Deterministic full-scenario analysis for maximum credible earthquake hazards

Domain: earth_science
Published: 2023-10-19
Editorial outcome: major_revision

Abstract
Greatearthquakesareoneofthemajorthreatstomodernsocietyduetotheir
greatdestructivepowerandunpredictability.Themaximumcredibleearth-
quake(MCE)foraspecificfault,i.e.,thelargestmagnitudeearthquakethat
mayoccurthere,hasnumerouspotentialscenarioswithdifferentsource
processes,makingthefutureseismichazardhighlyuncertain.Weproposea
full-scenarioanalysismethodtoevaluatetheMCEhazardswithdeterministic
broadbandsimulationsofnumerousscenarios.Thefull-scenarioanalysisis
achievedbyconsideringalluncertaintiesofpotentialfutureearthquakeswith
sufficientscenarios.Hereweshowanapplicationofthismethodintheseismic
hazardanalysisfortheXiluodudaminChinabysimulating22,000,000MCE
scenariosin0–10Hz.Theproposedmethodcanprovidearbitraryintensity
measures,ground-motiontimeseries,andspatialground-motionfieldsforall
hazardlevels,whichenablesmorerealisticandaccurateMCEhazardevalua-
tions,andthushasgreatapplicationpotentialinearthquakeengineering.

Introduction
Earthquakesareoneofthemajornaturalhazardsthatthreatenhuman
societyduetotheirseverelydestructivenatureandtheoccurrenceof
uncertaintyinbothtimeandspace1.Greatearthquakesoccurringnear
urbanareasormajorprojectslikenuclearpowerstationsorhighdams
canleadtocatastrophicdamage,suchasthe1906M 7.9SanFran-
w
ciscoEarthquake2andthe2008M 7.9Wenchuanearthquake3.How-
w
ever,theearthquakehazardsarenotdeterminedbytheirmagnitude
alone, and moderate earthquakes may also cause severe disasters
under specific circumstances, e.g., the 1994 M 6.7 Northridge
w
earthquake4andthe2014M 6.2Ludianearthquake5.Howtoevaluate
w
theseismichazardforspecificsitesaccuratelyisstillanessentialissue
fordisaster riskreduction1.Inthepastfewdecades,seismichazard
analysis methods based on the empirical ground-motionprediction
equations(GMPEs),e.g.,probabilisticseismichazardanalysis(PSHA)
ordeterministicseismichazardanalysis(DSHA),havebeenwidely
usedinthedesignofmajorprojectsandtheplanningofland-usefor
theaimofseismicriskmitigation6,7.However,theempiricalGMPEsare
usually constrained by the lack of proper ground-motion records,
especiallythenear-faultrecordsfromlargeearthquakes.Theycannot
accuratelyaccountforthecomplexruptureprocessandspecificsite
conditionseither8,andtheirestimatesofseismichazardmayhavean
unexpected upward bias9. Additionally, performance-based seismic
design and analysis require ground-motion time series10, but the
empirical GMPEs can only give estimates of the ground-motion
intensitymeasures(IMs).

Deterministicbroadbandground-motionsimulationshavebeen
validated by the records of historical earthquakes and the well-
recognized empirical ground-motion prediction models11–14. Com-
paredwiththeempiricalGMPEsthatarewidelyusedinthetraditional
seismic hazard analysis methods, physics-based ground-motion
simulation methods can comprehensively consider the source
mechanism,thepropagationpath,andtheeffectoflocalconditions
and thus have vast application prospects in the field of earthquake
engineering.Recently,severalphysics-based seismichazard analysis
approacheshavebeendevelopedusingdeterministicground-motion
predictionmethodsandshowgreatpotentialtoaccuratelyevaluate
theseismichazard9,15–17.However,thosephysics-basedseismichazard
analysis approaches are usually constrained in the low-frequency
range.Infact,high-frequencygroundmotionsareofgreatimportance
intheseismicdesignofengineeringstructures.Moreover,thecom-
plex physical process of earthquakes is not comprehensively taken
intoaccountinthesemethodsfortworeasons.First,thenumberof
consideredearthquakescenariosinthesemethodsistoosmallcom-
paredtothehundredsofthousandsofvariablesinkinematicsource
modelsforgeneratingbroadbandgroundmotions.Second,thekine-
maticparametersofthesourceprocess,includingthefaultlocation,
thehypocenter,andthedistributionofslip,rupturetime,risetime,
andrake,arenotfullytakenintoaccountinthesemethods.Therefore,
the obtained seismic hazard results may not adequately reflect the
hazardofpotentialearthquakesthatmayattackthetargetsiteinthe
future.

Inthisstudy,wearecommittedtodevelopingafull-scenario
seismic hazard analysis method for the maximum credible
earthquakes (MCEs) based on fully deterministic broadband
ground-motion simulations. Herein, the term MCE refers to the
earthquake with the largest magnitude that can reasonably be
expected to be generated by a specific source on the basis of
seismological and geological evidence18. Since there may be sev-
eralsignificantactivefaultswithdifferentuppermagnitudelimits
inthevicinity,thetargetsitemayhavemultipleMCEs.Duetothe
complexity and computational cost of implementation, the pro-
posedmethodismoresuitableforevaluatingtheseismichazard
of major engineering projects subject to extreme earthquakes
occurring in the near field of the target site. Given that the seis-
micdesignofmajorengineeringprojects,suchashighdamsand
nuclear power plants, particularly emphasizes their safety under
extreme seismic conditions, the proposed method is currently
intended for evaluating the seismic hazard of major engineering
projects under MCEs. The MCE hazards, i.e., the hazards for the
target site caused by the largest magnitude earthquakes at all
considered active faults, are analyzed using comprehensive MCE
scenarios at the significant faults near the target site. The newly
proposed multidimension source model is used to describe the
complex source process of earthquake scenarios. The multi-
dimensionsourcemodel,composedofmultiscaleandself-similar
subsources, can generate broadband ground motions while con-
sideringspecificruptureprocessesandhasbeenvalidatedbythe
records of historical earthquakes and the empirical GMPEs19.
Moreover, the variable space dimension of the seismic source is
greatly lowered by applying the self-similarity feature of sub-
source parameters inthe multidimension source model20.Inthis
way, the full-scenario analysis for the maximum credible earth-
quakes can be realized by a holistic consideration of the uncer-
tainties in all kinematic parameters of the source process with
comprehensive potential earthquake scenarios. Next, broadband
groundmotions(0–10Hz)ofuptotensofmillionsofearthquake
scenarios are generated using the adjoint simulation method.
Finally, the seismic hazard results of the target site can be
obtainedbystatisticallyanalyzingtheIMsofallgeneratedground
motions. In this method, as broadband ground motions at the
target site are explicitly generated for all earthquake scenarios,
the seismic hazards of arbitrary IMs can be obtained, not just
spectral accelerations. Therefore, for specific major engineering
structures, the proposed method can provide personalized seis-
mic hazard results by using the optimal IMs of them. Moreover,
this method can give earthquake scenarios with the specified
seismic hazard levels and the corresponding broadband ground
motions, which can be directly used in performance-based seis-
mic design and analysis. The spatial ground-motion field around
the target site can also be generated using the earthquake sce-
narios, which is particularly important in the seismic design for
large-spanstructuressuchasdamsand bridges.

Results
ModelandsettingforanalyzingMCEhazard
WeapplythismethodtoanalyzetheMCEhazardoftheXiluodudam
in China. The Xiluodu dam is located in southwest China with a
heightof285.5m,anditsreservoircapacitycanreach12.67billion
cubicmeters.Thedamsiteisatthejunctionoftheactivetectonic
blockswithahighseismicrisk21.Therefore,theseismicsafetyofthis
dam, especially its seismic performance subject to destructive
earthquakes,e.g.,MCEs,isasevere concerninthewhole cycle of
constructionandoperation.
ToevaluatetheseismicsafetyunderMCEsfortheXiluoduarch
dam,potentialfaultswhereMCEsmayoccurareidentifiedbasedon
theexplorationresultsoffaultstructuresandhistoricalearthquakes
aroundthetargetsite.Therearetwoimportantfaultstructuresinthe
nearfieldoftheXiluodudamsite:theYazibafault,withapotential
magnitudelimitof7.5,andtheLeibofault,withapotentialmagnitude
limitof7.0(Fig.1).Itshouldbenotedthatthefaultstructuresinthe
areahavenotbeenwellexploredandtheirlocationsindeepunder-
groundaresubjecttolargeuncertainties.Therefore,inconsideration
oftheuncertaintyoffaultlocation,whichisofspecialimportancefor
theseismichazardofthenear-faultsites,itisassumedthatMCEsmay
occurintheseismiczonewithin5kmonbothsidesofthemainfault,
andthefaultrupturesofMCEsaresetupevery1kmintheseismiczone
(Supplementary Fig. S2). On this basis, the seismic hazards of the
Xiluodu dam site under MCEs are studied based on deterministic
broadbandgroundmotionsimulations.
The topography in the model domain is considered using the
digitalelevationmodeldatawitharesolutionof30m.Basedonthe3D
wavevelocitystructureofEastAsiaEARA201422–24andthegeological
explorationinformationoftheXiluodusite,the3Dnumericalmodelis
establishedtosimulatethegroundmotions.Awell-recognizedsoft-
warepackagebasedonthespectralelementmethod25,26,SPECFEM3D,
isusedtosimulatetheseismicwavepropagationinthemodeldomain.
Theminimumshearwavevelocityatthesurfaceofthemodeldomain
is 2000 m/s, and the shear wave velocity gradually increases to
4400m/satdepth.Toreducethecomputationalamount,theaverage
spacingofthegridpointsatthemodelsurfaceissetto50m,andthe
grid size is doubled at the depth to match the high velocity there.
Consideringthatthespectralelementmethodrequiresfivepointsfor
eachwavelengthofseismicwaveswhensimulatingtheseismicwave
field27,theeffectivefrequencyofthesimulatedgroundmotionsisup
to10Hzinthisstudy.
Basedonthe3Dnumericalmodel,thestrainGreen’stensorsfrom
theXiluodudamsitetoallpossiblesourcelocationsinthepotential
faultsarecalculatedbythreeindependentnumericalsimulations,and
thenthestrainGreen’stensorsarepost-processedandstored.Inthe
seismichazardanalysisfortheXiluodudamsite,22,000,000scenar-
iosofMCEaregeneratedfortheYazibafaultandtheLeibofault,i.e.,
1,000,000earthquakescenariosaregeneratedforeachseismicfault\inthepotentialseismiczones.TheGreen’sfunctionsofsubfaultsfor
each seismic fault are calculated using the pre-computed strain
Green’stensors.Forallearthquakescenarios,thegroundmotionsat
theXiluodudamsitearedirectlysynthesizedusingtheGreen’sfunc-
tionsofsubfaults.Ground-motionIMs,e.g.,thespectralaccelerations,
forallearthquakescenariosarecalculatedtoobtaintheseismichazard
resultsofthetargetsite.
Additionally,itisworthemphasizingthatourmethodiscapable
of incorporating all uncertainties related to potential future earth-
quakes.Inthisstudy,uncertaintiesofthefaultlocation,hypocenter,
and rupture process of earthquakes are considered in the seismic
hazard evaluations for the Xiluodu dam site, while the earthquake
magnitudeisfixedtothemaximummagnitudeofsurroundingfaults
fortheconsiderationofMCEs,andfaultdipsaredeterminedbasedon
faultexplorations.However,ourmethodisflexibleenoughtoincor-
porateothervariablesofearthquakes,suchasearthquakemagnitude
andfaultdip,ifnecessary.

MCEhazardsproducedbythemodel
TheexceedanceprobabilitycorrespondingtotheIMisregardedasthe
seismichazardsforthetargetsite,aspresentedinFig.2.Theseismic
hazards are obtained by summarizing the spectral accelerations at
different periods based on the broadband ground motions of all
earthquake scenarios. From Fig. 2, the ground-motion intensity of
earthquake scenarios occurring at the same fault shows significant
differences at the Xiluodu dam site. For instance, the Peak Ground
Acceleration(PGA)attheexceedanceprobabilityof95%is0.163gin
theriver-paralleldirectionfortheLeibofault.Incontrast,thePGAat
theexceedanceprobabilityof5%is0.443g,whichisabout2.7times
the PGA at the exceedance probability of 95%. Considering that
earthquake scenarios occurring at a specific fault have the same
magnitude,faultgeometry,fault-sitedistance,andpropagationpath,
thesignificantvariationintheintensityofgroundmotionsindicates
thatthecomplexruptureprocessofearthquakeshasagreatinfluence
ongroundmotionsatthespecificsite.
Besides, it can be found that the spectral accelerations of
ground motions generated by earthquake scenarios of the Leibo
fault are similar to that of the Yaziba fault at the same seismic
hazard level. For instance, PGA at the exceedance probability of
50% is 0.268g in the river-parallel direction for the Yaziba fault,
whilePGAatthesamehazardlevelis0.254gintheriver-parallel
direction for the Leibo fault. It is surprising that although the
MCE magnitude of the Yaziba fault (M 7.5) is obviously larger
w
than that of the Leibo fault (M 7.0), the seismic hazard (repre-
w
sented by spectral accelerations) of the Yaziba fault is compar-
able to that of the Leibo fault for the Xiluodu dam site.
Meanwhile,theMCEhazardsfortheXiluodudamsitearefurther
analyzed with four representative IMs (Supplementary Figs. S5
and S6), including the root-mean-square of acceleration (a RMS),
root-mean-square of velocity (v RMS), Arias intensity (Ia), and
cumulative absolute velocity (CAV). The four IMs at the river-
paralleldirectionfortheYazibaseismiczoneareobviouslyhigher
thanthosefortheLeiboseismiczone,indicatingthattheseismic
hazards represented by different IMs may have significant dif-
ferences for the same site. Therefore, with the optimal IM of
specific engineering structures, this study can provide persona-
lized seismic hazards for them, enabling more accurate and rea-
sonableevaluations oftheMCEhazards.

Earthquakescenariosofthespecifiedhazardlevel
TheseismichazardsoftheXiluodudamsiteareobtainedbythe
deterministic full-scenario analysis for MCEs. However, the
performance-based seismic design and analysis of engineering
structuresusuallyrequirebroadbandground-motiontimeseries.
For this issue, the seismic hazard analysis method proposed in
this study can also give the earthquake scenarios with specified
seismic hazard levels and the corresponding broadband ground
motionsatthetargetsite.Figure3showstheruptureprocessof
the earthquake scenarios at both the Yaziba fault and the Leibo
faultcorrespondingtothe50%exceedanceprobabilityofPGAin
the river-parallel direction. The corresponding acceleration time
series at the Xiluodu dam site is also shown in Fig. 3. Ground
motionsgeneratedbytheearthquakescenarioattheYazibafault
have a long duration, and the river-perpendicular component is
stronger than the river-parallel component. Meanwhile, ground
motionsgenerated bythe earthquake scenarioattheLeibofault
are stronger in the river-perpendicular direction. The relative
distinction of ground-motion intensity in the two horizontal
directions may be attributed to the differences in source
mechanismandfaultgeometryofearthquakescenariosatthetwo
faults.
