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			<titleStmt><title level='a'>Performance of Slab Geometry Constraints on Rapid Geodetic Slip Models, Tsunami Amplitude, and Inundation Estimates in Cascadia</title></titleStmt>
			<publicationStmt>
				<publisher>Seismica</publisher>
				<date>09/25/2023</date>
			</publicationStmt>
			<sourceDesc>
				<bibl> 
					<idno type="par_id">10579415</idno>
					<idno type="doi">10.26443/seismica.v2i4.1406</idno>
					<title level='j'>Seismica</title>
<idno>2816-9387</idno>
<biblScope unit="volume">2</biblScope>
<biblScope unit="issue">4</biblScope>					

					<author>Kevin Kwong</author><author>Brendan Crowell</author><author>Amy Williamson</author><author>Diego Melgar</author><author>Yong Wei</author>
				</bibl>
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			<abstract><ab><![CDATA[Tsunamigenic megathrust earthquakes along the Cascadia subduction zone present a major hazard concern. We can better prepare to model the earthquake source in a rapid manner by imbuing fault geometry constraints based on prior knowledge and by evaluating the capabilities of using existing GNSS sensors. Near-field GNSS waveforms have shown promise in providing rapid coarse finite-fault model approximations of the earthquake rupture that can improve tsunami modeling and response time. In this study, we explore the performance of GNSS derived finite-fault inversions and tsunami forecasting predictions in Cascadia that highlights the impact and potential of geodetic techniques and data in operational earthquake and tsunami monitoring. We utilized 1300 Cascadia earthquake simulations (FakeQuakes) that provide realistic (M7.5-9.3) rupture scenarios to assess how feasibly finite-fault models can be obtained in a rapid earthquake early warning and tsunami response context. A series of fault models with rectangular dislocation patches spanning the Cascadia megathrust area is added to the GFAST inversion algorithm to calculate slip for each earthquake scenario. Another method used to constrain the finite-fault geometry is from the GNSS-derived CMT fault plane solution. For the Cascadia region, we show that fault discretization using two rectangular segments approximating the megathrust portion of the subduction zone leads to improvements in modeling magnitude, fault slip, tsunami amplitude, and inundation. In relation to tsunami forecasting capabilities, we compare coastal amplitude predictions spanning from Vancouver Island (Canada) to Northern California (USA). Generally, the coastal amplitudes derived using fault parameters from the CMT solutions show an overestimation bias compared to amplitudes derived from the fixed slab model. We also see improved prediction values of the run-up height and maximum amplitude at 10 tide gauge stations using the fixed slab model as well.]]></ab></abstract>
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<div xmlns="http://www.tei-c.org/ns/1.0"><head n="1">Introduction</head><p>Operational tsunami monitoring has traditionally relied on quick earthquake source approximations from seismic data and verification from open ocean buoys and coastal tide gauges that directly measure tsunami waves (e.g., <ref type="bibr">An et al., 2014)</ref>. However, this reliance on seismic data has limitations; in large earthquakes, the estimate of magnitude in the near-field can saturate, an effect that gets directly propagated into tsunami forecasts (e.g., <ref type="bibr">Hoshiba and Ozaki, 2014)</ref>. Furthermore, the W-Phase seismic solution <ref type="bibr">(Kanamori, 1993)</ref> is often the first reliable magnitude estimate, but rapid results can take up to &#8764;20 minutes or more, relative to the origin time, to obtain (e.g., <ref type="bibr">Hayes et al., 2009)</ref>. To aid in a more rapid and proper identification of large earthquakes in the near-field, <ref type="bibr">Blewitt et al. (2006)</ref> proposed using Global Navigation Satellite System (GNSS) data. GNSS data is particularly advantageous since it directly measures displacement of the ground in a noninertial reference frame and does not saturate for the largest earthquakes <ref type="bibr">(Wright et al., 2012;</ref><ref type="bibr">Melgar et al., 2015</ref><ref type="bibr">Melgar et al., , 2013))</ref>. Real-time applications of high-rate GPS data in earthquake early warning (e.g., <ref type="bibr">Allen and Ziv, 2011;</ref><ref type="bibr">Colombelli et al., 2013)</ref> have evolved to, in the past decade, include several GNSS-based rapid earthquake source algorithms such as BEFORES <ref type="bibr">(Minson et al., 2014)</ref>, G-larmS <ref type="bibr">(Grapenthin et al., 2014)</ref>, REGARD <ref type="bibr">(Kawamoto et al., 2016)</ref>, and GFAST <ref type="bibr">(Crowell et al., 2016;</ref><ref type="bibr">Murray et al., 2018)</ref>, the latter recently fully integrated into the U.S. West Coast-wide ShakeAlert system <ref type="bibr">(Murray et al., 2023)</ref>. ShakeAlert is now the world's first Figure <ref type="figure">1</ref> Map view of the Cascadia subduction zone boundary using data from <ref type="bibr">Bird (2003)</ref> in the Pacific Northwest. (a) Large left map shows locations of high-rate GNSS