Downloaded at California Institute of Technology on May 3, 2021 n rsJ Rosakis J. Ares and a genesis Elbanna tsunami Ahmed fault strike-slip of Anatomy PNAS genesis. tsunami (11), for motion mechanism particular strike-slip further this by warrants into impact investigation triggered humanitarian be studied devastating tsunamis to possible all their believed of are fraction far small land- a this triggering though by Even supposedly (10). slides waves, can motion tsunami strike-slip generate (5–9), cases indeed many in observations, that consid- Field suggest (4). generally however, generation are tsunami for displacements, unfavorable vertical ered seafloor small ate gener- are 9.0 M∼ 2004 tsunamis plate the subduction-zone as Massive such along boundaries, earthquakes motion. great to seafloor attributed ally vertical enabling for the and of events these of impact plans. preparedness the better reducing cru- for natural is destructive of tsunamis cial of infrastructure most trillions modeling the predictive built and and among Quantitative and tsunamis hazards. lives environment makes of This the 3). thousands responsible to (2, of been damage hundreds have in of alone dollars loss tsunamis the century, land- for impacts. past volcanoes, meteorite and the earthquakes, releases, Over gas by submarine slumps, triggered or slides be may Tsunamis T motions bathymetry horizontal and vertical be to bays in need tsunamis faulting strike-slip near-source from that may risk which conclude re-evaluated. and of We hazards each differently. lagging phase, tsunami areas a postseismic coastal phase, the a affect in and dynamic phases phase, instantaneous distinct coseismic an three motion, identifies tsunamic bathymetry. model complicated require our or not Furthermore, landslides, do sources, which sizable seismic tsunami faulting, for complex the strike-slip mechanisms by for intrinsic generation to drivers tsunami point critical strike-slip findings and are These of faults, focusing hazard. characteristic long dynamic on displacements, that earthquakes horizontal show large We the candidates generation. results prime are tsunami strike-slip Our bays, for shallow along model. and propagating narrow tsunami traversing ruptures used the faults, supershear are in that models motions suggest boundary rupture The drive dynamic propagation. to spontaneous and from dynam- generation motions rupture ground tsunami horizontal and earthquake vertical of time-dependent three-dimensional frame- for models computational models with a generic ics integrates developed rather that under we m), end, work (>1 this tsunamis To to large conditions. contribute that of can demonstrate earthquakes gen- generation strike-slip we the the to Herein, due through coastal landslides. motions except ground to submarine insuf- tsunamis, hazard of considered large major eration been triggering a generally for has as ficient Oglesby) faulting recognized D. David Strike-slip been and Dias, areas. Frederic long Bouchon, Michel has deforma- by reviewed seafloor tions 2020; earthquake-induced 13, December from review generation for Tsunami (sent 2021 22, March Rosakis, J. Ares by Contributed and Greece; Athens, 10680 91125 Athens, CA of Academy Climatology, and Physics 90089; 61801; CA IL France; Angeles, Urbana, Los Urbana–Champaign, California, at Southern Illinois of of University Technology, and Science eateto ii n niomna niern,Uiest fIlni tUbn–hmag,Ubn,I 61801; IL Urbana, Urbana–Champaign, at Illinois of University Engineering, Environmental and Civil of Department eeal,tetuaiipc sascae ihtesize the with associated is impact tsunami the Generally, oouOieet.Srk-lpfut,wihgnrlygener- generally which faults, Strike-slip events. Tohoku-Oki ae eeae yipliegooia vns(1). events geological impulsive water by free-surface long, generated as defined waves classically are sunamis 01Vl 1 o 9e2025632118 19 No. 118 Vol. 2021 e eateto ii n niomna niern,Uiest fSuhr aiona o nee,C 90089; CA Angeles, Los California, Southern of University Engineering, Environmental and Civil of Department | tiesi faults strike-slip a,b g,1 oae Abdelmeguid Mohamed , | ueserruptures supershear 9. 2 uarnadte21 M∼ 2011 the and Sumatran | run-up d aoaor eG de Laboratoire | a ioMa Xiao , eologie, ´ g cl oml Sup Normale Ecole rdaeArsaeLbrtre,Clfri nttt fTcnlg,Pasadena, Technology, of Institute California Laboratories, Aerospace Graduate ´ a aslAmlani Faisal , doi:10.1073/pnas.2025632118/-/DCSupplemental at online information supporting contains article This 1 the under Published interest.y competing no declare authors The Riverside.y California, of University Universit M.B., Reviewers: ulse a ,2021. 3, May Published A.E., and data; paper. analyzed the wrote A.J.R. A.J.R. and and C.S., C.S., H.S.B., H.S.B., per- F.A., F.A., A.J.R. X.M., X.M., and M.A., X.M., M.A., M.A., A.E., A.E., research; research; designed formed A.J.R. and A.E. contributions: Author hysoe htepiil conigfrtednmcsource rupture dynamic the dynamic for fault. 3D accounting strike-slip explicitly a a that along from showed earthquake They supershear computed compo- a motion vertical of one- simulation the the a a by of and of dynamically model nents context driven wave the bathymetry, shallow-water in simple nonlinear implemented (1D) was conservation dimensional verti- forcing mass seafloor correct This the ensured wave (20). of thus, shallow-water derivative and, the time displacements in cal the term including crucial by supershear. a equation indeed recovered was then rupture fault P-K They the P-K that demonstrate the sively of conclusions, geometry Their Palu complex complex meter. trigger the the a of system. only and specifics of bathymetry may the order by Bay components, non- confounded the a are slip of however, included dip which waves and slip, tsunami it fault rake coupling equations, the negligible wave and that shallow-water system demonstrated (2D) they fault on two-dimensional propagation P-K the earthquake with complex the geometrically (18) dynamic emulated (3D) the al. pri- the that three-dimensional to et model the critical a rupture Ulrich were Using were tsunami. displacements generation. motion, earthquake tsunami devastating the supers- the ground that the triggered argued for strong (13, landslides, recognize source authors earthquake’s Socquet submarine to mary Several and the that 14). first (13) (13, postulated by the al. earthquake have among et for this 15–17) of Bao impact were nature (12). its (14) caused hear motion in al. and fault atypical system et of tsunami, fault type localized strike-slip this unexpected (P-K) Palu-Koro an the on owo orsodnemyb drse.Eal [email protected] Email: addressed. be may correspondence whom To 08Pl vns hc a etecs o nearth- an for Andreas case San the the the of be and segment Izmit northern may Fault. the 1999 which rupturing the events, quake in Palu as 2018 higher earthquakes, is risk supershear unrec- The worldwide. previously for cities a coastal is for hazard This ognized generation. with wave slumps necessar- associated or their without landslides underwater tsunamis, coseismic triggering devastating ily strike-slip generate for potential to unexpected faults uncovered has work Our Significance maie l 1)uiie erfutGSdt ofis conclu- first to data GPS near-fault utilized (19) al. et Amlani occurred earthquake Sulawesi 7.5 Mw 2018 September The c eateto eopc n ehnclEgneig University Engineering, Mechanical and Aerospace of Department rer,CR-M 58 S eerhUiest,706Paris, 75006 University, Research PSL 8538, CNRS-UMR erieure, ´ c NSlicense.y PNAS asaS Bhat S. Harsha , rnbeAps .. nvriyCleeDbi;adD.D.O., and Dublin; College University F.D., Alpes; Grenoble e ´ https://doi.org/10.1073/pnas.2025632118 b eka nttt o Advanced for Institute Beckman f eerhCnr o Atmospheric for Centre Research . d y https://www.pnas.org/lookup/suppl/ otsSynolakis Costas , y | e,f f11 of 1 ,

EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES effects uncovers high-frequency details in the early phases of Coupled Earthquake–Tsunami Framework the tsunami motion. They claimed these details may get missed Earthquake Model. We model a bilaterally expanding earthquake if only the static seafloor displacements are used. However, rupture by solving the elastodynamic wave equation, for the bulk they did not consider the effect of horizontal displacements in displacement field ui (x, t) for i = 1, 2, 3, in a 3D linear elas- the ground motion on deforming the bathymetry. Furthermore, tic medium surrounding a vertically dipping rectangular planar their 1D model could not account for the dramatic focusing fault. The Cartesian coordinate system is given by x = xi ei , where effect introduced by water waves converging at, and subsequently ei are the fixed mutually orthogonal unit vectors. We prescribe reflected and refracted from, the apex of any narrow bay. These absorbing boundary conditions along the lateral and bottom limitations possibly led to a noticeable underprediction of the boundaries of the domain to minimize artificial wave reflection calculated amplitude of the waves. due to simulation domain truncation. The top boundary, which The question, therefore, remains whether generic strike-slip corresponds to the seafloor, is modeled as a free surface. We faults, in the absence of secondary sources, such as coseis- impose an initially uniform shear stress everywhere on the fault mic underwater landslides, can generate large tsunamis. This surface, except for a small, squared, localized region that we question has important ramifications, as several metropolitan overstress to forcefully nucleate the rupture. The initial shear areas worldwide are located near bays (6, 7, 21–23) that are stress is applied along the fault strike-parallel direction with traversed by strike-slip faults similar to the P-K system. Fur- zero component in the dip direction. Furthermore, a uniform thermore, while early warning for far-field tsunamis (1, 24, 25) compressive stress acts on the fault. based on hydrodynamic inversions is now fairly routine, at least The fault strength is governed by a linear slip-weakening fric- in the North Pacific, little or no early warning is possible for tional law. Fault slip starts at a point when the shear stress near-field tsunamis, in which the tsunami originates just a few reaches the static shear strength level, given by the product of the kilometers away from the coastline. Most field scientists agree static friction coefficient and the compressive normal stress. The that, thus far, for coastal residents, earthquake shaking is the stress then decreases linearly with increasing slip, over a charac- warning for an impending tsunami from a nearshore source teristic slip-weakening distance, to the dynamic shear strength, (26, 27). set by the product of the constant dynamic friction coefficient To shed light on the basic mechanisms through which strike- and the compressive stress. slip faults may cause damaging tsunamis, we have developed The terminal speed of the nucleated rupture depends on the a computational framework that integrates mechanistic models fault stress level, as measured by the strength parameter S ∗, for earthquake rupture dynamics with hydrodynamic models for which is given by the ratio of two stress measures (42, 46, 47). tsunami generation and propagation. Possibly with a few excep- The first is the difference between static shear strength and tions, the initial condition in tsunami models is computed by initial shear stress. The second is the difference between ini- using the static algorithms of Mansinha and Smylie (28), sub- tial shear stress and dynamic shear strength. The S ∗ parameter sequently parameterized by Okada (29), which translate finite thus quantifies the proximity of the fault initial stress state to its fault slip models into static seafloor displacements. In recent static strength, scaled relative to its dynamic stress drop. High S ∗ years, there has been an increased interest in developing mod- values, corresponding to low-stressed faults, generally favor sub- els that account for dynamic generation (18, 30–33). Here, Rayleigh ruptures with the rupture propagation speed limited we use our dynamic generation model and focus on a planar by the Rayleigh wave speed. Low values of S ∗, corresponding strike-slip fault traversing a shallow bay with a simple geome- to highly stressed faults, enable the rupture tip to break the try. Tsunami evolution over a more complex bathymetry may shear wave speed barrier and become supershear, propagating hide the effects of the dynamic rupture. Our approach is thus at intersonic speeds. designed to unravel the underlying physics governing tsunami In this work, we vary the value of the initial shear stress to generation due to the intrinsic nature of strike-slip faulting. simulate both supershear and sub-Rayleigh ruptures. We note In other words, we seek to understand the basic phenomenol- that varying the initial shear stress will change the stress drop and ogy first, before applying our model to complex geophysical slip accumulation during the two rupture scenarios. This, in turn, geometries. will affect some of the tsunami-generation features. More details The 2018 Palu earthquake and tsunami highlighted the com- of the earthquake model are given in Materials and Methods. plex dynamics of tsunamis generated by intersonic earthquakes. In supershear, or intersonic, earthquakes (34–40), the rupture tip Tsunami Model. We model the tsunami initiation and subsequent propagates faster than the shear wave speed (41–43). This leads propagation in the bay using the 2D nonlinear shallow-water to the emergence of large localized deformation bands along the equations, assuming an inviscid and incompressible flow model shear shock wave fronts, also known as Mach cones (34, 35, 38, (30, 48). The coupling between the earthquake and tsunami 39, 44). Dunham and Bhat (38) proved the presence of a second models is realized through the time-dependent 3D seafloor Mach front associated with Rayleigh waves that carry significant displacement and velocity fields computed from the dynamic vertical