Furthermore, by employing the source process of earthquake
scenarios corresponding to the specified hazard level, the spatial
ground motion field around the target site can be derived by forward
simulations. ShakeMaps (PGA of the spatial ground-motion fields)
generatedbyforwardsimulationsfortheearthquakescenariosatthe
YazibafaultandLeibofault,asshowninFig.3,arepresentedinFig.4.
From the ShakeMaps, it is demonstrated that the realistic spatial
ground-motion field around the target site can be thoroughly pro-
ducedbyforwardsimulationsusingtheruptureprocessofearthquake
scenarioscorrespondingtospecifichazardlevels.Therefore,forlarge-
span structures (e.g., dams and bridges) that may be significantly
affectedbytheheterogeneousground-motionfield28,ourmethodcan
providemorerealisticground-motioninputfortheseismicdesignof
thesestructures.

Comparisonwiththeempiricalestimates
The seismic hazards are compared with four well-recognized
empirical ground-motion prediction equations (GMPEs)29–32. For
comparisonpurposes,theseismichazardsfromourstudyandthe
empiricalGMPEsareobtainedbasedontheseismicfaultlocated
inthecenteroftheseismiczones.AsshowninFig.5,theseismic
hazards in this study are generally in the range of one standard
deviation of the four empirical GMPEs, indicating that the pro-
posedmethodpredicateswellthespectralaccelerationsinawide
range of periods. Moreover, the comparison shows that the
seismic hazards of this study have much smaller standard devia-
tions of residuals (sigma) than the empirical GMPEs. Hence this
studysupportstheideathatthevariabilityoftheseismichazards
at specific sites for certain faults is significantly less than the
estimatesusing thesigmaoftheempiricalGMPEs9,33.

Methods
AnalysisprocedureforMCEhazard
Thisstudyproposesaphysics-basedseismichazardanalysismethod
toward broadband and full-scenario analysis of the maximum
credibleearthquakes thatmayattackthetargetsites.Theproposed
methodisillustratedinFig.6.Tobeginwith,themaximumpotential
magnitudeoffutureearthquakesthatoccurinthenearfieldofthe
target site is determined based on the historical earthquakes and
faultstructuresin thesurroundingregion.
Torealizefull-scenario
analysisoffutureearthquakeswiththemaximumpotentialmagni-
tude,i.e.,MCE,thevariablespacedimensionoftheruptureprocess
is greatly reduced by applying the self-similarity feature of the
multidimensionsourcemodel.Inthisway,stableseismichazardsof
thetargetsitecanbeobtainedbygeneratingsufficientscenariosof
MCEusingtheMonteCarlomethodwithaholisticconsiderationof
all kinematic parameters of the rupture process, e.g., the fault
location,thehypocenter,andthedistributionofslip,rupturetime,
risetime,andrakeangle.
Intheseismichazardsanalysisprocedure,thetargetsiteiscon-
sideredasaspecificlocation.Todealwiththemassivecomputation
amountforgeneratingbroadbandgroundmotionsofallearthquake
scenarios,theadjointsimulationmethodisfirstusedtocalculatethe
strainGreen’stensorsfromthesitetoallpossiblesourcelocations.
Next,Green’sfunctionsofthesubfaultsofthemultidimensionsource
model areobtained by convolving the rupture process on different
layersofthesubfaultswiththecorrespondingstrainGreen’stensors.
With the pre-obtained Green’s functions of subfaults, broadband
groundmotionsofallearthquakescenariosaresynthesizeddirectly,
andthefinalseismichazardsofthetargetsiteareobtainedbystatis-
ticalanalysisoftheground-motionIMsforallearthquakescenarios.
Furthermore,aftertheseismichazardsareobtained,earthquakesce-
narioscorrespondingtothespecifiedseismichazardlevelsandtheir
broadbandgroundmotionsatthetargetsitecanalsobegivenand
usedintheseismicanalysisofengineeringstructures.

Multidimensionsourcemodel
ToevaluatetheseismichazardofMCEwithdeterministicbroadband
ground-motion simulations, the multidimension source model is
adopted to consider all possible scenarios of MCE. In the multi-
dimensionsourcemodel,theruptureprocessontheseismicfaultis
described by several superimposed layers with different subsource
scalestogeneraterealisticbroadbandgroundmotions,asshownin
Fig.7.Foraspecifiedruptureprocess,thelayernumbermisdeter-
minedbytheupperlimitoftheexpectedfrequencycontents(f up),
m=dlog
2
ðf
up
Tp
m
r
i
e
n
Þe ð1Þ
whereTpre istheminimumrisetimeofthespecifiedruptureprocess.
min
ThetotalseismicmomentM isassignedtodifferentlayersaccording
0
to
R
M i=M
0
P
m
i
R
ð2Þ
k=1 k
whereR iandR kisthesubsourcesizeforLayeriandLayerk,respec-
tively.Besides,thekinematicparametersofsubsources,includingslip,
rupturetime,risetime,andrake,ondifferentlayersarederivedfrom
thespecifiedruptureprocess.Specifically,theslip,therupturetime,
andtherakeofsubsourcesondifferentlayersareallconsistentwith
the specified rupture process, while the rise time of subsources on
differentlayersisscaledby
T ij=
R
R iTp
j
re ð3Þ
T
m
h
e
e
th
a
o
d
d
jo
b
in
y
t
a
pp
e
l
t
y
h
i
o
d
g
s
th
c
e
an
re
c
e
ip
ne
ro
ra
c
t
it
e
y
a
o
ll
f
th
ee
d
s
e
t
d
rai
s
tr
G
ai
r
n
ee
G
n
r
’
e
s
e
t
n
e
’
n
s
s
t
o
e
r
n
s
s
t
o
e
r
s
39
–4
r
1
s
.
1
with only three numerical simulations. The Green’s function of the
subfaultu isthenobtainedbyconvolutingwiththepre-obtainedstrain
j j
Green’stensorswiththeruptureprocessofalllayersofthesubfault.
Oncecompleted,broadbandgroundmotionsatthetargetsiteofall
consideredearthquakescenarioscanbeeasilyandquicklysynthesized
withtheGreen’sfunctionsofsubfaults.Broadbandgroundmotionsof
the MCE scenarios are then statistically analyzed to get the seismic
hazards of the target site. By convention, the seismic hazards are
presented using the exceedance probability curves of the spectral
accelerations.However,asbroadbandgroundmotionsareexplicitly
obtained for all considered earthquake scenarios, any IM can be
adoptedfortheseismichazardanalysisinourmethod.

Summaryofseismichazardanalysismethod
Our seismic hazard analysis method starts with some basic seismic
information,includingthehistoricalearthquakesandthefaultstruc-
turesnearthetargetsite,whichareusedtodeterminethemagnitude
andthepotentialseismiczonesofthemaximumcredibleearthquakes.
Basedonthespecifiedmagnitudeandthepotentialseismiczones,the
scenariosetsofMCEaregeneratedwiththeMonteCarlomethodby
consideringallkinematicparametersoftheruptureprocess,e.g.,the
hypocenter,thedistributionofslip,rupturetime,risetime,andrake
on the seismic fault. After the Green’s functions of subfaults of the
multidimension source model are obtained with the pre-computed
strainGreen’stensors,broadbandgroundmotionsatthetargetsiteare
directlysynthesizedforallearthquakescenarios.Finally,theseismic
hazardsareobtainedbystatisticallyanalyzingthebroadbandground
motionsofallscenariosofMCE.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript presents results from numerical simulafions of ground shaking from two faults in China, randomizing some earthquake source parameters. The study mixes hazard analysis (characterizing earthquake sources and resulfing shaking) with adjustments to the method for predicfing shaking. The use of earthquake scenarios for hazard analysis, and the use of numerical simulafions to predict ground mofions, are both areas of research that have been studied for decades. The authors should be clearer about where their intended contribufion is, as many of the statements of the paper are largely repeafing statements made elsewhere. Without a clear innovafion here, the manuscript does not appear suitable for publicafion. A few minor comments are below as well.\n\"Maximum credible earthquake\" is a discouraged terminology in recent decades. It was previously used to refer to earthquake ground mofions before its phasing out, and it is unclear here whether the term is being used to refer to a ground mofion or an earthquake magnitude (the full set of earthquake source parameters is a vector and so doesn't have a clear maximum). There is no \"maximum\" earthquake ground mofion either, as the authors acknowledge through their use of millions of stochasfic simulafions. An alternate terminology would be preferred.\nWhy generate millions of ground mofion simulafions, but consider only a single fixed earthquake magnitude, dip, etc. for each fault? Some thought and discussion is needed regarding uncertainfies in potenfial future earthquake scenarios, and how they are reflected in the analysis.\nLine 108, 2000 m/s at the surface is very sfiff. Is this represenfing a measured value at the site, or is this high value necessary due to numerical modeling needs? A clarificafion is needed.\nSincerely,\nJack Baker", "reviewer_2": "NOTEWORTHY RESULTS\nThis paper provides a case study of potenfial ground shaking from earthquakes on two faults close to a major dam in China, demonstrafing that the hazard is similar from both faults despite the variafions in potenfial maximum credible earthquakes. In most respects the method here is more noteworthy than the specific results for the case study, using an extremely large number of ‘scenarios’ to befter define uncertainty in ground shaking at a specific site.\nSIGNIFICANCE OF THE WORK\nThe field of earthquake hazard and ground mofion simulafion is large, and so such a study will no doubt be of interest to a large number of specialists. However, I’m unclear of the wider interest or implicafions for this work beyond providing slight decreases in output variability from exisfing methods. Perhaps I missed this in the Introducfion secfion, but it’s unclear to me how the suggested approach is driving the science forward beyond incremental gains, and the focus on a very specific case study doesn’t help in this regard.\nIt appears to me that the main significance of the work is the ability to match hazard esfimates from exisfing Ground Mofion Predicfion Equafions albeit with reduced variability/uncertain. While I don’t quesfion this is an important step forward, I’m unconvinced this is a substanfially significant contribufion for a mulfi-disciplinary audience.\nDOES THE WORK SUPPORT THE CONCLUSIONS AND CLAIMS\nPartly. The method is able to produce a large number of simulafions and produce results that are in keeping with previous findings with reduced variability. However, I’m not sure the approach makes the advances that the authors claim in the Introducfion secfion\nARE THERE ANY FLAWS IN THE DATA ANALYSIS, INTERPRETATION AND CONCLUSIONS?\nIn the main, this study appears robust, with suitable data analysis and interpretafion. Where I am left confused is in the conclusions and how other researchers can and should take this work forward. If this is some major leap forward in the science of earthquake hazard derivafion then I must be missing it, and I would recommend the authors make this point more clearly. Perhaps I am under-playing the technical advancements that have gone into achieving these results, but to me this seems like a fairly standard Monte Carlo model using exisfing assumpfions and understanding, rather than generafing some new understanding. Even for this parficular case study, the results appear to simply confirm the exisfing knowledge from empirical GMPEs. I would encourage the authors here to make a befter ‘sales pitch’ as to why this approach is so important, and in parficular focus on making that clear and obvious to a broader audience – at present I imagine much of the detail is really only relevant for a sub-set of specialists in ground mofion modelling.\nIS THE METHODOLOGY SOUND? IS THERE ENOUGH DETAIL PROVIDED IN THE METHODS FOR THE WORK TO BE REPRODUCED?\nFrom what I can tell, the method is appropriate and robust, and the paper describes the approach in sufficient detail to allow reproducfion. However, the precise details of the approach are slightly beyond my specific experfise and so other referees may have more perfinent comments.\nMy main concerns here are around the wider applicability and assumpfions that go into the model. If the authors envisage this approach being widely adopted, then I would suggest they focus on describing how this method can be applied elsewhere, parficularly in regions where there is liftle informafion on historical earthquakes and fault structures (i.e. most of the world’s fault-lines!). Further, there appears to be no real scrufiny of the relafionships linking basic seismic informafion to the MCE. So, in reality, is the main contribufion of this paper the ability to provide a very large number of models using exisfing understanding and assumpfions?", "reviewer_3": "The paper is interesfing and well wriften and covers an important topic. It deals with the esfimafion of the MCE at a dam site using physics-based ground mofion.\nDescripfion\nThe authors state that the maximum frequency of the simulafions is up to 10Hz and that all important variability of the parameters influencing the results is considered.\nThey selected the faults and assigned the maximum expected magnitude. Running thousands of scenarios by changing source parameters, they computed accelerograms at the edge of a site by extracfing relevant intensity measurements.\nThey evaluated the distribufion of the different MIs. They claim that the results express the MCE.\nObservafions:\nThe topic is quite interesfing as both MCE assessment and the use of physics-based ground mofion simulafions are acfive research topics. However, more details about specific input pafterns need to be added. Also, authors must state what they mean by MCE. Since it is a seismic input for the structural analysis, it should represent the input that provides the maximum excitafion for the structure under analysis. Since the dam is very sfiff, it is possible that scenarios with lower magnitudes could excite the dam more than the scenarios considered here. So is it really MCE?\nTo really find the MCE as an input for the structural analysis, mulfiple scenarios should be combined, also considering lower magnitudes. A procedure to account for this, also through ground mofion simulafions, can be found in the reference aftached to the end.\nThe uncertainty in the structural model has not been considered (and this may explain part of the reduced variability with respect to the GMPE) and the distribufion of the parameters implemented in the source model is not well described.\nIn short, the paper presents interesfing aspects but lacks a thorough discussion on the possible limitafions of the presented results. A minor revision is therefore suggested to clarify the following specific comments.\nSpecific comments:\n- The structural model is not described\n- The velocity seems to be too fast to reach the specific condifions of the real site, please look into this\n- The maximum frequency is a funcfion of the source, the structural model and the precision of the site specific layers. The high frequencies are strongly influenced by the local soft layers. It seems they are not included in the model\n- Line 129: An occurrence model for magnitudes has not been used so it is befter not to call the IM distribufions \"hazard curves\".\n- Line 155: it is true that accelerograms are available, however since it is not imaginable to use all of them, it is necessary to apply an accurate selecfion procedure based on the dynamic properfies of the structure to be analysed.\n- Fig. 4: it is true that the PBGMS could be a tool to obtain more informafion on seismic hazard and also to limit uncertainfies. But in this case the variability appears to be very small. A discussion of this needs to be added. Uncertainty on soil parameters has also not been included and this would surely increase dispersion (parficularly at high frequency)\n- Line 210. See previous discussion on “What is MCE?\n- Line 217: At least in the supplementary material it might be helpful to explain the parameter distribufions and how that variability was evaluated.\nChieffo, N., Fasan, M., Romanelli, R., Formisano, A., Mochi, G., 2022. “Physics-Based Ground Mofion Simulafions for the Predicfion of the Seismic Vulnerability of Masonry Building Compounds in Mirandola (Italy)”, Buildings, 11, 667. hftps://doi.org/10.3390/buildings11120667\nHassan, H.M., Fasan, M., Sayed, M.A., Romanelli, F., ElGabry, M.N, Vaccari, F., Hamed, A., 2020. “Site-specific ground mofion modeling for a historical Cairo site as a step towards computafion of seismic input at cultural heritage sites”, Engineering Geology, Volume 268, 105524, hftps://doi.org/10.1016/j.enggeo.2020.105524\nFasan, M., Hassan, H.M., Magrin, A., Vaccari, F., Romanelli, F., ElGabry, 2023. “Mulfi-scenario Physics-Based Seismic Hazard Assessment of Cultural Heritage Sites”, in El-Qady, G.M., Margoftini, C. (eds) Sustainable Conservafion of UNESCO and Other Heritage Sites Through Proacfive Geosciences. Springer Geology. Springer, Cham. hftps://doi.org/10.1007/978-3-031-13810-2_26"}, "author_response": "Response to the comments\nThe authors would like to thank the three reviewers for their constructive comments, which\nwere of great help in improving the manuscript. The authors have carefully considered the detailed\ncomments, and the point-by-point responses to the reviewers’ comments are given bellow\n(Reviewers’ comments are in italic fonts, responses are in normal fonts and changes of the\nmanuscript are in bold fonts).