stations (green triangles) and epicenter locations of the 1300 events in the Cascadia FakeQuakes database (black circles). Triangles with gray outline shown in mapview represent the model mesh for the rupture simulations described in <ref type="bibr">Melgar et al. (2016)</ref>. The black arrow represents the plate motion of the Juan de Fuca Plate with respect to the North American Plate (GSRM v2.1). Extent of tsunami forecast modeling on the coastline is described by two transects: U.S.A (southern coast), red line and Canada (northern coast), orange line. Smaller maps on the right show discretized fault patch areas (gray rectangles) referred to as Slab models that range in having (b) 4 patches, (c) 8 patches, (d) 12 patches, (e) 24 patches, (f) 34 patches, (g) 68 patches, (h) 100 patches, and (i) 200 patches. Purple contour lines (20 km depth interval) represent depth to the slab interface model from Slab2 <ref type="bibr">(Hayes et al., 2018)</ref>.</p><p>Earthquake Early Warning (EEW) system that utilizes a real-time operating geodetic algorithm.</p><p>The GFAST (Geodetic First Approximation of Size and Time) algorithm was initially developed at the University of Washington (UW) to provide rapid characterization of large-magnitude earthquakes by determining estimates of (1) earthquake magnitude from measurements of peak ground displacement (PGD), (2) a centroid moment tensor (CMT) and (3) finite-fault (FF) slip inversion from coseismic offsets. GFAST aims to accurately model GNSS observations to take advantage of the fact that high-rate geodetic displacement data tend to be robust in capturing the true deformation field without the signal going off-scale, consequently alleviating a problematic issue that commonly arises in using traditional seismic data to measure large ground motions (e.g., <ref type="bibr">Melgar et al., 2019;</ref><ref type="bibr">Grapenthin et al., 2017)</ref>. A major benefit of having GFAST in real-time operation is the improved capability to initially calculate a robust magnitude estimate for a large event.</p><p>The debut of GFAST integrating with EEW systems has significant relevance to Tsunami Early Warning (TEW) and tsunami hazard approximation, especially combined with advances in tsunami numerical modeling for quantifying tsunami intensities that involve using rupture models of large subduction zone earthquakes (e.g., <ref type="bibr">Melgar et al., 2016;</ref><ref type="bibr">Crempien et al., 2020)</ref>. Our study and several others focus on the Cascadia Subduction Zone (CSZ) in the Pacific Northwest (PNW) which has the potential to produce a M9+ earthquake on the megathrust fault and generate a massive tsunami of major consequence at local shorelines (e.g., <ref type="bibr">Satake et al., 2003)</ref>. New methods in tsunami modeling are appealing for the CSZ region because of the region's density of onshore GNSS stations. To test the performance of rapid geodetic inversion of earthquake sources, we utilize synthetic rupture scenarios from <ref type="bibr">Melgar et al. (2016)</ref> that generated simulated 1-Hz displacement data at the GNSS network locations in Cascadia; these synthetic scenarios are here referred to as Cascadia FakeQuakes (Figure <ref type="figure">1</ref>).</p><p>The Cascadia FakeQuakes cover the entire Cascadia megathrust seismogenic zone. Modeling realistic rupture scenarios of these events requires knowledge of the fault geometry and, more broadly, the geometry of the regional subducting slab surface. Global models of subduction zone slab geometry divided within major regional slab segments, such as Slab2 <ref type="bibr">(Hayes et al., 2018)</ref>, updated from Slab1 <ref type="bibr">(Hayes et al., 2012)</ref>, are available to the public. High-resolution and sophisticated simulations of megathrust earthquake rupture like the Cascadia FakeQuakes dataset employ information from slab geometry models that can be used to build complex mesh discretization, for example, triangular mesh elements (e.g., <ref type="bibr">Barnhart and Lohman, 2010)</ref> to accurately simulate three-dimensional features of the fault surface (Figure <ref type="figure">1a</ref>). Currently, inverting GNSS or seismic observations for slip on finely discretized and complex meshes is computationally time-consuming and not immediately applicable to tsunami early warning.</p><p>In this study, we examine the role of using predefined fault catalogs in addition to CMT-derived fault geometries to see how these different approaches to fault parameterization impact rapid GNSS source modeling. <ref type="bibr">Williamson et al. (2020)</ref> explored GFAST's ability to recreate fault geometries that are comparable with the megathrust using geodetic CMT nodal plane information. They summarized that the finite-fault solutions generally resulted in fault dips steeper (&#8764;30 &#8226; ) than the expected shallow dipping megathrust geometry (&#8764;9 &#8226; ) but fault strike solutions were consistent with the rupture simulations. The generation of steeper and deeper GFAST CMT solutions from coseismic offsets arises from the tradeoff between point source and finite source solutions; fitting large offsets over a large geographic area to a single point source requires making the source deeper or rotating the moment tensor. The sources used in that analysis and in the work shown here are predominantly thrust faulting events to evaluate tsunami impact, although we acknowledge that slip on normal "outer-rise" faults, splay faults, and strikeslip faults are useful observations for additional future studies.