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Reconstruction of shallow coseismic slip following the 2015 Illapel earthquake 1 2In review at Earth and Planetary Science Letters, May 28, 2016. 3 4Amy Williamsona,*, Andrew Newmana 5 6a School of Earth and Atmospheric Sciences, Georgia Institute of Technology, 311 Ferst 7Drive, Atlanta, GA, 30332, United States 8 9* Corresponding author. E-mail address: amy.williamson@gatech.edu (A. Williamson) 10

11 12

Abstract 13

On 16 September, 2015, a moment magnitude 8.3 earthquake struck off the coast of 14

Central Chile, generating a large tsunami. Through a trans-coastal geodetic study, including 15

inferred seafloor vertical displacement determined from open-ocean pressure gauges 16

recording tsunami excitation, and sub-areal deformation observed through Interferometric 17

Synthetic Aperture Radar (InSAR) from the Sentinel-1 satellite, we identify that earthquake-18

generated slip dominantly occurred offshore and very near the trench. This tsunamigenic 19

near-trench rupture likely initiated about 80 s after the initial nucleation and is responsible for 20

open ocean tsunami waves up to 10 cm in amplitude. Tide-gauges across Chile and Peru 21

recorded sizable tsunami waves up to 4.7 m in height, with the most distal observation of 22

over 40 cm in the Kuril Islands across the Pacific Ocean. The prevalence of large and 23

shallow thrust along the subduction megathrust raises the question of the likelihood of future 24

such events along central Chile and its implications for future hazardous tsunamigenic 25

earthquakes. 26

27

Keywords 28

Chile, earthquake, Illapel, subduction zone, joint inversion 29

30

1. Introduction 31

The Atacama trench is globally one of the most seismically active regions with both a 32

contemporary and geologic record of generating great (M > 8) earthquakes with a short 33

2

recurrence interval. This propensity for large events is assisted by the region’s rapid plate 34

motion. In the vicinity of central Chile, the Nazca plate subducts beneath the South American 35

plate with a convergence rate of 74 mm/yr (DeMets et al., 2010)(Figure 1). This has led the 36

Atacama, also called the Peru-Chile trench, to be the focus of many studies on tectonic strain 37

accumulation, interseismic coupling, and earthquake excitation (Vigny et al., 2009; Moreno 38

et al., 2010; Moreno et al., 2011). 39

Many of the large earthquakes generated on this fault system also cause large tsunami 40

waves, with intensities that loosely correlate with the size and down-dip location of the 41

mainshock rupture. The largest-ever instrumentally recorded earthquake occurred near 42

Valdivia, Chile in 1960. This moment magnitude (MW) 9.5 event generated a large and 43

devastating transoceanic tsunami. Eyewitness observations near the source region suggest 10 44

to 15 m waves along the coast (NGDC, 2016). On a regional scale, tide gauge recordings 45

near the city of Concepción topped out with zero-to-crest amplitudes of over 2.5 m, and tide 46

gauges in northern Chile and Peru (2,000 to 3,000 km away) recorded waves between 0.5 and 47

1 m in height (NGDC, 2016). 48

More recently, the 2010 MW 8.8 Maule earthquake ruptured a patch of the megathrust 49

just to the north of the 1960 Valdivia earthquake. However, the size of tsunami that was 50

generated was modest in comparison to its mainshock. In the near field, tide gauges recorded 51

waves with amplitudes around 1 m, with the largest wave = 1.3 m occurring in a bay near the 52

city of Coquimbo. Far field recordings in Peru were less than 0.5 m. Nevertheless, the 53

earthquake and tsunami created over 30 billion dollars in damage and resulted in over 500 54

causalities in Chile (USGS report; Fritz et al., 2011). In 2014, the MW 8.1 Iquique earthquake 55

3

in northern Chile, while smaller, also produced an observable tsunami (An et al., 2014; 56

Gusman et al., 2015). 57

The latest tsunamigenic addition to the Atacama catalog is the 16 September 2015 58

MW 8.3 Illapel earthquake. This event nucleated offshore from Coquimbo Province 59