motion, moderately attenuated, to large distances. When rupture simulation and then imported to the tsunami model such earthquakes occur within a narrow bay, the associated large as time-dependent boundary motions. Specifically, we solve the horizontal displacements, as well as the moderately attenuated following set of nonlinear equations (49): vertical displacements (34, 39, 45), along the shear and Rayleigh ∗ ∗ shock wave fronts may cause significant motion in the bay bound- h,t + (ˆvβ h ),β = 0 β = 1, 2, [1a] aries, which, just as with a paddle wavemaker, could lead to the displacement of large volumes of water. Furthermore, in ∗ these scenarios, the triggered tsunami may exhibit multiple char- vˆα,t +v ˆβ (ˆvα,β ) + gh,α = gH,α α, β = 1, 2. [1b] acteristic time scales, ranging from a few seconds to several minutes. Here, t is time, H = H (x1, x2, t) is the depth of the bay, and In the following sections, we investigate the synergistic inter- vˆα =v ˆα(x1, x2, t) are the depth-averaged in-plane water par- actions between rupture speed, seafloor ground motions, and ticle velocities for α = 1, 2. (.),α denotes the differentiation bay geometry. We also examine several distinct features of the of the relevant variable with respect to the coordinate xα, and g is tsunami, including the emergence of an instantaneous dynamic the gravitational acceleration. We define h∗ = h + H , where h is phase and a slower coseismic phase, both of which lead to a the vertical sea-surface displacement measured from the initially ∗ gravity-driven postseismic phase. undisturbed sea-surface level (x3 = 0), and h is the total water

2 of 11 | PNAS Elbanna et al. https://doi.org/10.1073/pnas.2025632118 Anatomy of strike-slip fault tsunami genesis Downloaded at California Institute of Technology on May 3, 2021 Downloaded at California Institute of Technology on May 3, 2021 otewtrsraemto,a eonzdb aik and Tanioka by displacement recognized seafloor as a For motion, (50). Satake water-surface the to time-dependent the just not and displacements. model, dynamic the particle in seafloor velocities the and displacements seafloor the time-dependent for explicitly accounting by al ufc.Vcoso h etclsaorvlct r ueipsdo h lprt npht.Rpuefaue,sc steserMc oeadthe and the cone on Mach motion shear slip the lateral as right such the velocity features, with particle Rupture consistent seafloor snapshots. is slip-rate the arrows the on these on superimposed of superimposed fault highlighted. direction are are the also The displacements velocity from are seafloor. seafloor wave, supershear in-plane away the Rayleigh vertical extending at the on trailing the sharpen, propagates of motion and of and Vectors the Vectors emerge surface propagate. of surface. cones) the direction to fault (Mach reach the fronts continues to wave demonstrate expands rupture shock to subsequently the shear contours It seafloor, as region. the attenuation, overstressed On little an zone. with (x within seismogenic tip depth the rupture at saturating forward-propagating after nucleates the speeds rupture onto zooming the (x (B), plane, line s fault 7.4 dashed the and white 4.0, the 2.0, by 1.0, indicated 0.1, is times at shown velocity particle seafloor 1. Fig. Eq. in that note We height. column ntm fsrk-lpfuttuaigenesis tsunami fault strike-slip of Anatomy al. et Elbanna where eflo oini optda olw (51): follows as computed is motion profile seafloor bathymetry static initial an lystrtstesimgnczn.Terpuefis propagates first the rupture and eventu- The it at zone. rates as seismogenic surface slip the nucleates free saturates fault on the ally earthquake toward of rupture propagates The terms and supershear hypocenter velocities. in the fault particle of strike-slip seafloor development lateral right the a shows 1 Fig. Results in given are model tsunami Eq. the of of Details expansion involve through Taylor first-order approximately that the motions approaches computing to horizontal adopted the prefer widely of therefore, more incorporation We, other bathymetry over deformation. the it the of use of smoothness magnitude the by the restricted or not is and Eq. slope in expression The o eea ahmty oiotlmtoscudcontribute could motions horizontal bathymetry, general a For and (A) s 7.4 and 4.0, 2.0, 1.0, 0.1, times at shown rate slip fault the of Snapshots fault. strike-slip lateral right a on rupture supershear a of Evolution Γ s stefe ufc nteerhuk oe,adfor and model, earthquake the in surface free the is H (x 1 , x 2 , t = ) 2 sgnrleog oacutfrany for account to enough general is H o (x 1 H − 2 ,t = u H em eaeuigbt the both using are we term, 1 s )i h rtpnlof panel first the in 0) o , (x x x 1 1a 2 1 stesrk-aallcoordinate, strike-parallel the is − , aeil n Methods. and Materials , x u h 2 u i s ,t = ) ∗ 2 s ≡ ) = − u H h i u (x ,t (x 2 3 s + , . 1 1,5,53). 52, (18, t , ) H x 2 ∀ ,t oehrwt aro roshglgtn h ih aea es ftefutsi.On slip. fault the of sense lateral right the highlighting arrows of pair a with together B, 0) , Thus, . x ∈ the , [2] Γ s , utr i n ihntesokwv eina h dynamic the as region wave shock the within and the around tip persists strike. which fault rupture alter- field, the They velocity along vertical monotonic. values pronounced not negative The are and positive velocities between vertical nate The (t 4) comparison grows. s). rupture in 7.4 the diminished as are region, elsewhere front wave Velocities the shock the of within onset high be the and sub-Rayleigh (t fronts transition trailing wave veloc- shock supershear seafloor the the vertical as pronounced accompany well the 2) ities subplots); as in (all tip, highest front few rupture is wave a the velocity highlight vertical of to seafloor vicinity snapshots The slip-rate 1) the observations: on superimposed ity another in resulting (t surface, waves fault reflected the of of set edge inter- bottom locked-slipping the the by at capped face are fronts shock The 1B. Fig. transition (t the propagation fronts accompanying supershear surface, shock to fault stage, of the this on boundaries At develop bottom to back. start and reflected are top (t waves the zone domain, reaches seismogenic the front the rupture saturating the bay As the toward propagate delin- of to apex clear continue which the the fronts, and rupture the expansion of eation rupture we Then, subsequent region. the overstressed the observe within ( earthquake the Initially of ation times. different at supershear the into mode. transitioning before speeds, sub-Rayleigh at x 2 i.1A Fig. 1A Fig. stesrk-omlcodnt,and coordinate, strike-normal the is ipassasoso h lprt ntefutsurface fault the on rate slip the of snapshots displays lososvcoso eflo etclpril veloc- particle vertical seafloor of vectors shows also 2 = .0 4 = ) )tevria eoiiscniu to continue velocities vertical the 3) s); .0s). 2 = t 0 = https://doi.org/10.1073/pnas.2025632118 .0 x 3 .1 ) sw ildsussotyin shortly discuss will we as s), stedphws coordinate. depth-wise the is ) eosretenucle- the observe we s), 1 ≥ ) h oiino h fault the of position The 0). PNAS 4 = 1 = | .0 f11 of 3 . 0 and s).

EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES s s rupture propagates, has a direct imprint on the generated pushed landward (u1 > 0 and u2 > 0), which is equivalent to a tsunami, as will be discussed shortly. downward movement of the seafloor. On the negative side of the s s Fig. 1B illustrates the magnitude of the particle velocity on the fault, the slopes are pushed seaward (u1 < 0 and u2 > 0), which seafloor at different times, focusing on the forward-propagating is equivalent to an upward movement of the seafloor. The equiv- rupture tip. Initially, there is no visible disturbance as the waves, alent vertical motion of the seafloor due to the bulk in-plane emanating from the rupture at depth, have not reached the displacements is to be added to the direct vertical motion com- surface yet (t = 0.1 s). Then, as the rupture grows, parts of ing from the vertical displacements due to the strike-slip motion. the rupture front reach the surface, and we observe the onset The synergistic interaction between all of the displacement com- of intense ground motion (t = 1.0 s). As the rupture expands, ponents enrich the tsunami dynamics, on different time scales, as we observe key characteristics of the supershear propagation, we will discuss shortly. including 1) the sharp increase in the seafloor particle velocity We now turn our attention to the tsunami dynamics. Fig. 2A during the rapid acceleration of the rupture from sub-Rayleigh illustrates the bathymetry of the simulated bay. The bay geom- to supershear speeds (t = 2.0 s); 2) the development of shear etry is partially inspired by the geometry of the Palu Bay. The shock wave fronts, emerging due to the coherent interference of Palu Bay has a narrow (width ∼ 8 km) and shallow (maximum shear waves trailing the propagating rupture tip, which gradually depth ∼ 700 m) trench with a rounded apex at the end (54). extends into the bulk away from the fault (t = 4.0 s); 3) the devel- Here, we also consider a generic, narrow, and shallow bay with opment of a secondary Rayleigh wave front (36, 39, 44) that trails a rounded apex as an example of this class of geometries. The the shear shock wave front (t = 4.0 s); and 4) the sharpening of exact dimensions of our geometry are given in SI Appendix, sec- the shock fronts and their expansion into further distances within tion S2. We record the water-surface amplitude at a number of the bay, without significant attenuation (t = 7.4 s). stations located at various locations within the bay (along section At all times, the rupture tip lags behind the dilatational wave A-A) and along the coastline. We note that a spectrum of time front. The arrows in Fig. 1B represent the magnitude and direc- scales emerges for near-source tsunamis, like the one modeled tion of the resultant in-plane displacement. Since the fault slip here, which is usually overlooked in the more commonly studied has a right lateral sense, the seafloor is pushed away from the far-source tsunamis. Specifically, we define: fault surface, on the top side of the forward-propagating rupture tip (“positive” side, x2 > 0), while it is pulled toward the fault sur- 1. An instantaneous dynamic tsunami phase (on the scale of few face on the bottom side (“negative” side, x2 < 0) (t = 1.0 s). As seconds, as shown in Fig. 2 B–D), in which the water surface the rupture further expands, the magnitude of the in-plane dis- is directly, and almost instantaneously, driven by the coseis- placements, reflected by the size of the arrows, increases, but the mic motion of the seafloor (H,t =6 0), even at large distances sense of motion just described above persists (t = 2.0, 4.0, and from the fault plane, because of the unattenuated action of 7.4 s). These in-plane displacements are critical for the tsunami the shock waves. dynamics, as they may induce large seafloor bathymetric varia- 2. A coseismic tsunami phase that is initiated by the dynamic tions. In particular, if such a fault is traversing a bay, we expect seafloor motion adjacent to the fault, but propagates slower that on the positive side of the fault, the slopes of the bay are than the dynamic one, due to the diminishing effect of the

Fig. 2. Evolution of the earthquake-induced tsunami in a bay traversed by a supershear rupture. (A) Bay bathymetry, with the various observation stations (OP) and section A-A marked. The right-handed Cartesian coordinate system is also shown for reference. (B–H) Snapshots of the supershear tsunami scenario at times 1.0, 4.0, 6.0, 27.5, 45.5, 81.5, and 153.9 s, shown sequentially from left to right. Colors indicate the sea-surface height (h) relative to the undisturbed water level. B–D correspond to the “dynamic tsunami-generation phase.” E–G correspond to the “postseismic tsunami-generation phase.” The evolution of different tsunami-generation mechanisms, as well as coseismic rupture signatures, are observed. Note the common color-scale bar between all of the subplots. An alternative representation for these surface plots, in which multiple scale bars, adjusted for the local water-surface peak amplitude in each displayed time step, is provided in SI Appendix, Figs. S1 and S2

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The the et Elbanna coast. for the threat toward direct other a the are and waves bay heading the the toward initial traveling of this one cou- waves, center that two observe into the the dispersed We and is surface. from disturbance bathymetry sea the following the resulted of created of motion that uplift/depression are horizontal waves the disturbance between These dynamic pling bay. initial the of the banks the over 55). (45, but fronts tip, Mach rupture the the along at extends this localized case not which is true, in the displacement is supershear, out-of-plane satisfy This are surface. ruptures to free these earth when seafloor solid especially the the nonnegligible at at condition a stress emerges plane is that still component seafloor there vertical the displacements, predom- at generate horizontal faults displacement strike-slip inantly ini- While vertical earthquake. an the the have as to waves by due These surface, set bay. the amplitude fault of tial sides the both on from toward coastlines direction the emanate strike-normal region. the in apex that propagate the above, described waves with interaction tsunami its as The well as propagation, and at fault the from away to strike- proportional propagates tsunami fault speeds coseismic subsequently the the which with to the angle belong phase, at fronts shallow join These very that direction. a parallel fronts form observe wave and we water tip propagates, rupture secondary further More- of rupture bay. emergence the strike-slip the of the sides as both on are over, local emerge form These quickly that bay. very disturbances the that of water features banks ridge-like the the at by surface recognized water the in (highlighted variation profile motion 1B ground Fig. the in to due bathymetry the of i.2 Fig. 2 Fig. Furthermore, 2 Fig. history the by motion in set is tsunami