</p><p>We start by exploring various resolutions of fault discretization that will be appropriate to evaluate earthquake source inversions. Here, we construct predefined fault rupture patches along the shallow Cascadia megathrust seismogenic zone and use GFAST to determine finite-fault rupture models using the Cascadia FakeQuakes scenarios from <ref type="bibr">Melgar et al. (2016)</ref>. The 1300 scenarios for the Cascadia subduction zone provide a robust synthetic dataset to test the impact of the chosen fault discretization on the GFAST algorithm results. Specifically, we assess the accuracy of the GNSS-based earthquake and tsunami early warning source products determined within a few minutes after rupture initiation. Improvements in both of these aspects will be useful to implement a modified GFAST monitoring system for Cascadia and may provide additional framework and strategies for constructing and implementing future fault catalogs of other subduction megathrust regions. Finally, we look into run-up and amplitude predictions at tide gauges as another critical component to validating tsunami forecasting models.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2">Methods</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.1">Overview of Cascadia FakeQuakes</head><p>Characterizing variable earthquake and tsunami scenarios is an important strategy for approximating the impact of the hazard. We estimate variable earthquake sources and the resulting tsunami amplitudes using the FakeQuakes database showcased in <ref type="bibr">Melgar et al. (2016)</ref>, which offers an extensive range of stochastically derived rupture scenario data that focus on models of large-magnitude tsunamigenic slip events located across the entire Cascadia megathrust fault region (Figure <ref type="figure">1</ref>). The FakeQuakes are fault-slip models derived from the Karhunen-Loeve (K-L) expansion method <ref type="bibr">(LeVeque et al., 2017)</ref> to create synthetic displacement waveform data modeled at the locations of 426 regionally located GNSS stations that encompass networks considered useful to early warning for the Pacific Northwest such as the NOTA, PANGA, and BARD networks.</p><p>There are a total of 1300 events in the FakeQuakes database, each with a unique stochastic heterogeneous forward slip model (primarily dip-slip solution), moment magnitude (ranging between M7.5 -M9.3) and hypocentral location. The generation of stochastic slip distribution models provides dense and diverse observations for an earthquake-generating fault zone that lacks direct variable observations of historical great earthquakes, such as the 1700 event. A large catalog of rupture scenarios is also useful for probabilistic tsunami hazard assessment, since fault slip can have an important effect on the resulting tsunami. The Fake-Quakes database provides the opportunity to test the performance of current near-field GNSS configurations and geodetic earthquake and tsunami algorithms for events that occur across the entire Cascadia coastline.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.2">Slip Model Discretization</head><p>For optimizing rapid estimation of slip on a fault, we discretized a fault area with rectangular dislocation subpatches prior to the source inversion process. This approach allows the inversion of multiple segments with varying strike, dip and patch sizes that can better approximate major curvature changes on the subducting megathrust than a single rectangular geometry. We split the Cascadia subduction zone into two main segments:, a northern segment striking at &#8764;24 &#8226; NW roughly parallel to the coastline of Vancouver Island (segment 1) and a southern segment stretching from the Mendocino triple junction to the Strait of Juan de Fuca (segment 2), striking &#8764;0 &#8226; NS (Figure <ref type="figure">1</ref>). Depth to slab surface data from the Slab2 model <ref type="bibr">(Hayes et al., 2018)</ref> helped to approximate the geometry of the two segments. We constrain the segment down to a depth of 40 km, the seismogenic depth extent of the FakeQuakes dataset. This depth is also roughly the start of the episodic tremor and slip zone in Cascadia (e.g., <ref type="bibr">Nuyen and Schmidt, 2021;</ref><ref type="bibr">Brudzinski and Allen, 2007)</ref>. These two main fault segments are further subdivided into even rectangular sub-patches. We showcase 8 different fault model discretizations that range from sub-faults with 25 by 50 km in dimension to 100 by 800 km in size. An overview of the subdivisions is outlined in Table <ref type="table">1</ref> and shown in Figure <ref type="figure">1</ref>. The fault models with the least and most sub-patches range from 4 and 200 respectively. These predefined fault catalogs will be referenced as the "Slab