazard map in Figure 12(f) is significant. The majority of the maximum aftershock PGV values exceeds 10 267
cm/s almost everywhere across the City of Victoria. 268
269
Figure 12. Mainshock PGV map and maximum aftershock PGV hazard map by day 7 for the City of Victoria 270
corresponding to (a, b) 10th percentiles, (c, d) 50th percentiles, and (e, f) 90th percentiles of the total loss. 271
272
14
273
Figure 13. DS distributions of wood-frame houses due to the mainshock (left panels) and additional damage to the 274
aftershock sequence within 1 week (right panels) corresponding to (a, b) 10th percentiles, (c, d) 50th percentiles, and 275
(e, f) 90th percentiles of the total loss. 276
277
The DS distributions of wood-frame houses by mainshock and mainshock-aftershock sequences on day 7 are 278
shown in Figure 13. For the 10th percentile scenario, the number of houses with DS1 and DS2, respectively, is increased 279
by 103 and 4, due to aftershocks within 7 days after the mainshock. The aftershocks from the 10th percentile scenario 280
contribute to a few patches on the aftershock hazard map with PGV > 10 cm/s in Figure 12(b), which could not cause 281
significant damage to houses. Most of the houses would remain intact or experience minor damage (DS1). In terms of 282
the 50th percentile scenario, the M7.5-class event causes some moderate damage to the houses in Victoria. From 283
Figure 13(c) and (d), the number of houses with DS1, DS2, and DS3 due to the mainshock is 4,164, 267, and 19, 284
respectively. After one week, the numbers of houses with DS1, DS2, and DS3 increase to 4,372, 343, and 22, 285
respectively. More houses are changed to DS2 in the eastern part of Victoria, which is consistent with the aftershock 286
15
hazard map in Figure 12(d). The impact of the M7.0-class event from the 90th percentile scenario on the seismic risk 287
assessment is substantial. The number of houses with DS1, DS2, and DS3 by the mainshock is 3,264, 2,345, and 900, 288
respectively. After one week of the mainshock, due to the M7.2 aftershock, the number of houses with DS1, DS2, and 289
DS3 is 3,081, 2,537, and 931, respectively. 290
291
Figure 14. Seismic loss distribution of wood-frame houses due to the mainshock (left panels) and additional damage 292
to the aftershock sequence within 1 week (right panels) corresponding to (a, b) 10th percentiles, (c, d) 50th percentiles, 293
and (e, f) 90th percentiles of the total loss. 294
295
Figure 14 shows the block map of seismic loss distributions of wood-frame houses in the City of Victoria 296
by mainshock and the mainshock-aftershock sequence up to day 7. In total, the aggregate seismic loss of the 10th 297
percentile case shown in Figure 13(a) and (b) is increased from 18 to 20 million CAD$. The aggregate losses of the 298
50th percentile case from Figure 13(c) and (d) are increased from 71 to 77 million CAD$. For the 90th percentile case, 299
16
the aggregate loss is increased by 9 million CAD$ in Figure 13(f) in comparison with 215 million CAD$ for the 300
mainshock alone. 301
For the post-earthquake risk management of M9.0 events, after 1 week of the mainshock, the quasi-real-time 302
aftershock hazard and risk assessments in Figures 12-14 can be helpful for the building tagging and inspection of 303
wood-frame houses, assuming the seismic vulnerability models for residential houses are applicable. For example, the 304
output of the framework can provide the probability distribution of the DSs on the day of the inspection for building 305
tagging and daily forecasts of the DSs in a short-time period after the inspection day. This can be part of building 306
inspection along with conventional building tagging [46] to provide additional information for structural inspectors. 307
308
Figure 15. Single simulation corresponding to the 90th percentile of the total loss: (a) aftershock epicentres, (b) 309
latitudinal distribution of aftershocks with time to day 30 after the mainshock, (c) mainshock hazard map, and (d) the 310
maximum aftershock hazard map within 30 days after the mainshock for the City of Victoria. 311
312
3.3 Extreme case with a triggered crustal aftershock near Victoria 313
A more destructive crustal aftershock case is presented as a worst scenario. An example of the 90th percentiles of total 314
losses within one month after the mainshock is shown in Figure 15. To show the potential impact of destructive 315
aftershocks on hazard and risk assessment for the City of Victoria, a single simulation with a lower maximum 316
mainshock PGV is considered (81 cm/s) in Figure 15(c), compared with 90 cm/s in the 90th percentile of the 317
mainshocks simulations in Figure 8. An M6.5 aftershock is triggered near Victoria, which is a shallow crustal 318
aftershock (48.39°N, 123.24°W) with a rupture distance less than 10 km to Victoria. The maximum aftershock PGV 319