postseismic the While iutnosy rvt-rvntuaiwvssatt evolve to start waves tsunami gravity-driven Simultaneously, w ae ae ihcet ln h al strike-parallel fault the along (x crests with (x direction waves 2 water Fig. two in shown (as H ae oan hspaei rvnb rvt n spoeto prone geometry. is bay and the gravity by amplification by and 2 simu- driven refraction, is the reflection, Fig. phase exited This in have domain. waves shown lated elastodynamic as all after minutes, emerges several to seconds ,t 2 direction). em sterpuefotzp ln h al plane fault the along zips front rupture the as term, E–H B–D uigtednmcrpue eut napronounced a in results rupture) dynamic the during ute eosrt h otesi snm onset tsunami postseismic the demonstrate further 1 ,t ieto)mvn ntesrk-omldirection strike-normal the in moving direction) 0 = hwtednmc n oesi,tsunami- coseismic, and dynamic, the show .I h aeo a-edtuai,tepost- the tsunamis, far-field of case the In ). C √ .Ti hs a edsrbdas described be can phase This B–D). and gH D spr ftegaiydie,post- gravity-driven, the of part as ,t embcmsngiil sthe as negligible becomes term ) hwta h oiotlmotion horizontal the that show E–H that ) ntergtsd fteby(h at bay obvious antisymmet- the (h most of not side side is is right deviation the solution This on the surface. that fault t note the water coastlines. about to bay the ric the important of for disturbance is hazard initial substantial It a the differ- constitute past at and long level, emerge depth. points, waves the water focal high-amplitude diminishing approaches ent these is the that front level by observe wave water amplification We the traveling to in due radially increase coastline fur- the sudden expands as right) A the coast. observed to the plots toward contour black the the ther by in the (marked shown while apex and coast, the arrow from the front by toward wave (marked traveling further radially propagate waves arrow) tsunami tsunami- white postseismic postseismic the the The highlights phase. 3A, generation Fig. to compared three wave. larger-amplitude a form to fault coastline, the the from toward away propagating surface wave tsunami the with coalesces faster. travels bay depth. the water of At varying center the the as by toward bay, governed propagating is front the The fronts period of the time of the center speed over direc- the The 2 s. Fig. toward the in other insets in the the in expanding and detailed coast one the fronts, red of propagating tion other disturbances two initial the these in of by each results Subsequently, highlighted 3A. is Fig. in valley arrow The in (x respectively. valley right banks, the and the over crest profile to pronounced water-surface leads the surface instantaneous the sea an the of of of sides emergence displacement the vertical of fronts. the motion and shock horizontal bay the the by between to carried coupling corresponding The displacements 3A, Fig. seafloor location, in vertical arrows fault red the the the to of one close by profile highlighted water-surface the in turbance ytesmercntr ftesrk-omlsaorhorizon- seafloor strike-normal the of displacement tal nature symmetric the by phase tsunami-generation dynamic post- the and (t Within coseismic, obser- follow. dynamic, Several vations the respectively. at phases, during located snapshots tsunami-generation A-A, 2A), shows seismic section Fig. 3 along in Fig. level (shown level. water water the the of spatio- of the evolution investigate temporal we mechanisms, tsunami-generation triggered ent of absence the in field, amplification even displacement substantial amplitudes, landslides. 3D wave to water contribute full the may the in slopes and bay interaction the dynamics, the with rupture Specifically, model- bays. the when narrow of in motions hazard horizontal sim- tsunami strike-slip and ing the geometry wave importance considering bay the water of simple highlights complex characteristics the The earthquake-source from bay. ple emerges the that in existing pattern interaction and waves bathymetry these other shoreline with the of by due amplitude amplification apex, backward the propagate The they to the as back. grow hitting at to bay, continue further waves slopes the reflected located of the interior regions of the coastal toward displacements backward apex dynamic radially the disturbance, travels the initial with high-amplitude by interact the they set that as observe waves We tsunami region. the of warning. early refraction for time type little this very by allow poised they cou- as hazard a the tsunamis, unique beyond only of overland the them meters highlights takes of This it hundreds shoreline. and cover form to seconds, minutes waves of of these tens ple that of scales note time We on attenuation. coast- much the without of and portion m line shallow 2.47 reaches the amplitude through wave propagates water persistently the region, apex the In 120.0 = 6 = hs etclsaehsbe dutdb atrof factor a by adjusted been has scale vertical whose 3B, Fig. ogi ute nihsit h hrceitc fteediffer- these of characteristics the into insights further gain To and reflection the to relates phenomenon remarkable Another t 25.0 = .0 1 = ) eosreteeegneo ongiil dis- nonnegligible a of emergence the observe we s), ,weetemgiueo h ae ee shigher is level water the of magnitude the where s, .3 ,tefotpoaaigtwr h etro h bay the of center the toward propagating front the s, ) h ako efc niymtyi explained is antisymmetry perfect of lack The m). u 2 s hl h te w opnnso seafloor of components two other the while , = https://doi.org/10.1073/pnas.2025632118 −1.6 )cmae oteleft the to compared m) 2 < n et(x left and 0) t PNAS x 8 = 1 29.5 = .0 | o12.0 to 2 f11 of 5 > km 0)

EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES Fig. 3. Snapshots of sea-surface height h for cross-section A-A. The snapshots correspond to different phases of tsunami generation associated with different time scales. (A) Late dynamic tsunami phase to early postseismic phases at times 6, 8, 12, 20, and 25 s. (B) Fully developed postseismic tsunami phase at times 30, 50, 70, 80, and 120 s. Grayscale indicate the bathymetry variation along the cross-section where the depth varies from 700 to 10 m over a distance of 2 km. The instantaneous dynamic phase is marked by red arrows. The postseismic tsunami waves are marked by white arrows. The postseismic radially traveling wave front from the apex is marked by black arrows. These phases are highlighted for x2 ≥ 0, but a similar pattern exists for x2 ≤ 0. The evolution of the early phases of the postseismic tsunami waves over the banks of the bay is emphasized in the zoomed-in plots in the left column. Contour plots (Right) show the reflected and refracted tsunami waves, which are also part of the postseismic tsunami phase, propagating backward from the apex toward cross-section A-A. The black arrows in B correspond to the black dots in the contour plots in the rightmost column. A more detailed breakdown for the dynamic tsunami-generation phase between times t = 4.0 s and t = 7.5 s is provided in SI Appendix, Fig. S3.