models". We tested how "true" slip from the FakeQuakes distributed under the rectangular fault sub-patch areas compare in moment release, and how much is recovered. For each of the 1300 stochastic slip distributions, we average the slip on our fault models such that each triangular element (true slip value) beneath a rectangular fault patch was averaged and assigned a moment. The sum of the moment from each patch was used to calculate a separate moment magnitude (M w ) for each event, representative of the moment normalized under a given fault model discretization area. We compared this M w with the FakeQuakes derived M w to see how our normalized slip models match with the moment from the simulations so there is no magnitude bias in our tsunami predictions (see Supplementary Figure <ref type="figure">S1</ref>).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.3">Overview of GNSS Slip Modeling</head><p>We use the GFAST algorithm <ref type="bibr">(Crowell et al., 2016)</ref> to model coseismic slip based on methodologies described in <ref type="bibr">Crowell et al. (2012)</ref>. Their study showed that regional GPS networks, such as those in western North America and Japan, provide adequate coverage to record the displacements of large earthquakes (e.g. the 2003 M w 8.3 Tokachi-oki Earthquake and the 2010 M w 7.2 El Mayor-Cucapah Earthquake). These near-field geodetic data are used to compute finite-fault slip inversions in a homogeneous elastic half-space with Green's functions obtained from <ref type="bibr">Okada (1985)</ref>. We evaluate the performance of GFAST finite-fault inversions using two different approaches related to fault assumptions but keeping the same physics and modeling setup as previously described. The first approach calculates fault slip assuming no prior knowledge about the fault geometry. In this approach, the preferred geodetic centroid moment tensor (CMT) solution, determined within a separate module in GFAST, and the fault dimensions, calculated from the scaling relations of <ref type="bibr">Blaser et al. (2010)</ref>, provide the fault model parameters. Thus, the length and width of the slip patch can vary but the number of strike and dip elements is set to 20 and 5 respectively, thus allowing 100 sub-patches. The slip is separately prescribed onto both nodal planes of the CMT solution, and the fault plane with the lowest GNSS residual fit is set as the preferred solution. In the second approach, the fault slip is calculated based on the predefined slab models as described in section 2.2. Slip model solutions for each event are created at specified rupture times at 30 s intervals starting from 30 s to 300 s from the origin time. With both approaches, our regularization constraint requires the rectangular fault patches to be the same size.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.4">Overview of Tsunami Modeling</head><p>The amplitudes of the tsunami waves are predicted using the spatio-temporal information of the coseismic slip. The earthquake slip values are transformed into seafloor deformation by assuming an elastic half-space model <ref type="bibr">(Okada, 1985)</ref>. This seafloor deformation is instantaneously transformed into sea surface perturbations by assuming an incompressible water column. Two tsunami models are employed to compare tsunami impact offshore and onshore with the "true observations", which are the model results computed from the generic FakeQuakes.</p><p>We use the GeoClaw software package <ref type="bibr">(Berger et al., 2011)</ref> that solves the two-dimensional non-linear shallow-water equations (NSWE) with high-resolution finite-volume methods to perform the tsunami simulation from the input deformation field, which is assisted by the adaptive mesh refinement technique. The code has been benchmarked during the National Tsunami Hazard Mitigation Program (NTHMP) series of benchmark tests <ref type="bibr">(Gonz&#225;lez et al., 2011)</ref>, and is used in <ref type="bibr">Williamson et al. (2020)</ref> with the legacy GFAST results. In the present study, the GeoClaw modeling results are sampled from offshore locations to examine the modeled maximum tsunami amplitudes, not the runup heights onshore, versus the FakeQuake "observations". This allows us to inspect large-scale model accuracy along the entire PNW coastline.</p><p>The impact of tsunami inundation onshore is calculated using existing tsunami forecast models along the PNW coastlines developed by the NOAA Center for Tsunami Research (NCTR). These forecast models are built upon the Method of Splitting Tsunamis (MOST) model that solves the NSWE in characteristic form with an explicit finite difference scheme. Similar to Geo-Claw, MOST is also benchmarked by the NTHMP tests <ref type="bibr">(Synolakis et al., 2009;</ref><ref type="bibr">Lynett et al., 2017)</ref> and is the operational model that provides real-time tsunami inundation forecasts at NOAA's Tsunami Warning Centers (TWCs). Each MOST-based forecast model consists of three one-way coupled grids, i.e., model boundary conditions are only passed down in one direction from an outer layer to its inner layer, with increasing grid resolutions. Being an operational tool, a forecast model usually computes tsunami inundation extent and runup heights onshore in the innermost grid with a grid resolution of 2-3 arc sec (&#8764;60-90 m). It is worth noting that the MOST-based inundation models compute tsunami waveforms at many National Ocean Service (NOS) tide gauges, including the ones along the PNW coastlines, to provide model validation and evaluation with observations <ref type="bibr">(Tang et al., 2009;</ref><ref type="bibr">Titov et al., 2016;</ref><ref type="bibr">Wei et al., 2008)</ref>. A Manning's coefficient of 0.025 is used in both models to represent the surface roughness of a bare earth.