\nReviewers' comments:\nReviewer #1 (Remarks to the Author):\nComment 1.1:\nThis manuscript presents results from numerical simulations of ground shaking from two faults in\nChina, randomizing some earthquake source parameters. The study mixes hazard analysis\n(characterizing earthquake sources and resulting shaking) with adjustments to the method for\npredicting shaking. The use of earthquake scenarios for hazard analysis, and the use of physics-based numerical simulations to predict ground motions, are both areas of research that have been\nstudied for decades. The authors should be clearer about where their intended contribution is, as many of the\nstatements of the paper are largely repeating statements made elsewhere. Without a clear\ninnovation here, the manuscript does not appear suitable for publication. A few minor comments\nare below as well.\nResponse: We appreciate Prof. Backer for carefully reading our manuscript and making the\ninsightful, critical, and constructive feedbacks. We agree that the novelty and contribution of our\nstudy are not elaborated in the original manuscript. The use of earthquake scenarios for hazard\nanalysis, and the use of physics-based numerical simulations to predict ground motions have been\nstudied for decades. However, this study provides a fully physics-based approach for assessing the\nMCE hazard by comprehensively considering the source process, propagation path, and local site\nconditions. To the best of the authors’ knowledge, it achieves two important breakthroughs over\nexisting research in these areas based on the latest advances in deterministic broadband ground-\nmotion simulations and our newly proposed multidimension source model for describing the rupture\nprocess.\nFirst, this study realized the deterministic broadband analysis for the MCE hazard. We applied\nthe newly-developed broadband ground-motion simulation method to the seismic hazard analysis\nprocedure, driving an order increase of effective frequency contents for the deterministic ground-\nmotion simulations, i.e., from the low frequency range (< 1 Hz) to the high frequency range up to\nearthquakes, e.g., the source process, propagation path, and local site conditions, is deterministically\nconsidered to obtain realistic ground motions at the target site.\nSecond, the proposed method achieved the full-scenario analysis for the MCE hazard by taking\nadvantages of self-similar subsources and adjoint simulations. Previous scenario-based seismic\nhazard analysis methods used a very limited number of earthquake scenarios, which includes only\npartial source variables, and thus could not comprehensively assess the risk of possible future\nearthquakes. In contrast, we obtained the MCE hazard through massive earthquake scenarios (up to\ntens of millions of scenarios) with a holistic consideration of the uncertainties in all kinematic\nparameters of the source process, enabling more comprehensive and accurate prediction for the\nseismic hazard.\nMoreover, the proposed method can generate the spatial ground-motion field for specified\nhazard levels around the target site by forward simulations. This is of great importance for major\nprojects with large-span structures (e.g., dams, bridges, and nuclear power stations), as the spatial\nheterogeneity of ground motions may have profound influences on those structures. Furthermore,\nthis study also revealed some essential findings through the quantitative analysis of the seismic\nhazards. For instance, the seismic hazards for the same site can have significant differences when\nthey are represented by different IMs.\nIn a word, we believe that these contributions, along with the detailed analysis and results\npresented in the manuscript, make our study valuable and relevant to the field of seismic hazard\nanalysis.\nAs broadband ground motions at the target site are explicitly generated for all\nearthquake scenarios, the seismic hazards of arbitrary IMs can be obtained, not just spectral\naccelerations. Therefore, for specific major engineering structures, the proposed method can\nprovide personalized seismic hazard results by using the optimal IMs of them. Moreover, this\nmethod can give the earthquake scenarios with the specified seismic hazard levels and the\ncorresponding broadband ground motions, which can be directly used in performance-based\nseismic design and analysis. The spatial ground motion field around the target site can also be\ngenerated using the earthquake scenarios, which is particularly important in the seismic\ndesign for large-span structures such as dams and bridges.\nMeanwhile, the MCE hazards for the Xiluodu dam site are further analyzed with four\nrepresentative IMs (Fig. S4 and S5), including the root-mean-square of acceleration ((cid:2183) ),\n(cid:2174)(cid:2169)(cid:2175)\nroot-mean-square of velocity ((cid:2204) ), Arias intensity (Ia), and cumulative absolute velocity\n(cid:2174)(cid:2169)(cid:2175)\n(CAV). The four IMs at the river-parallel direction for the Yaziba seismic zone are obviously\nhigher than those for the Leibo seismic zone, indicating that the seismic hazards represented\nby different IMs may have significant differences for the same site. Therefore, with the optimal\nIM of specific engineering structures, this study can provide personalized seismic hazards for\nthem, enabling more accurate and reasonable evaluations for the MCE hazards.\nMoreover, using the source process of earthquake scenarios corresponding to the\nspecified hazard level, e.g., those shown in Fig. 3, the spatial ground-motion field around the\ntarget site can be obtained by forward simulations. ShakeMaps for the spatial ground-motion\nfield generated by forward simulations with the two earthquake scenarios in Fig. 3 are shown\nin Figs. S6 and S7, respectively. From these ShakeMaps, ground motions generated by realistic\nearthquake scenarios can show significant spatial heterogeneity, which may have profound\neffects on major projects with large-span structures, e.g., dams, bridges, and nuclear power\nstations. Overall, this study demonstrates that the physical backgrounds of earthquakes,\nincluding the source process and the propagation path, have significant impacts on the ground\nmotions at specific sites and should be paid special attention in the seismic design and analysis\nthere.\nComment 1.2:\n\"Maximum credible earthquake\" is a discouraged terminology in recent decades. It was previously\nused to refer to earthquake ground motions before its phasing out, and it is unclear here whether\nthe term is being used to refer to a ground motion or an earthquake magnitude (the full set of\nearthquake source parameters is a vector and so doesn't have a clear maximum). There is no\n\"maximum\" earthquake ground motion either, as the authors acknowledge through their use of\nmillions of stochastic simulations. An alternate terminology would be preferred.\nResponse: We agree that the term of \"maximum credible earthquake\" in the original manuscript is\nnot clear due to its ambiguity. We use this term to refer to the earthquake with the largest magnitude\nthat can reasonably be expected to be generated by a specific source on the basis of seismological and\ngeological evidence (Earthquake Design and Evaluation for Civil Works Projects, ER 1110-2-\n1806, 2016). We also appreciate the comment on the lack of a clear \"maximum\" earthquake ground\nmotion. In this study, we used numerous earthquake scenarios to account for the uncertainties of all\nthe kinematic source parameters. The hazards of the earthquakes with the largest magnitude, i.e.,\nthe maximum credible earthquake hazard (MCE hazards), is then obtained using broadband ground\nmotions generated these earthquake scenarios. With the MCE hazards, ground motions\ncorresponding to the specified hazard levels can be directly used in performance-based seismic\ndesign and analysis. The meanings of \"Maximum credible earthquake\" and \"Maximum credible\nearthquake hazards\" are clarified in the revised manuscript.\nHerein, the term of MCE refers to the earthquake with the largest magnitude that can\nreasonably be expected to be generated by a specific source on the basis of seismological and\ngeological evidence18. Since there may be several significant active faults with different upper\nmagnitude limits in the vicinity, the target site may have multiple MCEs. The MCE hazards,\ni.e., the hazards for the target site caused by the largest magnitude earthquakes at all\nconsidered active faults, are analyzed using comprehensive MCE scenarios at those active\nfaults.\nComment 1.3:\nWhy generate millions of ground motion simulations, but consider only a single fixed earthquake\nmagnitude, dip, etc. for each fault? Some thought and discussion is needed regarding uncertainties\nin potential future earthquake scenarios, and how they are reflected in the analysis.\nResponse: In this study, uncertainties of all kinematic parameters of the source process, including\nthe fault location, the hypocenter, and the distribution of slip, rupture time, rise time, and rake,\nwere\ncomprehensively taken into account to obtain the MCE hazard for the target site. Moreover, we\nconsidered the earthquake scenarios with the maximum credible magnitude that is determined based\non the historical earthquake records and the fault exploration results1. The dip of the seismic fault\nwhere the earthquake scenarios occur is determined by the fault exploration results1. However, it\nshould be noted that our proposed method is not limited to a single magnitude and fault tendency.\nIf needed, the uncertainty of these two factors can also be considered in the seismic hazard analysis\nprocedure when the dip angle of fault and the maximum credible magnitude are not clear.\nComment 1.4:\nLine 108, 2000 m/s at the surface is very stiff. Is this representing a measured value at the site, or\nis this high value necessary due to numerical modeling needs? A clarification is needed.\nResponse: Velocity at the dam site is determined based on the exploration results of the engineering\nsite 1. In this study, the Xiluodu arch dam was selected as the research object. Due to the special\ncharacteristics of the arch dam, the foundation conditions are extremely demanding, and thus the\nengineering site of the Xiluodu arch dam is chosen on very hard bedrock. As the reviewer suggested,\nthe local site conditions of the Xiluodu dam are clarified in Supplementary Information of the\nrevised manuscript.\nHere it should be noted that the foundation conditions are very demanding for the arch dams\ndue to their structural characteristics. Therefore, the engineering site of the Xiluodu arch dam\nis chosen on the hard bedrock where the minimum shear wave velocity is about 2000 m/s.\nReviewer #2 (Remarks to the Author):\nComment 2.1:\nNOTEWORTHY RESULTS\nThis paper provides a case study of potential ground shaking from earthquakes on two faults close\nto a major dam in China, demonstrating that the hazard is similar from both faults despite the\nvariations in potential maximum credible earthquakes. In most respects the method here is more\nnoteworthy than the specific results for the case study, using an extremely large number of\n‘scenarios’ to better define uncertainty in ground shaking at a specific site.\nSIGNIFICANCE OF THE WORK\nThe field of earthquake hazard and ground motion simulation is large, and so such a study will no\ndoubt be of interest to a large number of specialists. However, I’m unclear of the wider interest or\nimplications for this work beyond providing slight decreases in output variability from existing\nmethods. Perhaps I missed this in the Introduction section, but it’s unclear to me how the suggested\napproach is driving the science forward beyond incremental gains, and the focus on a very specific\ncase study doesn’t help in this regard.\nIt appears to me that the main significance of the work is the ability to match hazard estimates from\nexisting Ground Motion Prediction Equations albeit with reduced variability/uncertain. While I\ndon’t question this is an important step forward, I’m unconvinced this is a substantially significant\ncontribution for a multi-disciplinary audience.\nResponse: We thank the reviewer for the constructive comments on our manuscript. Regarding the\nreviewer’s concern about the wider interest and implications of our study beyond providing slight\ndecreases in output variability from existing methods, we would like to emphasize that the proposed\napproach is driving the science forward beyond incremental gains. We propose a seismic hazard\nanalysis method based on the full-scenario deterministic analysis of MCE. Compared to traditional\nseismic hazard analysis methods, our method can provide the hazard results for any intensity\nmeasure, not just the spectral accelerations. Therefore, for major engineering structures such as\ndams, long-span bridges, and high-rise buildings, this method can give personalized seismic hazard\nresults by using optimal intensity measures instead of the spectral accelerations that are commonly\nadopted in the conventional approaches.\nAdditionally, the proposed method can provide earthquake scenarios and broadband seismic\nmotions corresponding to any hazard level, which can be directly used for structural response\nanalysis. The spatial ground motion field around the target site can also be generated using the\nearthquake scenarios of specific seismic hazard levels, which is particularly important for large-\nspan structures such as dams and bridges.\nMoreover, our method can generate a massive amount of near-field broadband ground motions,\nwhich can be used to improve the results of empirical ground motion prediction equations for near-\nfield large earthquakes. This is of great significance for seismic hazard analysis research because\nthe empirical ground motion prediction equations are limited by the lack of records of the near-field\nlarge earthquake and thus their predictions for the near-field hazard of large earthquake are usually\nnot reliable.\nWe acknowledge this comment regarding the focus on a specific case study, and we have added\nadditional discussions in the manuscript to highlight the general applicability of the proposed\napproach beyond the specific case study presented in this work.\nCompared to traditional seismic hazard analysis methods, our method can provide\nhazard results for any intensity measures (IMs), not just the spectral accelerations. Therefore,\nfor major engineering structures such as dams, nuclear power plants, long-span bridges, and\nhigh-rise buildings, this method can give personalized seismic hazard results by using optimal\nIMs to provide more accurate seismic hazard evaluations. Herein, four representative IMs\n(root-mean-square of acceleration ((cid:2183) ), root-mean-square of velocity ((cid:2204) ), Arias\n(cid:2174)(cid:2169)(cid:2175) (cid:2174)(cid:2169)(cid:2175)\nintensity (Ia), and cumulative absolute velocity (CAV)) are adopted to analyze the MCE\nhazard. These IMs are defined as follows,\n1 tD 1/2\na = (cid:4678) (cid:3505) a(cid:4666)t(cid:4667)2dt(cid:4679) （S1）\nRMS t\nD 0\nwhere t is the total duration of ground motions, and a(t) is the acceleration time series.\nD\n1 tD 1/2\n(cid:2204) = (cid:4678) (cid:3505) (cid:2204)(cid:4666)t(cid:4667)2dt(cid:4679) （S2）\nRMS t\nD 0\nwhere (cid:2204)(t) is the velocity time series.\ntD\nCAV = (cid:3505) |a(cid:4666)t(cid:4667)|dt （S3）\n0\nπ tD\na 2g\nscenario earthquakes occurred in the Yaziba seismic zone and the Leibo seismic zone are\npresented in Fig. S4 and S5, respectively. In contrast to the seismic hazard results represented\nby the spectral accelerations (Fig. 2), which are comparable for the two seismic zones, the four\nIMs at the river-parallel direction are obviously higher for the Yaziba seismic zone than those\nfor the Leibo seismic zone. It is demonstrated that the seismic hazard results for different IMs\nmay have significant differences for the same site. Therefore, adopting the optimal IM for\ndifferent engineering structures can provide more reasonable seismic hazard evaluations.\nFig. S4 Seismic hazard results for four different IMs at the Xiluodu dam site for scenario\nearthquakes occurred in the Yaziba seismic zone. The four IMs corresponding to all MCE\nscenarios are summarized to obtain the seismic hazard results at the Xiluodu dam site. The\nseismic hazard results in the river-parallel direction, river-perpendicular direction, and\nvertical direction are presented for the Yaziba seismic zone.\nFig. S5 Seismic hazard results for four different IMs at the Xiluodu dam site for scenario\nearthquakes occurred in the Leibo seismic zone. The four IMs corresponding to all MCE\nscenarios are summarized to obtain the seismic hazard results at the Xiluodu dam site. The\nseismic hazard results in the river-parallel direction, river-perpendicular direction, and\nvertical direction are presented for the Leibo seismic zone.\nShakeMaps generated by forward simulations for the scenario earthquakes at the Yaziba\nseismic zone and Leibo seismic zone, as shown in Figure 3, are presented in Fig. S6 and S7,\nrespectively. These ShakeMaps demonstrate that the realistic spatial ground motion field\naround the target site can be thoroughly produced by forward simulations using the specified\nrupture process of earthquake scenarios corresponding to specific hazard levels. Therefore,\nfor large-span structures (e.g., dams and bridges) that may be significantly affected by the\nheterogeneous ground-motion field, our method can provide more realistic ground motion\ninput for the seismic design of these structures.