s s displacement u1 , u3 are antisymmetric. This is consistent with sense of motion that seems consistent with the particle velocity the field observations of Fritz et al. (56). pointing from regions of higher to lower water-surface eleva- In Fig. 4, we show snapshots of the in-plane water-particle tions behind the backward-propagating reflected front. In the velocity as vectors superposed on the water-surface height dur- region where the water surface is unperturbed (h = 0), the par- ing the different tsunami-generation phases. Fig. 4A shows that ticle velocity maintains its strike-normal direction, as discussed the arrival of the rupture tip at the apex, at t = 6.0 s, leads to above. 3) In the shallower parts of the apex region, we observe an abrupt variation in the water-surface level. Since the fault slip that the forward-propagating wave (moving up the slope) is com- is right lateral, the flat portions of the seafloor would move up pressed, while the backward-propagating wave (moving down on the positive side (x2 > 0) of the fault, and down on the neg- the slope) is rarefied. This is accompanied by an increase in ative side (x2 < 0). This causes the water-particle velocity to be the water in-plane particle velocity in both forward and back- pointing downward (from higher to lower water-surface eleva- ward directions at the edge of the basin (Fig. 4B, zoom in B). tions) along the segments of the fault not traversing the coastline The water in-plane particle velocities are of the order of 1 m/s, slopes. In the meantime, within the apex region, this right lateral which may be significant enough to impact the morphology of the motion pushes the shoreline landward on the positive side of the shoreline (57). fault surface, but pushes it seaward on the negative side. As a Fig. 4C shows further evolution of the in-plane water-particle result, the water surface is depressed on the positive side, while velocities at a later time. We observe differences in the mag- it is elevated in the negative side. This causes the water-particle nitude of the particle velocity at the lateral sides of the bay. velocity in the apex region to point upward along the x2 direc- Specifically, the particle velocity over the bay banks on the nega- tion. As highlighted in the zoomed plot in Fig. 4A, this direction tive side of the fault is 1.375 times larger the particle velocity on of water-particle velocity in the apex region is opposite to the the positive side. This may be explained as follows. On the nega- direction of the water-particle velocity in the rest of the water tive side of the fault, the water-particle velocity is amplified. This surface along the fault line (x2 = 0). is due to the constructive interference of the reflected water wave Fig. 4B shows snapshots of the in-plane water-particle velocity from the apex and the increased water-surface height generated at a later time (t = 45.5 s), well within the postseismic tsunami from the seaward motion of the side of the bay. On the positive phase. Several observations follow in this case: 1) The particle side of the fault, the water-particle velocity is reduced. This is velocity within the deeper portion of the apex region points pre- due to the destructive interference between the reflected wave dominantly in the strike-normal direction from the negative side from the apex and the decreased water-surface height generated of the fault to the positive side. This sense of motion is the from the landward motion of the side of the bay. This variation result of the motion of the banks of the bay due to the hori- in interaction patterns between the different waves propagating zontal displacements of the strike-slip fault. Specifically, the bay within the basin intensifies the contrast in the particle-velocity slopes on the negative side are pushed seaward, while those on amplitudes at the two sides of the bay. the positive side are pushed landward. This leads to the water We also examined tsunami generation in a bay traversed by a body having a momentum component, in the strike-normal direc- sub-Rayleigh rupture. The simulation domains for the tsunami tion, pointing from the negative to the positive sides of the fault. and earthquake models have identical material properties and 2) The backward-propagating fronts that are reflected from the dimensions in both the sub-Rayleigh and supershear cases. To apex locally modify the direction of the in-plane particle velocity generate a sub-Rayleigh rupture, we reduce the value of the (Fig. 4B; zoom in A). Specifically, we observe an anticlockwise initial shear stress, as outlined in Materials and Methods.

6 of 11 | PNAS Elbanna et al. https://doi.org/10.1073/pnas.2025632118 Anatomy of strike-slip fault tsunami genesis Downloaded at California Institute of Technology on May 3, 2021 Downloaded at California Institute of Technology on May 3, 2021 ntm fsrk-lpfuttuaigenesis tsunami fault strike-slip of Anatomy al. et Elbanna by refracted further and apex the propagating from reflected radially is the (t which from resurgence front, wave water high-amplitude to the leads Finally, that wave tsunami to mic (up slope the of displacement t horizontal front the wave from tsunami ensued the that of arrival the amplitude to corresponding of depressed, surface time water at of m uplift 0.26 abrupt at an located causes front OP-1, wave station in at shown rupture, stations supershear (x different the the For at 2A. profiles Fig. rupture both for tude representation. for 0.8 of factor of factor a a by by scaled scaled are are magnitudes magnitudes vector vector The The bay. bay. the the of of apex sides the two near motion the water between of structure ( the representation. highlighting for s, 0.8 45.5 at at phase phase tsunami-generation tsunami dynamic postseismic The The (A) water. undisturbed the to i.4. Fig. ∼ 1 i.5ilsrtstetm itr ftewtrsraeampli- water-surface the of history time the illustrates 5 Fig. , 50.0 x 2 (27 = ) npht ftei-ln ae atcevlct etr tdfeetpae ftuaignrto.Clr niaetesasraeheight sea-surface the indicate Colors generation. tsunami of phases different at vectors velocity particle water in-plane the of Snapshots ) e loFg .Ti sfloe yaohrpostseis- another by followed is This 3. Fig. also see s); ,4) .5, t 5 = h asg fteshock the of passage the 5A, Fig. in shown km C . 1 h otesi snm hs t159s eeln h olsigwv rnsadhglgtn h ako efc antisymmetry perfect of lack the highlighting and fronts wave coalescing the revealing s, 125.9 at phase tsunami postseismic The ) .Floigti pit h ae ee is level water the uplift, this Following s. ∼ 1.0 min). t = .Tevco antdsaesae yafco f2 o ersnain (B) representation. for 20 of factor a by scaled are magnitudes vector The s. 6.0 ,crepnigt h yai xiainb h asg fthe of time passage at the m by 0.24 excitation of dynamic level the at to water bay corresponding the the s, in of increase apex an the observe near located 2, the gradually. in more amplitudes vary and the smaller that are supers- except case the sub-Rayleigh cases, across sub-Rayleigh 5 similar and Fig. are hear in features m highlighted tsunami 0.09 further postseismic is of The This order wave. observe the Rayleigh we of the case, pulse tsunami sub-Rayleigh time dynamic at the smaller in much waves a around shock at of arrives absence geometry, bay the i.5B Fig. t 10.0 = lutae h ae-ufc yaisa tto OP- station at dynamics water-surface the illustrates ,wihi soitdhr ihtepsaeof passage the with here associated is which s, https://doi.org/10.1073/pnas.2025632118 t 2 = (34. . 25 ,1) 5, i.Det the to Due min. m gi,we Again, km. PNAS A, h | t relative f11 of 7 6 = Inset. .0

EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES shock waves. This is followed by a large-amplitude depression of (−1.7 m) at t ∼ 1.1 min. Subsequently, a rapid increase in the water surface is observed, with the maximum water-level height reaching 2.174 m at t ∼ 1.25 min. While we do not attempt to model Palu Bay explicitly, it is interesting to note that Palu city is located exactly at the apex of the Palu Bay, and this is where our simulation predicts the largest amplification in the water level. The rapid variation in the water-level amplitude (4 m) from depression to resurgence, occurring over a time span of just 0.15 min, is only observed at this location and may have important implications for liquefaction potential. On the other hand, the sub-Rayleigh case shows a smaller range of variation in the water-level amplitude, as low as half the corresponding amplitude in the supershear case. In both cases, we observe the emergence of multiple oscillations trailing the peak wave. These oscillations are artifacts of the numerical dis- cretization of the shallow-water wave equations using low-order finite elements. The reader is referred to SI Appendix, section S2 for further discussion on the nature of these oscillations. Specif- ically, SI Appendix, Fig. S5 demonstrates that the amplitude and wavelength of the trailing oscillations, observed in the water level at OP-2, are reduced when the mesh is refined. This, however, comes at a significant computational cost. The main features, such as the peak amplitude and arrival times, show convergence and are consistent at different element sizes. At the other side of the bay, Fig. 5C shows the time history for station OP-3 at (31.5, −3.65) km. The dynamic disturbance from the passage of the dynamic rupture is observed at t = 5.7 s and is manifested in the local water-surface depression of amplitude 0.257 m. After half a minute, we observe the tsunami wave asso- ciated with the slope motion, followed by the near-fault tsunami wave, and, finally, the radially propagating front arrival. All of the key features are observed at an earlier arrival time than station OP-1, due to the proximity of station OP-3 to the apex. Finally, Fig. 5D presents the time history of water level at station OP-4, which mirrors station OP-1 in location. Accordingly, the time his- tory is similar, but with opposite polarity, consistent with the sense of motion on the fault and subsequent displacement of the slopes. The smaller amplitude of tsunami waves in the sub-Rayleigh case is attributed mainly to the smaller vertical and strike-parallel s s seafloor displacements u3 , u1 , respectively. The effect of smaller vertical displacements is evident in the absence of a strong dynamic tsunami pulse. The weaker strike-parallel seafloor dis- placement leads to diminished bathymetric motions at the apex, resulting in substantially lower uplifts and reduced water wave amplitudes. These observations have two major implications. First, for a given fault area, a tsunami generated by a supershear earthquake will be larger than that generated by a sub-Rayleigh one. Second, the difference between the two tsunamis is not simply a mat- ter of scaling the sub-Rayleigh rupture to generate a slip equal to the supershear one. If it was an issue of scaling, the ratio between the time histories in the two cases would have been the same throughout. Rather, it is evident that different features in the time histories from the two tsunamis have different relative amplitudes. For reference, the maximum slip in the simulated supershear rupture is 8.4 m, while the corresponding value in the sub-Rayleigh rupture is 6.3 m. However, the tsunami waves Fig. 5. Comparison between water-level time histories corresponding to a generated by the supershear rupture have amplitudes at peak supershear and a sub-Rayleigh rupture traversing the same bay. Time histo- values that range between one and four times as large as the ries obtained for the tsunami at stations OP-1 (A), OP-2 (B), OP-3 (C), and one generated by the sub-Rayleigh one. This suggests that there OP-4 (D) are shown. The locations of the stations are shown in Fig. 2A. Black exists a synergistic effect between the details of the dynamic rup- solid lines correspond to water-surface height associated with supershear ture in both modes, the relative amplitude of strike-parallel and rupture. Blue dashed lines correspond to water-surface height associated with the sub-Rayleigh rupture. The arrival of dynamic, rupture-induced strike-normal components of displacements, the motion of the water wave is highlighted in the zoomed portion. A modified version of bathymetry, and the subsequent water-level motion. this figure, in which the water-level time history is scaled by the average slip Furthermore, SI Appendix, Fig. S5 displays the water-level time in each rupture scenario, is presented as SI Appendix, Fig. S4. history scaled by the average slip for each of the rupture scenarios.

8 of 11 | PNAS Elbanna et al. https://doi.org/10.1073/pnas.2025632118 Anatomy of strike-slip fault tsunami genesis Downloaded at California Institute of Technology on May 3, 2021 Downloaded at California Institute of Technology on May 3, 2021 ntm fsrk-lpfuttuaigenesis tsunami fault strike-slip of Anatomy al. et Elbanna lt.Asgeto h otesi snm hs tsainO- around OP-1 2A. station Fig. in at shown phase zoomed tsunami the postseismic within the The t highlighted (B). of depth is OP-2 segment and constant stations A (A) both of plots. OP-1 at bathymetry stations water-level phase at flat shown tsunami the a are dynamic shows histories with time line ocean The dashed open 3). (case red the horizontal The in when history 2) history time time (case (case water-level excluded included the corre- are are shows line motions line motions dash-dot all black when blue solid history The The time 1). rupture. water-level supershear the a to by sponds traversed bay a for 6. Fig. resid- the have by waves These determined rupture. amplitude dynamic an the with from fault displacements ual the at up set to 1. postseismic identical case subsequent in is the than seafloor, smaller However, much the 1. is on tsunami case waves for shock observed the that with of associated signature, passage tsunami weak the a dynamic indicates The included, ver- signal. the is only tsunami motion which seafloor in geometry. of 2, bay case component reflected for the tical history is time by the that refracted contrary, the subsequently front On and propagating apex radially the tsunami the from postseismic then the then and by phase, followed wave, tsunami phase, dynamic consid- tsunami the are coseismic of motion a arrival of the components observe all we which ered, in 1, case For cases. open depth. an constant the in of 3) bathymetry of and flat considered; a all the with being ocean motion to with seafloor compo- vertical contributing the bay the of only motion a with nent bay earthquake- a seafloor in in 2) the 1) deformation; supershear bathymetry of cases: the components three three compare for tsunami we induced tsunami, induced difference. water-level amplitude the the nor in time, changes of function the com- a in not as does profile difference slip the in difference explain the pletely that shows figure scaled The ∼ h otesi snm ncs sgnrtdb h waves the by generated is 2 case in tsunami postseismic The 6A Fig. the on displacements horizontal of role the emphasize To sas ihihe na ne.Telctoso h ttosare stations the of locations The inset. an in highlighted also is s 90.0 h feto nldn h oiotlmto nabsnbathymetry basin a on motion horizontal the including of effect The lutae h epnea tto P1i h three the in OP-1 station at response the illustrates ertesoeadi oiindsc hti rvre bay is a hazard tsunami traverses the it coastline, that the such toward positioned heading is is or and area located shore is fault the in strike-slip displacements near the coastline horizontal if the Specifically, larger to generation. these tsunami the respect leveraging that with in out fault critical is turns strike-slip It the of displacements. positioning vertical limited but poten- ments, be observations. may in field observed unexplained here scales and time records introducing tsunami multiple near-source the are deciphering in we helpful tially motions bay tsunami the classification by The to of bathymetry. refraction propensity the probably and by its amplification reflection to is and apex, geometry, due tsunamis, the phases at coseismic three the effects the histo- focusing and affect of the dynamic hazardous to of most the minutes memory the both carries several of which to phase, ries seconds This phase, region. postseismic of coastal gravity-driven tens a takes 3) which and the seafloor of than time; effect speed with diminishing slower dynamic the velocities a to the due at phase, while propagates tsunami emerges but dynamic active, phase still shak- tsunami is the coseismic rupture with A synchronously and, 2) areas second, coastal ing. per the kilometers reaches several it is hence, phase of this speed The of rupture. propagation dynamic elasto- the the from by emanating motions: advected field is wave dynamic that associated phase we dynamic