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3">Results</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.1">Earthquake Magnitude Determination</head><p>For the Slab models, the standard deviations of the M w bias are small (Supplementary Figure <ref type="figure">S1</ref>), and models with a small number of fault patches (4-34) and a large area tend to, on average, overestimate the moment. The moment release from the Fakequakes mapped within the areas of our discrete fault models shows a small magnitude bias, so we feel confident in using the eight models to resolve magnitude and slip. We compare GFAST's magnitude estimates with results calculated using the eight predefined slab models and the CMT method. To estimate the magnitude residuals (the difference between the calculated and true magnitude) corresponding to the 1300 events, the GFAST determined magnitudes are subtracted from the "true" M w from the rupture scenario. While our approach computes a source model that includes a magnitude estimate at 30 s intervals from the origin time to 300 s after, we emphasize that analysis of robust results in under 3 minutes (180 s) is a goal we hope to achieve in geodetic tsunami early warning, as it would show an improvement in the speed of rapid response compared to traditional seismic methods. Figure <ref type="figure">2</ref> shows the statistical distribution of the magnitude residuals at 60 s, 120 s and 180 s after the earthquake source origin time. The median residual is within -0.5 to 0.5 for both the CMT and slab model derived model results. We observe a systematic trend; the median magnitude residual increases with increasing number of sub-faults over the total fault area. We attribute this systematic trend in magnitude to the generalized regularization equation proposed in <ref type="bibr">Crowell et al. (2012)</ref> that was optimized for fewer fault patches; the use of a generalized regularization equation reduces computation time significantly since the inversion does not need to search for the optimal smoothness (i.e., Lcurve norm tradeoff). Another trend is that the spread in the magnitude residual decreases with increase in source duration time. We also see that the Variance Reduction (VR) decreases significantly for the predefined slab model results as the number of sub-patches increases. The VR spread becomes tighter and smaller compared to the CMT results for the Slab models with 34 to 200 patches.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.2">GFAST Rupture Models</head><p>With eight slab model discretizations, we analyze which models can resolve heterogeneous slip and provide better fit to the data compared to the models using the CMT parameters. We specifically explore whether coarse finite-fault models provide a meaningful interpretation of the rupture. The Slab models share the same fault location, geometry, and roughly span the same area as the shallow Cascadia segment from the Slab2 model (Figure <ref type="figure">1</ref>). In contrast, the event's unique fault parameters from the CMT solution provide varying fault locations on a single rectangular plane and the geometry is derived from the nodal plane solutions of the moment tensor. To fix outlier geometry models, the input of a known slab model will ensure an accurate fault location for modeling slip on the megathrust. Our results will focus on the spatial and temporal pattern of the finitefault models determined in under three minutes and differences in modeling slip using a two segment fault model that approximate the known slab location. The highly discretized Slab models tend to provide better fits to the data (Table <ref type="table">1</ref>). The GFAST algorithm chooses between three models with the lowest RMS to the GNSS data; either of the two nodal planes from the CMT inversion or from the specified slab model. Results using the Cascadia Fakequakes dataset show our most simplistic fault discretization (4 rectangular patches) is only chosen 0.4% of the time while the rest of the 1300 event database prefers the CMT derived solution. Further model discretization increases the likelihood that it will be the chosen fault model. For instance, the 24 subpatch model is chosen 49% of the time and the 100 subpatch model is chosen 94% of the time. These statistics are indicated under "% of GFAST best models" in Table <ref type="table">1</ref>.