\nFig. S6 ShakeMap for the scenario earthquake at the Yaziba seismic zone shown in Figure\n3. PGA of the model domain for this scenario earthquake are presented by different colors. The\nblack triangle represents the dam site.\nFig. S7 ShakeMap for the scenario earthquake at the Leibo seismic zone shown in Figure\n3. PGA of the model domain for this scenario earthquake are presented by different colors. The\nblack triangle represents the dam site.\nComment 2.2:\nDOES THE WORK SUPPORT THE CONCLUSIONS AND CLAIMS\nPartly. The method is able to produce a large number of simulations and produce results that are\nin keeping with previous findings with reduced variability. However, I’m not sure the approach\nmakes the advances that the authors claim in the Introduction section\nResponse: We agree that the application scope of the proposed method is not fully elucidated in the\noriginal manuscript. Here we clarified that the comparison with the empirical GMPEs is only to\nverify the proposed method. Our method can provide much richer results over the conventional\napproach, e.g., arbitrary intensity measures and the spatial ground motion field for the specified\nhazard levels (please see the response to Comment 2.1), which cannot be provided by the\nconventional approach. Moreover, the advance of the proposed method is further elaborated in the\nresponse to Comment 1.1.\nComment 2.3:\nARE THERE ANY FLAWS IN THE DATA ANALYSIS, INTERPRETATION AND CONCLUSIONS?\nIn the main, this study appears robust, with suitable data analysis and interpretation. Where I am\nleft confused is in the conclusions and how other researchers can and should take this work forward.\nIf this is some major leap forward in the science of earthquake hazard derivation then I must be\nmissing it, and I would recommend the authors make this point more clearly. Perhaps I am under-\nplaying the technical advancements that have gone into achieving these results, but to me this seems\nlike a fairly standard Monte Carlo model using existing assumptions and understanding, rather\nthan generating some new understanding. Even for this particular case study, the results appear to\nsimply confirm the existing knowledge from empirical GMPEs. I would encourage the authors here\nto make a better ‘sales pitch’ as to why this approach is so important, and in particular focus on\nmaking that clear and obvious to a broader audience – at present I imagine much of the detail is\nreally only relevant for a sub-set of specialists in ground motion modelling.\nResponse: We appreciate the reviewer’s positive feedback on the robustness of our study and our\ndata analysis and interpretation. We are also grateful for the valuable comments on the conclusions\nand the importance of our work for a broader audience, and the general applicability and novelty of\nour proposed method are elaborated in the response to Comment 1.1 and 2.1.\nComment 2.4:\nIS THE METHODOLOGY SOUND? IS THERE ENOUGH DETAIL PROVIDED IN THE\nMETHODS FOR THE WORK TO BE REPRODUCED?\nFrom what I can tell, the method is appropriate and robust, and the paper describes the approach\nin sufficient detail to allow reproduction. However, the precise details of the approach are slightly\nbeyond my specific expertise and so other referees may have more pertinent comments.\nMy main concerns here are around the wider applicability and assumptions that go into the model.\nIf the authors envisage this approach being widely adopted, then I would suggest they focus on\ndescribing how this method can be applied elsewhere, particularly in regions where there is little\ninformation on historical earthquakes and fault structures (i.e. most of the world’s fault-lines!).\nFurther, there appears to be no real scrutiny of the relationships linking basic seismic information\nto the MCE. So, in reality, is the main contribution of this paper the ability to provide a very large\nnumber of models using existing understanding and assumptions?\nResponse: We appreciate the reviewer’s positive feedback on the robustness and reproducibility of\nthis study. The meaning of MCE in this study and the main contributions of our proposed method\nhave been described in the response to Comment 1.2. Herein, we emphasize that our proposed\nmethod has good universality and is applicable to different regions. Similar to the conventional\napproach, our method can be applied to the analyze the seismic hazard at the target sites with some\nbasic seismic information in the region, e.g., historical earthquakes and fault structures.\nNevertheless, we believe that this does not overly restrict the proposed method because, these basic\nseismic information is usually available for densely populated urban areas and major engineering\nsites that are the focus of seismic hazard analysis.\nReviewer #3 (Remarks to the Author):\nComment 3.1:\nThe paper is interesting and well written and covers an important topic. It deals with the estimation\nof the MCE at a dam site using physics-based ground motion.\nDescription\nThe authors state that the maximum frequency of the simulations is up to 10Hz and that all important\nvariability of the parameters influencing the results is considered. They selected the faults and\nassigned the maximum expected magnitude. Running thousands of scenarios by changing source\nparameters, they computed accelerograms at the edge of a site by extracting relevant intensity\nmeasurements. They evaluated the distribution of the different MIs. They claim that the results\nexpress the MCE.\nObservations:\nThe topic is quite interesting as both MCE assessment and the use of physics-based ground motion\nsimulations are active research topics. However, more details about specific input patterns need to\nbe added. Also, authors must state what they mean by MCE. Since it is a seismic input for the\nstructural analysis, it should represent the input that provides the maximum excitation for the\nstructure under analysis. Since the dam is very stiff, it is possible that scenarios with lower\nmagnitudes could excite the dam more than the scenarios considered here. So is it really MCE?\nTo really find the MCE as an input for the structural analysis, multiple scenarios should be\ncombined, also considering lower magnitudes. A procedure to account for this, also through ground\nmotion simulations, can be found in the reference attached to the end.\nResponse: We are grateful for the reviewer’s suggestion regarding MCE. As mentioned in the\nresponse to Comment 1.2, MCE refers to the earthquake with the largest magnitude that can\nreasonably be expected to be generated by a specific source on the basis of seismological and\ngeological evidence (Earthquake Design and Evaluation for Civil Works Projects, ER 1110-2-1806,\n2016). Meanwhile, we have also provided additional details about the specific input patterns.\nWe also fully agree with the reviewer that multiple earthquake scenarios with different\nmagnitudes should be considered to really find the MCE for the target site. According to the seismic\nsafety evaluation report of engineering site for the Xiluodu arch dam 1, there are two important fault\nstructures in the near field: the Yaziba fault with a potential magnitude limit of 7.5 and the Leibo\nfault with a potential magnitude limit of 7.0. Earthquake scenarios occurred at the two fault\nstructures are considered to analyze the MCE hazard for the Xiluodu dam site. We found that\nalthough the magnitude of scenario earthquakes at the Leibo fault (Mw7.0) is significantly less than\nthat of scenario earthquakes at the Yaziba fault (Mw7.5), scenario earthquakes at the Leibo fault can\ncause similar seismic risk to the Xiluodu dam site. As the reviewer suggested, following 2, we further\ncombined the ground motions generated by the scenarios at the two considered fault structures to\nfind the final MCE for the target site. The seismic hazards for the Yaziba seismic zone, the Leibo\nseismic zone, and the combination of the two seismic zones are shown in Fig. R1. However, the\nseismic hazards of different faults may differ significantly when different IMs are adopted (the\nresponse to Comment 2.1). Considering that the structural dynamic response analysis requires the\nground-motion time series as inputs, the seismic hazards represented by just a single IM may not be\nstrongly associated with the real dynamic response of the structures, because the ground-motion\ntime series with the same IM but different physical backgrounds can result indifferent structural\nresponse3. Therefore, we think it may be more reasonable to evaluate the seismic hazards of different\nfaults separately and select the ground-motion time series corresponding to the specified hazard\nlevels at these faults for the structural dynamic analysis.\nFig. R1 Seismic hazards of the Xiluodu dam site. Spectral accelerations of all MCE scenarios\nare summarized to obtain the seismic hazard results at the specified periods. The seismic hazards\nin the river-parallel direction and the river-perpendicular direction are presented for the Yaziba\nseismic zone, the Leibo seismic zone, and the combination of the two seismic zones.\nComment 3.2:\nThe uncertainty in the structural model has not been considered (and this may explain part of the\nreduced variability with respect to the GMPE) and the distribution of the parameters implemented\nin the source model is not well described.\nIn short, the paper presents interesting aspects but lacks a thorough discussion on the possible\nlimitations of the presented results. A minor revision is therefore suggested to clarify the following\nspecific comments.\nResponse: We agree with the reviewer that the epistemic uncertainty in the structural model can\ncontribute to the variability of the seismic hazard results. However, with further refinement of the\nvelocity models, these differences are expected to diminish 4. In our previous studies of ground-\nmotion simulations for the 1992 Landers earthquake and the 1994 Northridge earthquake 5,6, we\nfound that by coupling the regional velocity model with the local geophysical information, the\nsimulated ground motions achieve a fairly good agreement with the recorded ground motion in a\nwide frequency range (0-8 Hz for the 1992 Landers earthquake and 0-5 Hz the 1994 Northridge\nearthquake). Therefore, we did not consider the epistemic uncertainty of the structural model in this\nstudy. Meanwhile, we added a detailed description of the parameters implemented in the source\nmodel in the revised manuscript.\nSpecific comments:\nComment 3.3:\n- The structural model is not described\nResponse: The structural model is further described in the supplementary materials of the revised\nmanuscript.\nTo simulate the seismic wave propagation of source-path-site, a three-dimensional (3D)\nnumerical model for the vicinity of the Xiluodu dam site is constructed with the high-\nresolution topography and realistic velocity structures. The topography is considered using\nthe digital elevation model data with a resolution of 30 m. Since this study only focuses on\nground motions at the engineering site, accurate local velocity structures are of great\nimportance for generating realistic ground motions there1. In this study, we construct a three-\ndimensional (3D) numerical model (Fig. S1) by coupling the regional velocity model,\nEast Asia\nEARA2014, with the geological exploration information at the dam site. Here it should be\nclarified that the foundation conditions are very demanding for the arch dams due to their\nstructural characteristics. Therefore, the engineering site of the Xiluodu arch dam is chosen\non the hard bedrock with the minimum shear wave velocity of about 2000 m/s.\nFig. S1 Velocity structures around the Xiluodu dam site. The shear wave velocity in the\nmodel domain is presented by different colors as shown in the color bar. The black triangle\nindicates the Xiluodu dam site.\nComment 3.4:\n- The velocity seems to be too fast to reach the specific conditions of the real site, please look into\nthis\n- The maximum frequency is a function of the source, the structural model and the precision of the\nsite specific layers. The high frequencies are strongly influenced by the local soft layers. It seems\nthey are not included in the model\nResponse: Velocity at the site is determined based on the geological exploration data of the\nengineering site. The Xiluodu dam site is chosen on very hard bedrock. According to the geological\nexploration 1, there are no soft soil layers at the dam site. We have found that the simulated ground\nmotions can achieve a fairly good agreement with the records by coupling the regional velocity\nmodel with the local geophysical information 5,6. As the Xiluodu dam site has no local soft layers,\nthe nonlinear material behaviors there will be slight, and the obtained ground motions in this study\nshould be relatively reasonable.\nComment 3.5:\n- Line 129: An occurrence model for magnitudes has not been used so it is better not to call the IM\ndistributions \"hazard curves\".\nResponse: As the reviewer suggested, the IM distribution is renamed “seismic hazards”.\nComment 3.6:\n- Line 155: it is true that accelerograms are available, however since it is not imaginable to use all\nof them, it is necessary to apply an accurate selection procedure based on the dynamic properties\nof the structure to be analysed.\nResponse: We are grateful for this insightful and valuable suggestion on applying our method to\nthe practice of structural dynamic analysis. Our method generates numerous ground-motion time\nseries (up to tens of millions in this study), but the structural dynamic analysis can only use a very\nlimit number of them. We fully agree with the reviewer that a selection method is needed to apply\nthe generated ground-motion time series to the structural dynamic analysis. Currently, we are\nstudying the application of this method to the practice of the performance-based seismic design and\nanalysis, e.g., generating the physics-based conditional mean spectrum and the associated ground-\nmotion time series. However, as this study mainly aims to develop a seismic hazard analysis method\nfor MCE and limited by the space, we will investigate the selection method for ground-motion time\nseries in a subsequent study.\nComment 3.7:\n- Fig. 4: it is true that the PBGMS could be a tool to obtain more information on seismic hazard\nand also to limit uncertainties. But in this case the variability appears to be very small. A discussion\nof this needs to be added. Uncertainty on soil parameters has also not been included and this would\nsurely increase dispersion (particularly at high frequency)\nResponse: Parameters of the local site are described in the response to Comment 1.4, and the\nvariability of the seismic hazards is discussed in the response to Comment 3.2.\nComment 3.8:\n- Line 210. See previous discussion on “What is MCE?\nResponse: In this study, MCE refers to the earthquake with the largest magnitude that can\nreasonably be expected to be generated by a specific source on the basis of seismological and\ngeological evidence. It is now added in the revised manuscript.\nComment 3.9:\n- Line 217: At least in the supplementary material it might be helpful to explain the parameter\ndistributions and how that variability was evaluated.\nResponse: As the reviewer suggested, the details about parameter distributions and variability are\nprovided in the supplementary materials.\nTable S2 Distribution range of the source process parameters for earthquake scenarios at the\nYaziba fault and the Leibo fault.\nFault name Parameter Distribution range Constraint\nHypocenter All locations on the fault ——\nSlip (m) 0-6.72 Average=1.68\nRupture velocity\nYaziba 2.5-3.5 ——\n(km/s)\nRise time (s) 1-4 Average=2.5\nRake (deg) 40-140 70≤Average≤110\nHypocenter All locations on the fault ——\nSlip (m) 0-3.0 Average=0.75\nRupture velocity\nLeibo 2.5-3.5 ——\n(km/s)\nRise time (s) 0.5-2.5 Average=1.5\nRake (deg) 130-230 160≤Average≤200\nTable S2 presents the distribution range of the source process parameters for earthquake\nscenarios at the Yaziba fault and the Leibo fault. For the generated earthquake scenarios, the\nhypocenters of them can be anywhere on the fault ruptures of earthquake scenarios. Based on\nthe constraints on the slip, rupture velocity, rise time, and rake angle ranges in the source\ninversion study6 and the stochastic source process model7, the source parameter ranges of the\nearthquake scenarios are defined in this study. The slip amount of each subfault is allowed to\nvary from 0 to 4 times the average slip value for the earthquake scenarios, while the average\nof them remains constant, i.e., 1.68 m for the Yaziba fault and 0.75 m for the Leibo fault. By\nsolving the Eikonal equation, the rupture time of each subfault is derived from the distribution\nof rupture velocity that varies from 2.5 km/s to 3.5 km/s. The rise time of each subfault is\nallowed to vary from 1 s to 4 s for the Yaziba fault and 0.5 s to 2.5 s for the Leibo fault, while\nthe average of them is equal to 2.5 s for the Yaziba fault and 1.5 s for the Leibo fault,\nrespectively. According to the fault exploration results, the Yaziba fault is a reverse fault while\nthe Leibo fault is a strike-slip fault. To determine the rake, the average rake is firstly allowed\nto vary from 70° to 110° for the Yaziba fault and from 160° to 200° for the Leibo fault. Next\nthe rake of each subfault is allowed to vary in the range of ±30° around the average rake.