the instantaneous Notably, an in 1) bays. phases narrow distinct traversing three recognize faults strike-slip by erated complex may by faults strike-slip masked tsunamigenic. which become not through reveal mechanisms are they intrinsic Rather, results some motions. ground our geom- complicated smooth respect, or and topography that idealized with on In bay scenarios etry. a rupture traversing dynamic faults simple planar on of typi- based simulations are the is results without numerical These tsunamis landslides. what large underwater cause trigger unlike to may need faults, 59), 58, strike-slip (15, assumed that cally suggest results Our Conclusions landslides. of absence significant the a in pose even thus hazard, may nar- tsunami coastlines traversing toward heading faults or bays Strike-slip row faulting. those to normal compared from insignificant be resulting not of may displacements that vertical surface water to the leading bathymetry, bay the or to displacement coastline significant cause may faults 39) strike-slip (36, long on earthquakes supershear of hor- characteristic large motions The faults. izontal strike-slip by generation tsunami seconds. in few motions a over rapidly change and may meters, surface few sea reach water may the height dis- wave horizontal include of tsunami presence the not the placements, In do prob- earthquakes. anyway slow for of which effects problematic has the analyses, particularly mechanism hazard is tsunami generation this abilistic of and type overlooked this sizable been Hence, generate not waves. only do which surface displacements, models, seafloor tsunami vertical conventional include reason This depression. the or possibly uplift water is substantial no is there that strates h bevto tto,adtercre ae-ee amplitude zero. by water-level to pass recorded decays simply the subsequently fault waves and The fur- the station, uniform. amplified observation is near not the depth are field water waves the these displacement tsunami since 2, ther, postseismic residual and 1 the the cases by Unlike by surface. followed up of then shock set signature the is identical wave of This an passage fronts. see the to again wave corresponding depth we tsunami the case, dynamic where this the his- 3, time case In the in uniform. include amplitude is also water-surface we the comparison, for they For tory as slope. amplified the weakly up only run are and amplitude small relatively tiesi alsuulygnrt ag oiotldisplace- horizontal large generate usually faults Strike-slip gen- tsunamis of features distinct several identifies model Our horizontal of role critical the to point observations These nteasneo oiotlmto,Fg 6B Fig. motion, horizontal of absence the In https://doi.org/10.1073/pnas.2025632118 ute demon- further PNAS | f11 of 9

EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES amplified. The presence of an apex at the tip of a bay further strike-slip faults in different geographic areas. Potential candi- enhances this effect, since it results in wave focusing, reflection, dates include the San Francisco Bay and the Tomales Bay in and refraction, enabling multiple interactions with the slopes Northern California, crossed by the San Andreas Fault; Izmit bay of the bay. The reason for this phenomenon is that in such in Turkey, crossed by the North Anatolian Fault; and Al-Aqaba geometries, the strike-normal and strike-parallel components of bay in Egypt, crossed by the Dead Sea Transform fault system. ground motion will cause horizontal deformations in the shore- Just as in Palu Bay, tsunamis have been reported in these regions line slopes, which, in turn, lead to vertical displacement of the in the past (22, 63–66), and some of these faults have also had water surface. If the slopes are steep enough, the resulting dis- supershear rupture earthquakes (19, 67, 68). We, thus, recom- turbance in the water surface may be significant. While the effect mend revisiting the tsunami risks associated with large submarine of coupling between the horizontal motion and water-level uplift strike-slip faults, particularly those traversing narrow bays, with has been recognized for tsunamis induced by subduction zone extraordinary caution needed in interpreting probabilistic hazard earthquakes (60–62), it has not been appropriately considered analyses which have not included strike-slip events in aggregating for strike-slip faults. We note that this effect may be nonnegligi- the hazard. ble, and overlooking it in the case of strike-slip faults may lead to gross underestimation of the associated tsunami hazards. Materials and Methods Another important conclusion of our work is that the details We used the crustal-deformation finite-element software PyLith for of rupture propagation matter. Supershear ruptures are capa- the earthquake rupture simulations. PyLith has been verified by using ble of generating larger tsunamis than sub-Rayleigh ruptures for community-driven benchmarks, which are in line with Southern California the same rupture area. The shock wave fronts, which emerge Earthquake Center/US Geological Survey Dynamic Rupture Code Verifi- during supershear propagation, carry in-plane and out-of-plane cation exercises, and it can be obtained at https://geodynamics.org/cig/ dynamic seafloor displacements and velocities to large distances software/pylith (69). More details on the elastodynamic governing equa- away from the fault without significant attenuation (34, 38, tions and simulation parameters are available in SI Appendix, section S1. The tsunami simulations were run by using SWIM, an in-house partial 39). They are also more efficient in focusing energy ahead of differential equation solver built on the MOOSE framework (70). This non- the rupture tip and along the direction of propagation. These linear solver discretizes the shallow-water equations spatially by using the focused unattenuated displacements result in a stronger inter- finite-element method and implicit time stepping for time integration. The action between the dynamic earthquake motion and shoreline tsunami is generated by the time-dependent motion of the bathymetry bathymetry, especially at the apex of bays, during the dynamic imported from the 3D dynamic rupture model in PyLith. A more detailed and coseismic phases of the tsunami. This, in turn, sets up higher description of the tsunami model setup is given in SI Appendix, section water-surface displacements, which subsequently get further S2. Furthermore, we have verified SWIM using several benchmark prob- amplified as they run up the slopes. lems in the literature (71–73). An example of the verification is presented in While for the same fault area, sub-Rayleigh ruptures produce SI Appendix, section S3. smaller slip than supershear ruptures, the reduction in slip alone Data Availability. All study data are included in the article and/or supporting does not explain the smaller tsunami wave heights in the sub- information. Rayleigh case. Rather, our results suggest that the full history of the source dynamics, which also result in different spatial distri- ACKNOWLEDGMENTS. A.E. was supported by NSF CAREER Award 1753249, butions of the final slip and ground motions, is critical to explain and A.J.R. was supported by the Caltech/Mechanical and Civil Engineering Big Ideas Fund and the Caltech Terrestrial Hazard Observation and Report- such discrepancy. This further motivates the need for integrated ing Center. This research is part of the Blue Waters sustained-petascale dynamic rupture–tsunami models like the one adapted here. computing project, which is supported by NSF Awards OCI-0725070 and Since our modeling has used generic features of the earth- ACI-1238993, the State of Illinois, and, as of December 2019, the National quake and tsunami sources, we expect that our results are not per Geospatial-Intelligence Agency. Blue Waters is a joint effort of the University of Illinois at Urbana–Champaign and its National Center for Supercom- se location-specific. Supershear rupture propagation, other sim- puting Applications. H.S.B. was supported by European Research Council ilar bay geometries, and horizontal displacements of shoreline Consolidator Grant PERSISMO a#865411. C.S was supported by NSF Award slopes all may combine to produce tsunami amplification from 1906162, Field Survey of the September 27, 2018, Sulawesi Tsunami.

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