</p><p>An important case for using GNSS technology is whether near-field geodetic inversions of high-rate displacement data can recover slip patterns that resemble the earthquake rupture. We highlight three specific rupture scenarios (Earthquake A, B, and C) that illustrate heterogeneous slip variability across the Cascadia megathrust (Figure <ref type="figure">3a</ref>,<ref type="figure">b</ref>,<ref type="figure">c</ref>). Earthquake A (M8.73) ini- tiates off the coast of Vancouver Island and Washington State and ruptures to the south, with a large slip asperity located off the northern coast of Oregon. The mostlyunilateral slip distribution is &#8764;300 km in length, with a maximum slip of &#8764;25 km. Earthquake B (M9.08) initiates where the megathrust is changing from a NNW to a roughly NS strike fault. The slip distribution is located updip with a rupture length of &#8764;600-700 km. Earthquake C (M9.01) features a &#8764;500 km length bilateral rup-ture pattern in the southern portion of the fault. These scenarios represent diverse rupture patterns along various parts of the Cascadia megathrust.</p><p>The resulting finite-fault model solutions we highlight here come from the fixed slab and CMT-geometry models, both containing 100 rupture patches. Figure <ref type="figure">3d</ref>,e shows GFAST finite-fault results of Earthquake A using the slab model and CMT model parameters. Both models show a compact unilateral rupture pattern. The CMT strike of the fault is 43 &#8226; NE, which directs the fault away from the Vancouver Island coastline. Despite the two finite-fault models having different strikes, they both capture the main slip in roughly the same location. The simulation of Earthquake B illustrates an almost full rupture of the Cascadia megathrust. The GFAST finite-fault slab model shows high-slip (15-30 m) directly updip from the epicenter at the edges of the two adjoining fault segments and captures slip on both segments along the coastline (Figure <ref type="figure">3f</ref>). The CMT-based solution shows a 138 &#8226; striking fault and a concentrated highslip region updip from the epicenter but the fault extends directly into East Vancouver Island and bypasses the coastline to the north (Figure <ref type="figure">3g</ref>). The slab model is more reliable in resolving a long rupture where a signif-icant change in strike in the subduction zone is present. Earthquake C is similar in moment release to Earthquake B but has a more compact slip distribution located off-shore southern Cascadia. The CMT-based solution places a higher concentration of slip south of the epicenter compared to the slab model (Figure <ref type="figure">3h</ref>,<ref type="figure">i</ref>). Superfluous slip in the slab model (Figure <ref type="figure">3h</ref>) is located in the northern fault segment, an area that did not rupture in the Earthquake C simulation. The geometry of the CMT solution does not align well with the megathrust location and the high slip region is placed seaward from the trench.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.3">GFAST Tsunami Amplitude Predictions</head><p>We compare tsunami predictions based on the Cascadia Fakequakes scenarios (observations) and GFAST finitefault solutions (models). In Figure <ref type="figure">4</ref>, the composite dataset indicates deviations in tsunami amplitude predictions with respect to magnitude. The increasing variation in amplitude predictions with increasing magnitude reflects the larger extent of tsunami impact along the coast, associated with complex and larger magnitude ruptures. The median amplitude bias (observations -model) are within -0.8 to 0 m for events with M&gt;7 and M&lt;9. Events with M&gt;9 show the most noticeable difference in amplitude bias between the two model datasets (CMT vs slab model). The median amplitude bias using the CMT fault and slab model is -2.2 and -0.5 m respectively. The negative values reflect a tendency of amplitude overestimation relative to observations. Analyses of the 1300 events help provide statistical descriptions of how the amplitude bias is more significant when using the CMT solutions in comparison to the slab model.</p><p>To illustrate the range of tsunami variation along the coast, we highlight three cases. Earthquakes A, B and C from Figure <ref type="figure">3</ref> are translated into coastal tsunami amplitudes referred to as Tsunami A, B and C (Figure <ref type="figure">5</ref> and <ref type="figure">6</ref>). The tsunami amplitudes (at 0.25 &#8226; latitude and longitude intervals) were computed along two coastal transects, one along Vancouver Island, British Columbia and one along the northwestern United States. The observed tsunami is compared to the tsunami based on the slab model (Figure <ref type="figure">5</ref>) and CMT parameters (Figure <ref type="figure">6</ref>). We show results at 3 minutes after the origin time to highlight the performance of advance warning at this temporal limit. The peak coastal amplitude for Tsunami A is &#8764;12 m at 45 &#8226; latitude, the slab model's prediction at this location is &#8764;7 m, and the CMT parameter model predicts an amplitude of &#8764;9 m.