values in Figure 15(d) are contributed by the triggered shallow crustal event. This type of shallow crustal event has 320
been previously identified as potentially damaging scenarios near Victoria in past studies, for example, the Leech 321
River Valley fault-M6.0 event and the Devil’s Mountain fault-M7.5 event [40,47]. 322
In Figure 16, due to the triggered crustal event, the number of houses with DS2 and DS3 increased by 2,213 323
and 440, respectively. Less than 10% of the houses remain in DS0. The aggregate losses are increased by 108 million 324
CAD$ in comparison with 121 million CAD$ due to the mainshock. The losses due to the aftershocks are almost the 325
same amount as those due to the mainshock. 326
17
The 90th percentile scenarios for different durations (1 week and 1 month) suggest that the impact of 327
destructive aftershocks on seismic risk assessment could be moderate events (e.g., an M6.0-class crustal event) with 328
short rupture distances in the shallow crust or large events (e.g., an M7.5-class subduction-zone event) with greater 329
rupture distances on the subduction-zone interface. The examples of the large M7.2 subduction-zone aftershock in 330
Section 3.2 and the shallow crustal event with the shortest rupture distance of less than 10 km to Victoria in this 331
section demonstrate the potential impact of destructive aftershocks on a municipality-wide risk assessment. 332
333
Figure 16. DS distribution of wood-frame houses for 90th percentiles of the total loss by (a) mainshock and (b) 334
mainshock-aftershock sequences on day 30. The block map of seismic loss distribution of wood-frame houses in the 335
City of Victoria by (c) mainshock and (d) mainshock-aftershock sequence on day 30. 336
337
4 CONCLUSIONS 338
This study developed a new simulation framework to assess spatiotemporal seismic hazard and risk due to M9.0 339
mainshock-aftershock sequences using a realistic building portfolio of wood-frame houses for Victoria, BC, Canada. 340
The ETAS simulation from Zhang et al. [15] with the suggested ETAS parameters from Zhang et al. [16] was applied 341
to generate stochastic M9.0 earthquake sequences for the CSZ. Applicable GMPEs were selected for the CSZ to 342
calculate the time-dependent hazard results at multiple sites accounting for spatial correlations of ground motions. The 343
hazard results were further applied to state-dependent fragility models to assess the spatiotemporal risk to multiple 344
wood-frame houses in the City of Victoria, BC, Canada. 345
The results showed that the impact of the variability of mainshock PGVs on total loss is significant. The 10th, 346
50th, and 90th percentiles of total mainshock loss (corresponding to the average mainshock PGV values with 14 cm/s, 347
25 cm/s, and 44 cm/s) are 14, 66, and 194 million CAD$, respectively. On average, aftershocks could cause additional 348
10% and 20% losses after 1 week and 1 year of the mainshock, respectively. Single simulations of mainshock-349
aftershock results show that the developed simulation framework can capture the subduction and crustal aftershock 350
rates in space and time and further estimate the DS and loss distributions for risk management decisions. Destructive 351
aftershocks could be triggered by M9.0 events. Occurrence of an M6.0-class crustal event or an M7.5-class 352
subduction-zone event could lead to 90th percentiles of the total loss. If the mainshock source model is available right 353
after the mainshock, this framework can facilitate the quasi-real-time aftershock hazard and risk assessments. 354
18
The limitations of this study include: (1) for more accurate hazard estimates, a high-resolution Vs30 map is 355
necessary; (2) other GMPEs for subduction-zone events that use PGV as the output and include M9.0 observed records 356
need to be considered; and (3) accurate loss estimations (considering different EDPs for structural and non-structural 357
components) would require state-dependent fragility curves that are applicable to other structure types, which are 358
beyond the scope of this study. 359
360
ACKNOWLEDGEMENTS 361
For this work, K.G. received funding from the Canada Research Chair program (950-232015) and the NSERC 362
Discovery Grant (RGPIN-2019-05898), and M.J.W. received funding from the European Union's Horizon 2020 363
research and innovation program (No 821115, RISE: Real-Time Earthquake Risk Reduction for a Resilient Europe). 364
L.Z. and M.J.W. appreciate the support from the London Mathematical Laboratory (http://lml.org.uk/). M.J.W. was 365
also supported by the Southern California Earthquake Center (No. 10013); SCEC is funded by NSF Cooperative 366
Agreement EAR-1600087 & USGS Cooperative Agreement G17AC00047. 367
368
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