\nReference:\n1. Seismic safety evaluation report for the project site of Jinsha River Xiluodu Hydropower Station\n(in Chinese). Beijing Zhongzhen Pioneering Engineering Technology Research Institute, (2011).\n2. Hassan, H. M. et al. Site-specific ground motion modeling for a historical Cairo site as a step\ntowards computation of seismic input at cultural heritage sites. Engineering Geology 268,\n105524 (2020).\n3. Wang, J.-T., Jin, A.-Y., Du, X.-L. & Wu, M.-X. Scatter of dynamic response and damage of an\narch dam subjected to artificial earthquake accelerograms. Soil Dynamics and Earthquake\nEngineering 87, 93–100 (2016).\n4. Baker, J. W., Luco, N., Abrahamson, N. A., Maechling, P. J. & Olsen, K. B. ENGINEERING\nUSES OF PHYSICS-BASED GROUND MOTION SIMULATIONS. in Proceedings of the 10th\nNational Conference in Earthquake Engineering (2014).\n5. Wang, X.-C., Wang, J.-T., Zhang, L. & He, C.-H. Broadband ground-motion simulations by\ncoupling regional velocity structures with the geophysical information of specific sites. Soil\nDynamics and Earthquake Engineering 145, 106695 (2021).\n6. Wang, X., Wang, J. & Zhang, C. A Broadband Kinematic Source Inversion Method Considering\nRealistic Earth Models and Its Application to the 1992 Landers Earthquake. JGR Solid Earth 127,\n(2022)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I am sfill not convinced that this manuscript makes the type of advancement that is typical of a Nature Communicafions paper. Using numerical simulafions to characterize ground mofion hazard is an acfive field with many similar studies already in existence, and choice here of what uncertainfies to consider and what to omit is seemingly arbitrary.", "reviewer_2": "The authors have done a commendable job here addressing each of the reviewers comments, and this current version of the manuscript is significantly improved compared to the original. I'm pleased to see the authors have now more clearly described the wider contribufion this paper intends to make to the field, with a reduced focus on the specific case study, which is now appropriately highlighted as an exemplar of the approach.\nThere are sfill some minor areas that could be addressed to improve the paper and its readability.\nFirst, the term Maximum Credible Earthquake sfill seems fraught to me. The other reviewers highlighted this inifially and the authors have responded and now clearly define what they mean by MCE. However, given the context of the paper is really on the ground shaking at any given site, I find the focus on a single magnitude confusing. The authors themselves note that even moderate earthquakes have caused substanfial impacts in the past. I remain unconvinced that we should simply take at face value that the biggest magnitude earthquake can cause the largest shaking at a given site, considering complex interacfions of seismic waves with ground properfies. My understanding is that this is actually quite a minor point and that the proposed method could easily consider different magnitudes for each fault, but the authors here simply choose to demonstrate their approach via the \"MCE\". My issue therefore is that by choosing to focus on the term MCE the authors detract from their own work via readers focussing too intently on this term, rather than engaging fully with the method proposed.\nSecondly, in the supplementary informafion (and in the response to reviewers) the authors show figures of ground mofion from one of their scenario earthquakes, but include no informafion on what parameters were involved in this scenario. In order for these figures to make sense, its important that readers are provided those key details - which of your 22 million scenarios is this? In addifion, I wonder if the authors have considered a figure (or figures) here showing the spafial variafion in ground shaking across all their scenarios? I think this would be a valid contribufion.\nFinally, I am surprised to see so many of the perfinent methods details buried in the supplementary informafion and not the main text. I appreciate the word limit and requirements of Nat Comms, but to me some of the most important details and descripfions are buried away here when they really belong in the main text. The authors have done a solid job of addressing the reviewers comments through changes to the SI, but I think the paper would benefit from including parts of this in the main manuscript itself.\nOverall, these are relafively minor and I believe the authors have done a reasonable job of addressing the concerns previously posed.", "reviewer_4": "The manuscript presents a comprehensive understanding of the significant threat posed by major earthquakes to modern society, emphasizing their destrucfive potenfial and inherent unpredictability. The concept of the maximum credible earthquake (MCE) for a specific fault, characterized by various potenfial scenarios with differing source processes, contributes to the complex and uncertain nature of future seismic hazards. The abstract introduces a solufion in the form of a full-scenario analysis method that employs determinisfic broadband simulafions across a mulfitude of scenarios. This approach seeks to address the intricate nature of MCE hazards by considering all possible source process parameters along the fault, thereby facilitafing a more comprehensive assessment.\nWhile the abstract successfully explains this novel full-scenario analysis method and applies it to the seismic hazard assessment of China's Xiluodu dam, there appears to be potenfial for improvement in terms of pracfical applicafion. Furthermore, the proposed method's capacity to give a variety of intensity measures, ground mofion fime series, and spafial ground-mofion fields hold promise for a more precise and realisfic evaluafion of MCE hazards, with possible applicafions in earthquake engineering.\nIn conclusion, the paper presents an intriguing approach to tackling the uncertainty associated with MCE hazards and it would be appropriate to accept it for publicafion. Although the method's conceptual foundafion and potenfial contribufions are commendable, a closer examinafion and improvement in the applicafion phase could elevate the paper's overall impact.\n1. How does the incorporafion of numerous potenfial scenarios with different source processes contribute to the uncertainty in predicfing maximum credible earthquakes?\n2. Can you elaborate on the significance of conducfing determinisfic broadband simulafions as part of the proposed full-scenario analysis method?\n3. Could you provide more insight into the specific parameters and variables considered within the full-scenario analysis approach for evaluafing MCE hazards?\n4. In what ways could the refinement of the pracfical applicafion aspect enhance the pracficality and adaptability of the proposed method in real-world scenarios?\n5. Considering the potenfial for more realisfic MCE hazard evaluafions, how might the proposed method influence decision-making processes in earthquake engineering projects, parficularly in areas prone to seismic acfivity?"}, "author_response": "Response to the comments\nThe authors would like to thank the reviewers for their constructive comments, which\nwere of great help in improving the manuscript. The authors have carefully considered the detailed\ncomments, and the point-by-point responses to the reviewers’ comments are given bellow\n(Reviewers’ comments are in italic fonts, responses are in normal fonts and changes of the\nmanuscript are in bold fonts).\nREVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nComment 1.1\nI am still not convinced that this manuscript makes the type of advancement that is typical of a\nNature Communications paper. Using numerical simulations to characterize ground motion hazard\nis an active field with many similar studies already in existence, and choice here of what\nuncertainties to consider and what to omit is seemingly arbitrary.\nResponse: We sincerely appreciate the reviewer for providing the valuable comments on our work.\nThe comments in this and the original review have indeed guided us in refining and enhancing the\nmanuscript. We regret that the previous revision may not have adequately highlighted the\ncontributions and advancements of our study. Herein, we would like to further elaborate the\nadvancements and contributions of this study over existing research on evaluating the seismic\nhazard using earthquake scenarios and numerical simulations. Moreover, the uncertainties\nconsidered in this study are also interpreted below.\n(a) Advancements and contributions of this study\nWe acknowledge that there have been many studies that use earthquake scenarios and\nnumerical simulations to predict the seismic hazard (Graves et al., 2011; Denolle et al., 2014;\nRobinson et al., 2018; Panza and Bela, 2020; Milner et al., 2021; Zhang et al., 2021). As Baker et\nal. (2014) pointed out, “numerical simulations of earthquake strong ground motions have improved\nto the point where it is worth investigating the predictive power of these physics-based methods in\nseismic hazard analysis”. However, there are still some crucial issues that limit their applications in real-world scenarios, such as the restriction to low-frequency range (Baker et al., 2014). In this study,\nwe address two key issues constraining the applications of deterministic ground-motion simulations\nin seismic hazard evaluations.\nFirst, current seismic hazard evaluations using earthquake scenarios and numerical simulations\nare mostly constrained to the low-frequency range. For instance, 0-0.5 Hz in (Graves et al., 2011;\nMilner et al., 2021), 0-1 Hz (Panza and Bela, 2020; Zhang et al., 2021). However, high-frequency\nground motions are of most interest for earthquake engineering practice (Fu et al., 2017; Baker et\nal., 2021). Although some efforts have been made for fully deterministic broadband ground-motion\nsimulations, e.g., 0-4 Hz for a sequence of small earthquakes (< Mw 4.4) in the Volvi basin of Greece\n(Maufroy et al., 2015), 0-4 Hz for a M 7.0 scenario earthquake (Rodgers et al., 2018), 0-5 Hz for\ncomplexity of implementation and substantial computational efforts. Consequently, it is difficult to\neffectively account for the inherent uncertainties of earthquakes using these broadband simulation\nmethods, and this limits the usability of these methods in applications such as seismic hazard\nanalysis and source inversion (Wang et al., 2022).\nSecond, to describe the complex source process of earthquakes, especially that is associated\nwith high-frequency seismic waves, the source models in deterministic ground-motion simulations\nneed to include fine enough scales, leading to a large number of variables, which can be up to tens\nof thousands or even hundreds of thousands for moderate or large earthquakes (Graves and Pitarka,\n2010; Anderson, 2015; Crempien and Archuleta, 2015). It is recognized that the ensemble of\nearthquake scenarios should be large enough to comprehensively capture the variability in the\nsource parameters of earthquakes (Baker et al., 2014). However, existing studies only consider\npartial source variables, e.g., hypocenter and slip distribution (Graves et al., 2011), and use a very\nlimited number of earthquake scenarios to represent the potential future earthquakes, such as, less\nthan 100 scenarios (Denolle et al., 2014; Robinson et al., 2018), a total of 415000 scenarios for 7000\nruptures (that is, less than 60 scenarios for each rupture) (Graves et al., 2011). With such a number\nof scenarios and only partial variables considered, it is challenging to comprehensively evaluate the\nseismic hazard of potential future earthquakes, which has a large number of rupture variables (even\nup to hundreds of thousands for simulating broadband ground motions).\nIn this study, we propose a ground-breaking way for the seismic hazard analysis based on\nearthquake scenarios and numerical simulations. It is conducted based on our newly developed\ndeterministic broadband ground-motion simulation method (Wang, Wang, Zhang, and He, 2021;\nWang, Wang, Zhang, Li, et al., 2021; Wang et al., 2022), which has be validated through\ncomparisons with historical earthquake records and empirical ground-motion prediction models.\nParticularly, with the inverted rupture process for the 1992 Landers earthquake, the simulated\nground motions of our broadband numerical simulation method even had an impressive agreement\nin waveforms with the records in a wide range of frequency, as shown in Figure R1. Compared to\nexisting studies, our method achieves significant advancements in the following ways:\n By employing the developed ground-motion simulation method, we have achieved significant\nbreakthroughs in seismic hazard evaluations by expanding the effective frequency contents\nfrom the low frequency range (< 1 Hz) to the high frequency range up to 10 Hz. This broad\nfrequency range meets the current requirements of seismic design for most engineering\nstructures.\n To the best of our knowledge, this study has achieved, for the first time, a deterministic full-\nscenario analysis for the seismic hazard by applying the self-similar feature of our proposed\nmultidimension source model. The seismic hazard is evaluated by considering all uncertainties\nof potential future earthquakes with sufficient scenarios ((up to tens of millions of scenarios or\neven more), enabling more comprehensive and accurate prediction for the seismic hazard.\n Our method provides much richer outputs compared to traditional seismic hazard analysis\nmethods. For instance, it can generate a wide range of intensity measures, ground-motion time\nseries, and spatial ground-motion fields with specific hazard levels. These enriched outputs\npave the way for realistic and customized assessments of seismic hazard for specific\nengineering structures.\nFig. R1. Comparison of the velocity time series, Fourier velocity spectra, and acceleration\nresponse spectra for 5% damping between the records and the simulated ground motions at two\nrepresentative stations in the 1992 Landers earthquake (For each station, left: E-W; right: N-S).\nThe velocity time series of both the records and the simulated ground motions are bandpass\nfiltered between 0.1 and 8Hz (Wang et al., 2022).\nWith the above-mentioned advancements, our method has great potential in real-world\nscenarios and may have significant implications in the field of earthquake engineering. Here we list\ntwo important potential applications of our method in the seismic design practice:\n(1) Accurate evaluations of seismic hazards for major projects near significant faults. By\nincorporating the realistic physical process of earthquakes and Earth models, our method assesses\nthe seismic hazard based on deterministic broadband ground-motion simulations, enabling to\nconsider complex physical phenomena such as the rupture directivity, topographic effects, and basin\neffects. Specifically, our method has also been applied to evaluate the safety of several planned\nmajor projects which are located in seismically active areas in China and has revealed some\nsignificant phenomena. A typical example is provided in the response to Comment 4.6.\n(2) Seismic design fully based on realistic and unified physical backgrounds. Except for\nproviding the seismic hazard results, our method can further obtain spatial ground-motion fields\nthrough forward simulations, which is important for the seismic design of major projects with large\nspatial scales such as dams and bridges. Recently, we have proposed a source-to-structure simulation\nmethod by integrating regional ground-motion simulations and structural dynamic response analysis\nmethods (Zhang et al., 2020), and used the fault-to-structure simulation to reasonably reproduce the\ndynamic response of the Pacoima dam during the 1994 Northridge earthquake (Zhang et al., 2023).\nTherefore, with the fault-to-structure simulation technique, our study is promising for more\nambitious goals to achieve the seismic design fully based on realistic and unified physical\nbackgrounds of earthquakes, from seismic hazard evaluations to structural dynamic analysis.\nBased on fully deterministic broadband ground-motion simulations, to the best of our\nknowledge, this study for the first time achieved a deterministic full-scenario analysis of seismic\nhazard by considering all uncertainties of the earthquake source through an extensive range of\nscenarios. The proposed method is promising for more realistic and accurate evaluations of seismic\nhazards and has great application potentials in earthquake engineering. We believe that these\nadvancements and contributions in our study are of great interest to the readership of Nature\nCommunications.