</p><p>In Tsunami B, the modeled coastal amplitudes (up to 22 m) exceed the observations (&#8764;9 m) in the southern region. However, the slab model does not overpredict the observations as much as the model from the CMT geometry. In Tsunami C, the models underpredict the maximum amplitude area and overpredict amplitudes at locations specifically along the Vancouver Island coastline. The CMT-geometry based model overpredicts the tsunami amplitudes specifically at regions with latitudes between 39 &#8226; to 43 &#8226; , with peak amplitudes at &#8764;60 m. Predictions from the slab model are below 25 m and are closer to the observations.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.4">Inundation Modeling</head><p>The main assessment of the MOST-based inundation modeling study is to compare the GFAST finite-fault (CMT vs. Slab model) results to the Cascadia Fakequakes measurements. For the present study, we modeled the tsunami impact resulting from the GFAST finite-fault models for 10 coastal communities along the coast: Port Angeles, Neah Bay, La Push, Westport in Washington, Garibaldi, Newport, Florence, Port Orford in Oregon, and Crescent City and Eureka in California. It is worth noting that there is currently no tide gauge that is being Figure <ref type="figure">4</ref> Statistical representation of tsunami amplitude residual (in meters) from all 1300 scenario events between the observations (Cascadia Fakequakes) and predictions (GFAST models) with respect to earthquake magnitude and fault model type. For each box plot, the data distribution is sorted in 0.5 magnitude bins with respect to either the CMT or slab model, and the white circle inside the density distribution represents the median value. operated in Florence, Oregon to provide real-time water level observation. Instead, we placed a virtual gauge at Florence, also termed as a "warning point", that can provide rapid model estimates of wave amplitudes at the shore during an event. Overall, comparisons of runup height and maximum amplitude at the tide gauge show that, statistically, the Slab model predictions are more accurate to the FakeQuakes than the CMT geometry predictions.</p><p>Figure <ref type="figure">7</ref> summarizes the model accuracies of runup heights and the maximum tsunami amplitude at tide gauge locations at the 10 sites and also features the average values combined from those sites. The model accuracy is calculated as the ratio between the model results and the FakeQuake "observations". One can observe a significant improvement in model accuracy when using the GFAST Slab model over the GFAST CMT model. The improvements in runup height estimate range from 26.0% (Eureka) -72.5% (Garibaldi), with an average of 45.7% improvement across all 10 sites, reducing the average error from 167.69% using GFAST CMT models to 121.99% using GFAST Slab models. Similar improvements in accuracy can be also seen from the maximum tsunami amplitude estimate at the tide gauge locations, with the average reduced from 182.94% (GFAST CMT) to only 130.93% (GFAST Slab), a 51.9% improvement in model accuracy. The GFAST Slab model is able to reduce the model errors to &#8764;20% for runup heights and &#8764;30% for tide gauge observations, which fit well within the goal of achieving model accuracy greater than 70% for tsunami model forecast at the TWCs. Furthermore, at four tide gauge locations (Neah Bay, Westport, Newport, and Florence), the GFAST Slab models are capable of providing spot-on, 98-100%, predictions of the Fake-Quake observations. It is also worth noting that with impressive increases of the model accuracies, the GFAST Slab model gives conservative model forecast results for nine out of ten of the coastal communities, except for the &#8764;5% underestimation of the runup heights at Newport. Importantly, we document the performance of the two different finite-fault modeling approaches for varying fault geometries to highlight the variability in inundation modeling results.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="4">Discussion</head><p>GFAST offers a complementary toolset to obtain tsunami forecasts from earthquake source products and has the potential to be used concurrently with existing tsunami warning operations that use seismic measurements to rapidly determine an earthquake's size and use deep-water pressure sensors to track the propagation of tsunami waves. Through this study, we highlight the use of technology such as GFAST to enhance the real-time tsunami warning infrastructure in the Pacific Northwest in the context of measuring and modeling a scenario like a magnitude 9+ earthquake and tsunami. The last megathrust event occurred in 1700 and tsunami deposits indicate an average recurrence interval of 500-600 years (e.g., <ref type="bibr">Peters et al., 2007)</ref> which may suggest that Cascadia is late in the interseismic cycle. Observationally, near-field GNSS stations in the PNW have not recorded a significant enough event (M6.5+) within its region outside of the Mendocino fracture zone.</p><p>We find improvements in magnitude estimation, data variance reduction, and tsunami wave height and inundation estimation, when adding a fixed fault catalog to GFAST and moreover, find better performance when including more fault patches, allowing for greater slip heterogeneity. We plan to add to GFAST the option to compute rapid geodetic source models using pre-defined global fault databases that contain location points representing a 3D mesh model of the fault. The fault databases address the difficulties in constraining fault parameters using rapid inversion techniques and operations. <ref type="bibr">Williamson et al. (2020)</ref> showed that modeling large ruptures on a subduction zone using a single, planar fault model can lead to improbable fault parameters. Fault geometries derived from independent CMT solutions can result in models with locations and geometry that are not consistent with published slab geome- try models (e.g. Slab2). Fault mesh models that realistically describe the active tectonic region are used to improve the characterization of large complicated earthquake ruptures. Earthquakes with full and long ruptures on non-planar faults are not efficiently described with a single rectangular fault solution. Using the CMT parameters for a single fault plane in GFAST has resulted in difficulty in constraining ruptures along notable fault curvature regions such as the Cascadia slab. The east-ward convex bend along the Cascadia slab is located between the transition from Washington to Vancouver Island and Southwestern British Columbia (Figure <ref type="figure">1</ref>). The global database of 3D subduction zone geometry (Slab2), helped guide the reconstruction of a simplified fault discretization model for Cascadia. The fault mesh still preserves a rectangular planar geometry but hosts two fault segments that accommodate major along-strike variations of the fault. Nonetheless, retaining the option for the CMT-based slip inversions will allow GFAST to respond to complex ruptures, blind thrusts, splay faults, and other sources with geometries that are not well known prior to the event.</p><p>The discretized 100-patch slab model is highlighted in this study to assess the performance with regional GNSS data to determine earthquake magnitude and fault-slip for the Cascadia subduction zone. Rapid estimates of the earthquake size that can overcome magnitude saturation effects under 3 minutes using GNSS stations bring a more modern approach to minimizing the delay time of forecasts at the TWCs. The comparison of GFAST derived M w to the true magnitudes of the synthetic events in this study indicates the potential for integrating moment magnitudes from GNSS data for NOAA's Tsunami warning system operations. Automating GNSS finite-fault models is a more complicated but useful methodology in translating the earthquake source to the tsunami hazard domain, using information about fault slip to calculate tsunami amplitudes at the coastline. The slab discretization model with 100 rectangular patches is an appropriate fault catalog to use to model Cascadia subduction zone megathrust events. Example scenarios shown in the study highlight the ability of GFAST finite-fault inversions to resolve discrete slip asperities defined by 100 fault patches across the shallow Cascadia slab region and to recreate heterogenous slip distributions that roughly resemble the synthetic models. The prescribed sub-patch size (50 x 50 km) provides adequate spatial slip variability. While GFAST is fairly computationally efficient, incorporating a finer fault grid with more fault patches would potentially cause the inversion to fall behind real-time timescales (i.e., each iteration takes longer than 1 second), and thus, we find the 100 fault patch model to be sufficiently detailed without sacrificing real-time performance. </p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5">Conclusion</head><p>Adding catalogs of known faults is a worthwhile priority to incorporate into GFAST inversion strategies. As shown in this study, a discretized slab model that contains reliable fault geometry information improves inversions for early finite-fault rupture models and resolves the issue of finite-fault models positioned in inaccurate locations. The finite-fault models provide detailed slip information that is useful to infer local coastal tsunami amplitude information. We show that GFAST inversions using the slab model tend to result in a lower model RMS and also result in more accurate coastal tsunami amplitude estimates compared to using the CMT solution as the fault geometry constraint.</p><p>Local real-time GNSS data is a technology that is proving to enhance rapid earthquake and tsunami monitoring in several regions around the world. Tsunami hazards along the Cascadia coastline are better assessed with detailed rupture simulations that illustrate the variability of tsunami-generating earthquakes. Going forward to other subduction zones and tsunami generating regions, generation of predefined fault catalogs is an impactful goal for tsunami early warning.</p></div><note xmlns="http://www.tei-c.org/ns/1.0" place="foot" n="7" xml:id="foot_0"><p>SEISMICA | volume 2.4 | 2025</p></note>
			<note xmlns="http://www.tei-c.org/ns/1.0" place="foot" n="10" xml:id="foot_1"><p>SEISMICA | volume 2.4 | 2025</p></note>
			<note xmlns="http://www.tei-c.org/ns/1.0" place="foot" n="13" xml:id="foot_2"><p>SEISMICA | volume 2.4 | 2025</p></note>
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