\n(b) Interpretation on the uncertainties considered in this study\nWe are sorry that the choice of what uncertainties to consider and what to omit is not clearly\ndescribed in the manuscript. It is recognized that the physical process of earthquakes primarily\ninvolves three parts, i.e., the source process, propagation path, and local site conditions. Among\nthese, the propagation path and local site conditions are determined by the velocity structure and\ntopography. For a specific site, both the velocity structure and topography are fixed, although with\npotential limitations in accuracy, particularly for regional velocity structure. Uncertainties of the\npropagation path and local site conditions are then considered as epistemic uncertainties, which are\nexpected to be improved with further refinement of the Earth model (Baker et al., 2014). Therefore,\nthis study does not consider the uncertainties associated with the propagation path, and local site\nconditions, i.e., the epistemic uncertainties in the velocity structure and topography. Instead, we\nmainly focus on the uncertainties associated with the seismic source.\nGiven the current understanding of earthquakes, the sources of potential future earthquakes are\nhighly uncertain with great randomness. Consequently, we evaluate the seismic hazard of the target\nsite by considering the possible scenarios of potential future earthquakes. It should be highlighted\nthat our method is able to take into account all variables of earthquakes, such as the fault location,\nhypocenter, and rupture process (the distribution of slip, rupture time, rise time and rake on the\nseismic fault), which are considered in the case of Xiluodu dam as presented in the manuscript. In\nrelation to the other variables such as earthquake magnitude and fault dip, we want to provide some\nclarification. As highlighted by Reviewer 2 in Comment 2.2, our approach is adaptable and can\nreadily incorporate these variables as well. For the presented case of Xiluodu dam in this study,\nhowever, we adopted the maximum magnitude of the surrounding faults for the consideration of\nextreme earthquakes that the site might encounter, and the fault dips are determined based on the\nexplorations of these faults. If required, our method is flexible enough to incorporate different\nearthquake magnitudes and fault dips for evaluating the seismic hazard of the target site.\nIn summary, except for epistemic uncertainties related to Earth models, which are expected to\ndiminish with further refinement of regional velocity structures, our method is equipped to\nincorporate all uncertainties related to the potential future earthquakes. This comprehensive\nconsideration of uncertainties demonstrates the robustness and adaptability of our approach in the\nface of the unpredictable nature of earthquakes. We added the following text to the revised\nmanuscript to describe the uncertainties considered in this study.\nAdditionally, it is worth emphasizing that our method is capable of incorporating all\nuncertainties related to potential future earthquakes. In this study, uncertainties of the fault\nlocation, hypocenter, and rupture process of earthquakes are considered in the seismic hazard\nevaluations for the Xiluodu dam site, while the earthquake magnitude are fixed to the\nmaximum magnitude of surrounding faults for the consideration of MCEs, and fault dips are\ndetermined based on fault explorations. However, our method is flexible enough to\nincorporate other variables of earthquakes such as earthquake magnitude and fault dip if\nnecessary.\nReviewer #2 (Remarks to the Author):\nComment 2.1\nThe authors have done a commendable job here addressing each of the reviewers comments, and\nthis current version of the manuscript is significantly improved compared to the original. I'm\npleased to see the authors have now more clearly described the wider contribution this paper\nintends to make to the field, with a reduced focus on the specific case study, which is now\nappropriately highlighted as an exemplar of the approach.\nThere are still some minor areas that could be addressed to improve the paper and its readability.\nResponse: We sincerely appreciate the reviewer for the encouraging comments and positive\nfeedback on the improvements made in the revised manuscript. We agree that there are still some\nminor areas that could be further enhanced to improve the manuscript. A point-by-point response to\nthe comments is attached below.\nComment 2.2\nFirst, the term Maximum Credible Earthquake still seems fraught to me. The other reviewers\nhighlighted this initially and the authors have responded and now clearly define what they mean by\nMCE. However, given the context of the paper is really on the ground shaking at any given site, I\nfind the focus on a single magnitude confusing. The authors themselves note that even moderate\nearthquakes have caused substantial impacts in the past. I remain unconvinced that we should\nsimply take at face value that the biggest magnitude earthquake can cause the largest shaking at a\ngiven site, considering complex interactions of seismic waves with ground properties. My\nunderstanding is that this is actually quite a minor point and that the proposed method could easily\nconsider different magnitudes for each fault, but the authors here simply choose to demonstrate\ntheir approach via the \"MCE\". My issue therefore is that by choosing to focus on the term MCE the\nauthors detract from their own work via readers focussing too intently on this term, rather than\nengaging fully with the method proposed.\nResponse: We fully agree with the reviewer that the proposed method can consider any magnitude\nfor the given faults, not only the biggest magnitude. Our method is highly adaptable, capable of\nincorporating all variables of earthquakes (certainly including different earthquake magnitudes) in\nthe evaluations of the seismic hazard of the target site. However, due to the complexity and\ncomputational cost of implementation, the proposed method is more suitable for assessing the risk\nof major engineering projects subject to extreme earthquakes occurring in the near field of the target\nsite. Meanwhile, the seismic design of major engineering projects, e.g., high dams and nuclear\npower stations, particularly emphasizes their safety under extreme seismic conditions. Therefore, in\nthis study, following the guidelines for determining MCE, e.g., regulation for Earthquake Design\nand Evaluation for Civil Works Projects (ER 1110-2-1806, 2016) in America and code for Seismic\nDesign of Hydraulic Structures of Hydropower Project (NB 35047, 2015) in China, we take\nearthquakes with the maximum magnitude at the surrounding faults as the extreme earthquakes, i.e.,\nMCEs, to be considered. Certainly, as the reviewer pointed out, our method can easily consider\nearthquake scenarios with different magnitudes in the seismic hazard analysis for the target sites.\nIn subsequent research, we plan to address the consideration of earthquakes with different magnitudes,\nparticularly in areas where the threat of moderate to small-scale earthquakes are also seriously\nconcerned, such as densely populated urban areas.\nFor the reviewer’s another concern that if the biggest magnitude earthquake causes the largest\nshaking at a given site, we agree that magnitude is not the only determining factor for the ground-\nmotion intensity at the specified site. As revealed in the manuscript (Fig. 2), due to the complex\nphysical process of earthquakes from source to site, earthquakes with identical magnitude, which\nalso occur at the same fault, can generate ground motions with considerably different intensities at\nthe target site. However, for the same fault, under the same probability exceedance level,\nearthquakes with higher magnitude generally indicate more severe seismic hazards at the same site.\nTo substantiate this conclusion, we analyzed the seismic hazard posed by earthquakes with the\nmagnitude of Mw7.0, which occur at the main rupture of the Yaziba fault (F5 in the Yaziba seismic\nzone in Fig. S2 of the Supplementary Information), using 1 million scenarios. Fig. R2 shows\ncomparison of the seismic hazards of earthquakes occurring at the Yaziba fault with the magnitudes\nof Mw7.5 and Mw7.0, respectively. It can be found that for the same exceeding probability, the PGA\nvalue of Mw7.5 earthquakes is obviously larger than that of Mw7.0 earthquakes. This phenomenon\nis understandable. Assume an ideal case that a smaller magnitude earthquake occurs at a given fault.\nThen, imagine the same fault occurs a larger magnitude earthquake with the same rupture process\nin the area where the smaller earthquake rupture, but with the proportionally larger slip. In this case,\nadditional rupture and energy release occur for the larger earthquake. It is evident that the larger\nearthquake will surely generate stronger ground motions at the given site beyond what is observed\nfor the smaller earthquake, due to the additional released energy. Therefore, assuming the\npropagation path and local site conditions remain unchanged, a larger magnitude earthquake\ngenerally has a greater threat to the target site compared to a smaller magnitude earthquake\noccurring at the same fault.\nHowever, when it comes to different faults, the ground-motion intensity at a site cannot be\nsolely determined by magnitude due to various additional factors, e.g., fault type (strike-slip or\nthrust), distance from the fault to the site, relative site position from the fault (hanging wall or\nfootwall), and the medium properties along the propagation path. In particular, it is difficult to judge\nwhether larger magnitude earthquakes occurring farther away generate stronger ground motions at\nthe given site compared to smaller magnitude earthquakes occurring closer to the site. Therefore, in\nthis study, to find the most severe ground motion at a specific site, earthquake scenarios with the\nmaximum magnitude for each significant fault in the surrounding area, i.e., the Mw7.5 earthquakes\nat the Yaziba fault and the Mw7.0 earthquakes at the Leibo fault, are considered separately.\nFig. R2 Comparison of the seismic hazards of earthquakes occurring at the Yaziba fault with the\nmagnitudes of Mw7.5 and Mw7.0, respectively.\nDue to the complexity and computational cost of implementation, the proposed method\nis more suitable for evaluating the seismic hazard of major engineering projects subject to\nextreme earthquakes occurring in the near field of the target site. Given that the seismic design\nof major engineering projects, such as high dams and nuclear power plants, particularly\nemphasize their safety under extreme seismic conditions, the proposed method is currently\nintended for evaluating the seismic hazard of major engineering projects under MCEs.\nComment 2.3\nSecondly, in the supplementary information (and in the response to reviewers) the authors show\nfigures of ground motion from one of their scenario earthquakes, but include no information on\nwhat parameters were involved in this scenario. In order for these figures to make sense, its\nimportant that readers are provided those key details - which of your 22 million scenarios is this?\nIn addition, I wonder if the authors have considered a figure (or figures) here showing the spatial\nvariation in ground shaking across all their scenarios? I think this would be a valid contribution.\nResponse: The ShakeMaps in Figure S6 and S7 of Supplementary Information are generated by the\nearthquake scenarios shown Figure 3 of the original manuscript. As the reviewer suggested in\nComment 2.4, we have included these ShakeMaps in Figure S6 and S7 into the main text to afford\nreaders a clearer understanding of our results.\nIn addition, we appreciate the reviewer for the constructive comment on investigating the\nspatial variation in ground motions across all considered scenarios, which is of great importance for\nevaluating the potential seismic hazard throughout the study area. However, to obtain the ground\nmotions at the target site for all considered earthquake scenarios, it requires only 3 complete\nnumerical simulations on the supercomputer to calculate the required strain Green’s tensor from all\npossible source locations to the target site. In contrast, each ShakeMap of an earthquake scenario\nneeds an expensive forward simulation on the supercomputer. Therefore, generating ShakeMaps for\nthe 22 million earthquake scenarios considered in this study is not feasible, which requires 22\nmillion complete numerical simulations. To investigate the spatial variation of the ground-motion\nfield, based on the obtained seismic hazard results, we simulated 5 scenarios for each of the 3\nrepresentative seismic hazard levels (i.e., the exceedance probabilities of 10%, 50%, and 90%) for\nboth the Yaziba fault and the Leibo fault. A total of 30 scenarios were used to generate ShakeMaps\nby forward simulations. Analysis of the spatial variations of the ground-motion fields is added to\nthe Supplementary Information as follows.\nIn order to explore the spatial variations within the ground-motion field, 5 scenarios for\neach of 3 representative seismic hazard levels (i.e., exceedance probabilities of 10%, 50%, and\n90%) are derived based on the obtained seismic hazard results. These scenarios occurring at\nthe main rupture (F5 in Fig. S2) of both the Yaziba and Leibo faults are then simulated,\nyielding a total of 30 scenarios (15 for each fault). ShakeMaps of these scenarios are\nsubsequently produced through forward simulations. We then compute the average (Fig. S7),\nstandard deviation (Fig. S8), and variation coefficient (Fig. S9) for the ShakeMaps of these\nearthquake scenarios at both the Yaziba and Leibo faults. From Fig. S7-S9, the intensity of\nground motions gradually decreases from the upper edge of the fault outward, but exhibits\ncomplex spatial distributions in the model domain. In particular, consistent with previous\nresearch8, ground motions can be significantly amplified at the tops of hills and ridges, while\nit may decrease at the valleys. Additionally, the distribution of standard deviation and\nvariation coefficient reveals much greater variability of the ground-motion intensity in the\nnear-fault regions for different earthquake scenarios, indicating that the rupture process of\nearthquake scenarios has significant effects on the ground motions in regions close to the faults.\nTherefore, the influence of the earthquake rupture process should be paid special attention in\nthe evaluations of seismic hazard for the near-fault regions.\nFig. S7 Average of the ShakeMaps of earthquake scenarios at the Yaziba fault (a) and the\nLeibo fault (b). The average of PGA in the model domain are presented by different colors.\nThe red triangle represents the dam site. The top edges of the fault planes are indicated by\nthe red solid lines, while the bottom edges of them are represented by the red dotted lines.\nFig. S8 Standard deviation of the ShakeMaps of earthquake scenarios at the Yaziba fault\n(a) and the Leibo fault (b). The standard deviation of PGA in the model domain are\npresented by different colors. The red triangle represents the dam site. The top edges of the\nfault planes are indicated by the red solid lines, while the bottom edges of them are\nrepresented by the red dotted lines.\nFig. S9 Variation coefficient of the ShakeMaps of earthquake scenarios at the Yaziba fault\n(a) and the Leibo fault (b). The Variation coefficient of PGA in the model domain are\npresented by different colors. The red triangle represents the dam site. The top edges of the\nfault planes are indicated by the red solid lines, while the bottom edges of them are\nrepresented by the red dotted lines.\nComment 2.4\nFinally, I am surprised to see so many of the pertinent methods details buried in the supplementary\ninformation and not the main text. I appreciate the word limit and requirements of Nat Comms, but\nto me some of the most important details and descriptions are buried away here when they really\nbelong in the main text. The authors have done a solid job of addressing the reviewers comments\nthrough changes to the SI, but I think the paper would benefit from including parts of this in the\nmain manuscript itself.\nOverall, these are relatively minor and I believe the authors have done a reasonable job of\naddressing the concerns previously posed.\nResponse: We appreciate the reviewer for this insightful comment regarding the placement of\ncrucial details and descriptions of our method in the Supplementary Information. We agree that\nthese important contents should be accessible within to the main text instead of the Supplementary\nInformation. In response to this suggestion, we have revisited the manuscript and incorporated\nsignificant aspects of the proposed method and pertinent findings into the main text of the revised\nmanuscript, including descriptions on the input parameters and the ShakeMaps of the regional\nground-motion field. We believe this will enhance the clarity and overall impact of our study.\nFurthermore, by employing the source process of earthquake scenarios corresponding to\nthe specified hazard level, the spatial ground-motion field around the target site can be derived\nby forward simulations. ShakeMaps generated by forward simulations for the earthquake\nscenarios at the Yaziba fault and Leibo fault, as shown in Fig. 3, are presented in Fig. 4. From\nthe ShakeMaps, it is demonstrated that the realistic spatial ground motion field around the\ntarget site can be thoroughly produced by forward simulations using the rupture process of\nearthquake scenarios corresponding to specific hazard levels. Therefore, for large-span\nstructures (e.g., dams and bridges) that may be significantly affected by the heterogeneous\nground-motion field28, our method can provide more realistic ground motion input for the\nseismic design of these structures.\nFig. 4 ShakeMaps of earthquake scenarios at the Yaziba fault (a) and the Leibo fault (b).\nThe ShakeMaps are generated by forward simulations using the earthquake scenarios\npresented in Fig. 3. PGA of the simulated ground-motion field in the model domain is\npresented by different colors. The red triangle represents the dam site. The top edges of the\nfault planes are indicated by the red solid lines, while the bottom edges of them are\nrepresented by the red dotted lines.\nIn this study, to generate the earthquake scenarios with the Monte Carlo method, all\nkinematic parameters of the source process (including the hypocenter, the distribution of slip,\nrupture time, rise time, and rake) are randomly generated in certain ranges with necessary\nconstraints. For the source process of earthquake scenarios with, the average slip and rise time\nare constrained. Specifically, the average slip is determined by the empirical earthquake\nsource-scaling laws35, and the average rise time is specified according to the empirical relation\nfor the rise time36. According to the existing research, the hypocenter of an earthquake may\noccur at any position of the seismic fault37,38. However, due to the very limited number of\nearthquakes with accurate fault information derived from sufficient studies, as well as the\nsignificant randomness of the hypocenter locations, there is no well recognized conclusion\nregarding the spatial pattern of epicenters. Therefore, in this study, we simply assume that the\nhypocenters of earthquake scenarios occur randomly at any position of the seismic fault.\nFurthermore, it is worth emphasizing that our method is highly adaptable and can be updated\nto incorporate advancements in the understanding of earthquake nature, such as improved\nscaling laws for rupture parameters, as well as refined exploration information of faults and\nregional Earth model. By incorporating these advancements, our method can yield more\naccurate evaluations of the seismic hazard at the target site. Details of source parameters of\nthe generated earthquake scenarios are provided in the Supplementary Information.\nReviewer #4 (Remarks to the Author):\nComment 4.1\nThe manuscript presents a comprehensive understanding of the significant threat posed by major\nearthquakes to modern society, emphasizing their destructive potential and inherent\nunpredictability. The concept of the maximum credible earthquake (MCE) for a specific fault,\ncharacterized by various potential scenarios with differing source processes, contributes to the\ncomplex and uncertain nature of future seismic hazards. The abstract introduces a solution in the\nform of a full-scenario analysis method that employs deterministic broadband simulations across a\nmultitude of scenarios. This approach seeks to address the intricate nature of MCE hazards by\nconsidering all possible source process parameters along the fault, thereby facilitating a more\ncomprehensive assessment.\nWhile the abstract successfully explains this novel full-scenario analysis method and applies it to\nthe seismic hazard assessment of China's Xiluodu dam, there appears to be potential for\nimprovement in terms of practical application. Furthermore, the proposed method's capacity to give\na variety of intensity measures, ground motion time series, and spatial ground-motion fields hold\npromise for a more precise and realistic evaluation of MCE hazards, with possible applications in\nearthquake engineering.\nIn conclusion, the paper presents an intriguing approach to tackling the uncertainty associated with\nMCE hazards and it would be appropriate to accept it for publication. Although the method's\nconceptual foundation and potential contributions are commendable, a closer examination and\nimprovement in the application phase could elevate the paper's overall impact.\nResponse: We express our sincere gratitude to the reviewer for the thorough review and\nencouraging remarks on our study, particularly the recognition of our full-scenario analysis method\nand its potential contributions to the assessment of MCE hazards. We agree with the reviewer’s\ninsightful and constructive comments on further examining and improving the practical application\nof our proposed method. Guided by the detailed comments provided, we have improved our\nmanuscript by expanding the application of our method. A detailed point-by-point response is given\nas follows.\nComment 4.2\n1. How does the incorporation of numerous potential scenarios with different source processes\ncontribute to the uncertainty in predicting maximum credible earthquakes?\nResponse: As explained in the response to Comment 1.1, the uncertainty of earthquakes involves\ntheir highly complex physical process, including the source process, propagation path, and local site\nconditions. Specifically, the uncertainty in propagation path and local site conditions is associated\nwith the velocity structures and topography, known as the epistemic uncertainty, which is expected\nto be improved with further refinement of the Earth model. Therefore, this study did not address the\nuncertainty associated with propagation path and local site conditions that related to velocity\nstructures and topography, only focusing on the uncertainty associated with the earthquake source.\nGiven the current level of understandings for earthquakes, the source of potential future\nearthquakes is unpredictable and highly uncertain. Earthquakes can arise from different rupture\nprocess, resulting in a wide range of potential scenarios. However, by statistically analyzing the\nsource inversion results for historical earthquakes, some empirical earthquake source-scaling laws\n(Thingbaijam et al., 2017), such as the fault scaling, slip amount, and rise time, are concluded for\nthe seismic faults. Based on the recognized knowledge for earthquakes, our study considers the\nstochastic nature and uncertainty of the rupture process with numerous possible earthquake\nscenarios by constraining the rupture parameters within reasonable ranges. The seismic hazard at\nthe target site is obtained by statistically analyzing the ground motions at the target site for all\nearthquake scenarios. Moreover, for the seismic hazard evaluations for major projects and densely\npopulated urban areas, especially those prone to seismic activity, the significant faults around the\nconsidered sites usually have undergone detailed explorations, and some basic information of these\nfaults, e.g., the approximate fault locations and fault mechanism (strike-slip or thrust), are relatively\nclear. By incorporating the known fault information, our method can provide more realistic and\naccurate assessment for the seismic hazard of the target site.\nOverall, this study acknowledges the inherent unpredictability of earthquakes and aims to move\nbeyond a single deterministic viewpoint. By employing the full-scenario analysis method, we\naddressed the complex and uncertain nature of potential future earthquakes. The proposed method\nenables to capture the uncertainty of earthquakes and provides a more robust framework for\nassessing the seismic hazard by considering the actual faults, velocity structures and topography.\nComment 4.3\n2. Can you elaborate on the significance of conducting deterministic broadband simulations as part\nof the proposed full-scenario analysis method?\nResponse: We agree with the reviewer that the significance of applying deterministic broadband\nground-motion simulations in the proposed full-scenario analysis method should be further\nelaborated. Compared to the conventional seismic hazard analysis methods based on empirical\nground-motion models, e.g., PSHA and DSHA, this study has several significant advantages by\nemploying the latest deterministic broadband ground-motion simulation methods.\nFirst, conventional seismic hazard analysis methods typically provide a limited set of seismic\nparameters, such as PGA (Peak Ground Acceleration) and Sa(T1) (spectral acceleration at the first\nmode period of vibration). These simple parameters may not adequately characterize the seismic\nresponse of specific engineering structures(Luco and Cornell, 2007). In contrast, our research\nutilizes deterministic broadband ground-motion simulations to directly obtain the broadband\nground-motion time series at the target site. This enables to assess the seismic hazard at the target\nsite using any desired intensity measure or even broadband ground-motion time series, providing\nmore comprehensive and accurate evaluations for specific engineering structures.\nSecond, broadband deterministic ground-motion simulations allow for a thorough\nconsideration for the physical process of earthquakes from source to site, including the rupture\nprocess, propagation path, and local site conditions. Consequently, our study can take into account\nall factors that may influence the ground motions at the target site, e.g., the effects of rupture\ndirectivity (Somerville et al., 1997), amplification effects due to local topography (Lee, Chan, et al.,\n2009; Lee, Komatitsch, et al., 2009), and basin effects caused by sedimentary layers (Kawase, 2003).\nThis is particularly significant for assessing the seismic hazard at sites adjacent to the faults where\nlarge earthquakes may occur.\nFinally, by employing deterministic broadband ground-motion simulations, we can extend the\nanalysis beyond the site-specific hazard assessment. After obtaining the seismic hazard results at\nthe target site, we can further perform forward simulations for the obtained earthquake scenarios\ncorresponding to the specified hazard levels to obtain the regional spatial ground-motion field. This\nis of great importance for analyzing the dynamic response of large-span structures (e.g., dams,\nbridges, and tunnels), which can be significantly affected by the spatial heterogeneous ground\nmotions.\nOverall, the utilization of deterministic broadband ground-motion simulations offers several\nsignificant advantages over the conventional approaches. It provides the personalized information\nfor specific structures, enables a comprehensive consideration for the realistic physical process of\nearthquakes, and allows for the analysis of spatial ground motion effects on large-scale structures.\nWe believe these advantages contribute to a more robust and accurate seismic hazard analysis and\nhave important implications in the earthquake engineering field.\nComment 4.4\n3. Could you provide more insight into the specific parameters and variables considered within the\nfull-scenario analysis approach for evaluating MCE hazards?\nResponse: As explained in the response to Comment 1.1 and 4.2, in the proposed full-scenario analysis method,\nwe focus on the uncertainties associated with the earthquake source. The source of potential future\nearthquakes is inherently uncertain and characterized by randomness. To obtain the seismic hazard\nfor the target site, based on the recognized knowledge of earthquake and the explorations of the\nconsidered faults, this study comprehensively considers all uncertainties of the source of potential\nearthquakes, including the rupture location, hypocenter, rupture process (distributions of slip,\nrupture time, rise time and rake angle on the rupture fault), through massive earthquake scenarios\nwith different source process. Furthermore, it is worth emphasizing that our method is highly\nadaptable and can be updated to incorporate advancements in the understanding of earthquake\nnature, such as improved scaling laws for rupture parameters, as well as refined exploration\ninformation of faults and regional Earth model. By incorporating these advancements, our method\ncan yield more accurate evaluations of the seismic hazard at the target site. In line with the reviewer's\nsuggestion, we have added more detailed descriptions of the specific parameters and variables\nconsidered in our method to the revised manuscript, as described in the response to Comment 2.4.\nWe believe this addition will enhance comprehension of our study.\nComment 4.5\n4. In what ways could the refinement of the practical application aspect enhance the practicality\nand adaptability of the proposed method in real-world scenarios?\nResponse: We appreciate the reviewer for this constructive comment regarding the refinement of\nthe practical application aspect for enhancing the practicality and adaptability of our method in real-\nworld scenarios. To refine the practical application aspect of our method, we are committed to\nenhancing this method in the following ways:\n Method validation: In this study, the proposed method was validated through comparisons\nwith empirical ground-motion models. However, further validations should be conducted\nthrough comparisons with existing seismic hazard analysis methods in practical applications.\nCurrently, we are applying this method to evaluate the seismic hazard for several major\nhydraulic engineering projects in China that are located near significant faults with potential\nfor large earthquakes. A typical example is provided in the response to Comment 4.6, and the\nreliability and advantages of our method are further validated in real-world scenarios.\n Determining evaluation criteria: In this study, much richer results are provided for the\nseismic hazard evaluations, including arbitrary IMs, broadband ground-motion time series, and\nspatial ground-motion fields. However, we need to further study the evaluation criteria for the\nproposed method. For instance, which IMs should be selected in seismic hazard analysis for\nspecified engineering structures, and what hazard levels should be adopted for seismic design.\nProper evaluation criteria are crucial for the application of this method in real-world scenarios.\n Adaptability and integration: As explained in the response to Comment 4.4, one of the\nstrengths of our method lies in its adaptability. It can easily incorporate the latest knowledge\nof earthquakes and refined Earth models, leading to more accurate and reasonable seismic\nhazard results for the target sites. We are committed to continuously improving our method to\nenhance its practicality and facilitate its wider adoption in real-world applications.\n Fault-to-structure simulation: Current seismic response analysis for engineering structures\ntypically assumes uniform ground-motion inputs without considering spatial heterogeneity.\nHowever, by utilizing deterministic broadband ground-motion simulations, our method can\nprovide spatial ground-motion fields corresponding to specific seismic hazard levels through\nforward simulations. Therefore, our method can perfectly incorporate the newly-developed\nsource-to-structure simulation method (Zhang et al., 2023), to achieve more realistic seismic\nresponse analysis for engineering structures by comprehensively considering the realistic\nphysical process of earthquakes, as presented in the response to Comment 4.6.\nWe are actively conducting research in several ways to enhance the practicality and adaptability\nof this method in real-world scenarios. Our ongoing aim is to continuously refine our method,\neffectively addressing the challenges posed by real-world applications.\nComment 4.6\n5. Considering the potential for more realistic MCE hazard evaluations, how might the proposed\nmethod influence decision-making processes in earthquake engineering projects, particularly in\nareas prone to seismic activity?\nResponse: We agree with the reviewer that the potential impacts of our method on decision-making\nprocesses in earthquake engineering projects should be further elaborated. As explained in the\nresponse to Comments 1.1 and 4.3, our study has several significant advantages over conventional\napproaches. The proposed method can provide much richer results for seismic hazard evaluations,\nand thus has great potential to improve the decision-making processes of earthquake engineering\nprojects, particularly in areas prone to seismic activity. Here we list some potential applications of\nour method in the decision-making process of earthquake engineering projects.\n(a) Accurate evaluations considering complete physical backgrounds\nAs explained in the response to Comment 4.3, our method uses deterministic broadband\nseismic ground-motion simulation to generate 3D ground motions for the target site. By\nincorporating the actual faults and Earth model into the simulations, the proposed method takes into\naccount all factors that may influence the ground motions at the target site, e.g., the effects of rupture\ndirectivity, amplification effects due to local topography, and basin effects caused by sedimentary\nlayers. These are of great significance for assessing the seismic hazard of engineering projects,\nparticularly in areas prone to seismic activity where the source process has more significant effects.\nAdditionally, our method can consider the ground motions at specific directions, which is important\nfor engineering structures that are sensitive to specific directions of ground motions. For instance,\nthe seismic design of gravity dams pays more attention to ground motions in the river-parallel\ndirection.\nHere, we provide an example of the application of this method in the decision-making process\nfor selecting the site location of a high concrete gravity dam, which is currently in the planning stage\nin China. For this major project, preliminary exploration has identified two potential dam sites,\nSite A and Site B, both in close proximity to a significant fault (Fig. R3 (a)) of which the maximum\nmagnitude is 7.5. According to the seismic hazard evaluations using PSHA for the two dam sites,\nthe PGA of design earthquake (2% exceedance probability in 100 years) was 0.52 g for Site A,\nwhich is 5 km from the fault, and 0.525 g for Site B, which is 1.5 km from the fault. The PGA of\ncheck earthquake or MCE (1% exceedance probability in 100 years) was 0.64 g for Site A and 0.65\ng for Site B. According to the seismic hazard evaluations using PSHA, despite the different distances\nfrom the fault to the two sites (5 km for Site A and 1.5 km for Site B) and the different river-parallel\ndirections of them, the PGA values of the same hazard level are quite similar for the two sites!\nDue to the lack of historical records for large earthquakes at such close proximities, stronger\nspatial heterogeneity in near-field ground motion (as presented in the response to Comment 2.3),\nand the ergodic assumption in PSHA (Anderson and Brune, 1999), it is challenging to accurately\nassess the hazard from near-field major earthquakes using PSHA. Given the close proximity of the\ntwo sites, their seismic hazards might be similar for earthquakes occurring tens or even hundreds of\nkilometers away, assuming no significant differences of local conditions. However, in this example,\nfor near-field earthquakes within a few kilometers, the difference in distances of the two sites from\nthe fault (a factor of more than 3 between 1.5km and 5km) is significant. The assessment using\nPSHA for this project suggests a similar seismic hazard for the two sites. However, this conclusion\nmay not be entirely accurate, as it overlooks the differences in their relative positions to the fault,\nlocal site conditions, and river-parallel directions.\nCurrently, we have conducted a preliminary seismic hazard analysis for the two potential dam\nsites using the deterministic full-scenario analysis method. Based on the results derived from our\nmethod (Fig. R4), when we overlook the distinction in ground-motion direction at the dam sites\n(that is, adopting the east-west direction, i.e.,, the river-parallel direction of Site A, uniformly for\nboth Site A and Site B), the PGAs at 50% and 10% exceedance probabilities were 0.31 g and 0.53\ng for Site A, and 0.57 g and 0.88 g for Site B, respectively. Therefore, it is revealed by our method\nthat the seismic hazard of Site B is significantly larger than that of Site A. Furthermore, when\nconsidering the realistic river-parallel directions of different sites, at which the ground motions are\nmore critical for the seismic hazard of gravity dams (i.e., considering ground motions of east-west\nfor Site A and 30 degrees north of east for Site B), the seismic hazard for Site A remains unchanged,\nwhile that for Site B further increases, with PGAs at 50% and 10% exceedance probabilities\nreaching 0.67 g and 1.05 g, respectively. Therefore, our method demonstrated that for the project of\nhigh gravity dam, the seismic hazard of Site B is much more severe than that of Site A, rather than\nthe similar seismic hazards derived from PSHA. This provides significant reference for the decision-\nmaking process in site selection.\nOverall, for the seismic design of engineering projects prone to seismic activity, the seismic\nhazards at the engineering site are profoundly influenced by the actual physical backgrounds of\nearthquakes. Furthermore, when considering the directivity of ground motions, the ground motions\nat different sites close to the fault may exhibit substantial differences. Therefore, our method is\npromising for providing more realistic and accurate evaluations in the decision-making process for\nselecting the engineering sites of major projects, particularly those near significant faults.\nFig. R3 Map of the surrounding region of the considered dam sites. (a) The black triangles\nrepresent the dam sites and the red line indicates the considered fault around the dam sites; (b)\nThe river-parallel directions of the dam site A and B are indicated by the red arrows; (c) Velocity\nstructures around the dam sites are presented by different colors.\nFig. R4 The seismic hazards of the considered sites. (a) and (b) show the seismic hazards at the\nsame directions for both site A and site B, and (c) presents the seismic hazards at the realistic\ndirections for site B.\n(b) Personalized evaluations for specific structures\nOur method directly generates the ground-motion time series with deterministic broadband\nground-motion simulations and can produce arbitrary intensity measures (IMs) for evaluating the\nseismic hazard. As demonstrated in Figures S5 and S6 of Supplementary Information, seismic\nhazards represented by different IMs may have significant differences for the same site. Therefore,\nby adopting the optimal IM of specific engineering structures, our method can provide personalized\nseismic hazards for them, thus providing more accurate and reasonable seismic hazard evaluations\nfor earthquake engineering projects.\n(c) Seismic design fully based on realistic and unified physical backgrounds\nFor populated urban areas and some major engineering projects with large spatial scales (e.g.,\ndams, bridges, and tunnels), they may be significantly influenced by spatially heterogeneous ground\nmotions, which are difficult to be considered in conventional seismic hazard analysis approaches.\nHowever, in our method, after obtaining the seismic hazard for the target site based on deterministic\nbroadband ground-motion simulations, we can further generate spatial ground-motion fields with\ncorresponding earthquake scenarios by forward simulations, enabling to incorporate the effects of\nspatially heterogeneous ground motions into the dynamic response analysis of engineering\nstructures.\nCurrently, by integrating regional ground-motion simulations and structural dynamic response\nanalysis methods, we have developed a novel source-to-structure simulation method for analyzing\nthe dynamic response of structures under strong earthquakes. The source-to-structure simulation\nmethod was used to simulate the dynamic response of the Pacoima dam during the 1994 Northridge\nearthquake (Zhang et al., 2023). The simulation model and main results are shown in Figures R4,\nR5, and R5, and details of this simulation can refer to our recently published paper (Zhang et al.,\n2023). This simulation qualitatively reproduced the seismic response of Pacoima dam induced by\nthe 1994 Northridge earthquake, e.g., the ground-motion time series on the dam body (Fig. R6) and\nthe concrete damage distribution adjacent to the left block contraction joint (Fig. R7). Therefore,\nthe proposed method can provide realistic ground-motion fields to achieve the source-to-structure\nsimulation, thus enabling more realistic analysis of dynamic response for engineering structures.\nAs explained in the response to Comment 1.1, this study is promising for more ambitious goals\nto achieve the seismic design fully based on realistic physical process of earthquakes. By employing\ndeterministic broadband ground-motion simulations that consider the actual physical backgrounds\n(including fault structures, velocity structures, and topography), the proposed full-scenario analysis\nmethod can directly provide arbitrary intensity measures, broadband ground-motion time series, and\nspatial ground-motion fields for the specified hazard levels, which can be used directly in the seismic\ndesign of engineering structures, thereby adopting the unified earthquake scenarios with realistic\nphysical backgrounds and specified hazard levels in both seismic hazard evaluations and structural\ndynamic analysis..\nFig. R5 Source-to-dam model for simulating the nonlinear dynamic response of the Pacoima dam\nin the 1994 Northridge earthquake. (A) Regional numerical model for simulating the ground-\nmotion field (the red dashed frame and the star represent the rupture fault face and epicenter,\nrespectively); (B) Finite element model for the Pacoima dam (Zhang et al., 2023).\nFig. R6 Comparison of the calculated responses (red) and records (black) at Channel 8 installed\nat the Pacoima dam (Zhang et al., 2023).\nFig. R7 Concrete damage distribution on Pacoima dam faces: A, downstream face, B, upstream\nface (Zhang et al., 2023).\nBased on the deterministic broadband ground-motion simulation methods, this study\nachieves a deterministic full-scenario analysis for potential future earthquakes with a\nthorough consideration for the physical process of earthquakes. Compared with conventional\napproaches, this method can much richer results for seismic hazard evaluations, e.g., arbitrary\nIMs, broadband ground-motion time series, and spatial ground-motion fields for the specified\nhazard levels, enabling more realistic and accurate evaluations of seismic hazards.\nFurthermore, this study is promising for more ambitious goals to achieve the seismic design\nfully based on realistic physical process of earthquakes and holds significant implications in\nthe field of earthquake engineering.\nReferences:\nAnderson, J. G., 2015, The Composite Source Model for Broadband Simulations of Strong Ground\nMotions, Seismological Research Letters, 86, no. 1, 68–74, doi: 10.1785/0220140098.\nAnderson, J. G., and J. N. Brune, 1999, Probabilistic Seismic Hazard Analysis without the Ergodic\nAssumption, Seismological Research Letters, 70, no. 1, 19–28, doi: 10.1785/gssrl.70.1.19.\nBaker, J. W., N. Luco, N. A. Abrahamson, P. J. Maechling, and K. B. Olsen, 2014, ENGINEERING\nUSES OF PHYSICS-BASED GROUND MOTION SIMULATIONS, in Proceedings of the\n10th National Conference in Earthquake Engineering Anchorage.\nBaker, J. W., S. Rezaeian, C. A. Goulet, N. Luco, and G. Teng, 2021, A subset of CyberShake\nground-motion time series for response-history analysis, Earthquake Spectra, 37, no. 2,\n1162–1176, doi: 10.1177/8755293020981970.\nCrempien, J. G. F., and R. J. Archuleta, 2015, UCSB Method for Simulation of Broadband Ground\nMotion from Kinematic Earthquake Sources, Seismological Research Letters, 86, no. 1,\n61–67, doi: 10.1785/0220140103.\nDenolle, M. A., E. M. Dunham, G. A. Prieto, and G. C. Beroza, 2014, Strong Ground Motion\nPrediction Using Virtual Earthquakes, Science, 343, no. 6169, 399–403, doi:\n10.1126/science.1245678.\nFu, H. et al., 2017, 18.9-Pflops nonlinear earthquake simulation on Sunway TaihuLight: enabling\ndepiction of 18-Hz and 8-meter scenarios, in Proceedings of the International Conference\nfor High Performance Computing, Networking, Storage and Analysis Denver Colorado,\nACM, 1–12.\nGraves, R. et al., 2011, CyberShake: A Physics-Based Seismic Hazard Model for Southern\nCalifornia, Pure Appl. Geophys., 168, nos. 3–4, 367–381, doi: 10.1007/s00024-010-0161-\n6.\nGraves, R. W., and A. Pitarka, 2010, Broadband Ground-Motion Simulation Using a Hybrid\nApproach, Bulletin of the Seismological Society of America, 100, no. 5A, 2095–2123, doi:\n10.1785/0120100057.\nKawase, H., 2003, 61 Site effects on strong ground motions, in International Geophysics, Elsevier,\n1013–1030.\nLee, S.-J., Y.-C. Chan, D. Komatitsch, B.-S. Huang, and J. Tromp, 2009, Effects of Realistic Surface\nTopography on Seismic Ground Motion in the Yangminshan Region of Taiwan Based Upon\nthe Spectral-Element Method and LiDAR DTM, Bulletin of the Seismological Society of\nAmerica, 99, no. 2A, 681–693, doi: 10.1785/0120080264.\nLee, S.-J., D. Komatitsch, B.-S. Huang, and J. Tromp, 2009, Effects of Topography on Seismic-\nWave Propagation: An Example from Northern Taiwan, Bulletin of the Seismological\nSociety of America, 99, no. 1, 314–325, doi: 10.1785/0120080020.\nLuco, N., and C. A. Cornell, 2007, Structure-Specific Scalar Intensity Measures for Near-Source\nand Ordinary Earthquake Ground Motions, Earthquake Spectra, 23, no. 2, 357–392, doi:\n10.1193/1.2723158.\nMaufroy, E. et al., 2015, Earthquake Ground Motion in the Mygdonian Basin, Greece: The E2VP\nVerification and Validation of 3D Numerical Simulation up to 4 Hz, Bulletin of the\nSeismological Society of America, 105, no. 3, 1398–1418, doi: 10.1785/0120140228.\nMilner, K. R., B. E. Shaw, C. A. Goulet, K. B. Richards-Dinger, S. Callaghan, T. H. Jordan, J. H.\nDieterich, and E. H. Field, 2021, Toward Physics-Based Nonergodic PSHA: A Prototype\nFully Deterministic Seismic Hazard Model for Southern California, Bulletin of the\nSeismological Society of America, 111, no. 2, 898–915, doi: 10.1785/0120200216.\nPanza, G. F., and J. Bela, 2020, NDSHA: A new paradigm for reliable seismic hazard assessment,\nEngineering Geology, 275, 105403, doi: 10.1016/j.enggeo.2019.105403.\nPitarka, A., A. Akinci, P. De Gori, and M. Buttinelli, 2022, Deterministic 3D Ground-Motion\nSimulations (0–5 Hz) and Surface Topography Effects of the 30 October 2016 Mw 6.5\nNorcia, Italy, Earthquake, Bulletin of the Seismological Society of America, 112, no. 1,\n262–286, doi: 10.1785/0120210133.\nRobinson, T. R., N. J. Rosser, A. L. Densmore, K. J. Oven, S. N. Shrestha, and R. Guragain, 2018,\nUse of scenario ensembles for deriving seismic risk, Proc. Natl. Acad. Sci. U.S.A., 115, no.\n41, doi: 10.1073/pnas.1807433115.\nRodgers, A. J., A. Pitarka, N. A. Petersson, B. Sjögreen, and D. B. McCallen, 2018, Broadband (0–\nDimensional Structure and Topography, Geophys. Res. Lett., 45, no. 2, 739–747, doi:\n10.1002/2017GL076505.\nSomerville, P. G., N. F. Smith, R. W. Graves, and N. A. Abrahamson, 1997, Modification of\nEmpirical Strong Ground Motion Attenuation Relations to Include the Amplitude and\nDuration Effects of Rupture Directivity, Seismological Research Letters, 68, no. 1, 199–\n222, doi: 10.1785/gssrl.68.1.199.\nThingbaijam, K. K. S., P. Martin Mai, and K. Goda, 2017, New Empirical Earthquake Source‐\nScaling Laws, Bulletin of the Seismological Society of America, 107, no. 5, 2225–2246,\ndoi: 10.1785/0120170017.\nWang, X., J. Wang, and C. Zhang, 2022, A Broadband Kinematic Source Inversion Method\nConsidering Realistic Earth Models and Its Application to the 1992 Landers Earthquake,\nJGR Solid Earth, 127, no. 3, doi: 10.1029/2021JB023216.\nWang, X.-C., J.-T. Wang, L. Zhang, and C.-H. He, 2021, Broadband ground-motion simulations by\ncoupling regional velocity structures with the geophysical information of specific sites, Soil\nDynamics and Earthquake Engineering, 145, 106695, doi: 10.1016/j.soildyn.2021.106695.\nWang, X.-C., J.-T. Wang, L. Zhang, S. Li, and C.-H. Zhang, 2021, A Multidimension Source Model\nfor Generating Broadband Ground Motions with Deterministic 3D Numerical Simulations,\nBulletin of the Seismological Society of America, 111, no. 2, 989–1013, doi:\n10.1785/0120200221.\nZhang, Y., F. Romanelli, F. Vaccari, A. Peresan, C. Jiang, Z. Wu, S. Gao, V. G. Kossobokov, and G.\nF. Panza, 2021, Seismic hazard maps based on Neo-deterministic Seismic Hazard\nAssessment for China Seismic Experimental Site and adjacent areas, Engineering Geology,\n291, 106208, doi: 10.1016/j.enggeo.2021.106208.\nZhang, L., J.-T. Wang, Y.-J. Xu, C.-H. He, and C.-H. Zhang, 2020, A Procedure for 3D Seismic\nSimulation from Rupture to Structures by Coupling SEM and FEM, Bulletin of the\nSeismological Society of America, 110, no. 3, 1134–1148, doi: 10.1785/0120190289.\nZhang, M.-Z., L. Zhang, X.-C. Wang, W. Su, Y.-X. Qiu, J.-T. Wang, and C.-H. Zhang, 2023, A\nframework for seismic response analysis of dams using numerical source-to-structure\nsimulation, Earthquake Engineering & Structural Dynamics, 52, no. 3, 593–608, doi:\n10.1002/eqe.3774."}, {"round": 3, "reviewer_comments": {"reviewer_4": "The paper fully addresses the suggestions made by the reviewer and can therefore be published in its current form."}, "author_response": "Response to the comments\nREVIEWERS' COMMENTS\nReviewer #4 (Remarks to the Author):\nThe paper fully addresses the suggestions made by the reviewer and can therefore be published in\nits current form.\nResponse: We sincerely appreciate the reviewer for helping improve our manuscript."}]

Decision letter