(approximately 31.57° S and 71.67° W) at approximately 22:54:32 UTC (NEIC Reference). 60

While this event was modest in size compared to other contemporary tsunamigenic 61

earthquakes near Chile, it produced a locally large tsunami (up to 4.7 m near Coquimbo as 62

measured by a local tide gauge). The tsunami became transoceanic, with tide gauges 63

recordings throughout the Pacific basin, including Oahu, Hawaii (0.23 m), Kuril Islands, 64

Russia (0.44 m), and Aburatsu, Japan (0.22 m). 65

Despite the lower magnitude, the Illapel event produced a transoceanic tsunami that is 66

more in line with a much larger earthquake, like the MW 8.8 Maule event which also 67

produced sub-meter tide gauge signals in Hawaii. The Illapel earthquake is not unique in this 68

disparity. The 1996 Chimbote, Peru earthquake, while only a MW 7.8, produced meter-level 69

waves locally around Peru and Northern Chile, and waves up to 0.3 m near Easter Island, 70

approximately 3800 km away. The disproportionately large tsunami generated by this event 71

is partially a function of its rupture along the shallow part of the megathrust (Heinrich et al., 72

1998). Its source location and its deficiency in radiating high frequency energy led this event 73

to be categorized as a tsunami earthquake by Newman and Okal (1998), a special subclass of 74

tsunamigenic earthquakes characterized by their ability to produce much larger waves than 75

expected given their magnitude (Kanamori, 1972). 76

Tsunami earthquakes are frequently both deficient in radiating seismic energy and 77

excessive in duration, charactering slow rupture propagation (Kanamori, 1972). They also 78

4

appear to exclusively rupture the shallow megathrust environment as was inferred from tide-79

gauge inversions of the MW 7.6 1992 Nicaragua earthquake (e.g. Satake 1994), and from 80

very-local coastal geodetic changes due to the MW 7.1 2010 Mentawai earthquake (Newman 81

et al., 2011). 82

To characterize the 2015 Illapel earthquake, we use both on-land Line-Of-Sight 83

(LOS) Interferometric Synthetic Aperture Radar (InSAR) observations and derived seafloor 84

vertical displacements determined from real-time open-ocean tsunami derived fault solutions. 85

The combination of the two datasets, which span the shoreline, allows for maximum 86

resolution of the earthquake slip environment across the subduction megathrust. As we detail 87

below, through a joint inversion of both data types, we find that the maximum coseismic slip 88

occurred along the shallowest portion of the megathrust, as shown in Figure 1. This puts the 89

Illapel event in a category similar to many past tsunami earthquakes, that along with the 1996 90

Chimbote, Peru earthquake, indicates that the Peru-Chile trench is very capable of generating 91

shallow and particularly tsunamigenic earthquakes. 92

93

2. Methodology 94

2.1 Data 95

This study incorporates real time fault solutions provided through the Pacific Marine 96

Environmental Lab (PMEL) and Tang et al. (2016), as well as InSAR derived ground-surface 97

displacements from the European Space Agency’s Sentinel-1 satellite to solve for the 98

magnitude and spatial extent of coseismic slip along the Chilean megathrust interface from 99

the Illapal earthquake. We validate our slip geometry by comparing a forward projected 100

tsunami model with observed tsunami waveforms at three regionally located Deep Ocean 101

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Assessment and Reporting of Tsunami (henceforth DART) pressure gauges, and through 102

comparisons of predicted and observed ground deformation along the Chilean coast. 103

We use the LOS displacement field derived from a pair of descending track scenes (24 104

August and 17 September 2015) made by the Sentinel-1 satellite, which was processed by the 105

European Space Agency (Copernicus Service information [2015]). The resultant image 106

(Figure 2) shows up to 150 cm of ground deformation in the LOS direction (looking 75° W 107

of N at approximately 41° off nadir near the maximum deformation, and is the orientation 108

used for this study). Because the data density and interdependence of pixels is extremely 109

high (on the order of 107 pixels per image), it is necessary to down-sample, to make it 110

manageable for computational inversions. To do so, we use a two-dimensional Quadtree 111

decomposition, with the goal of retaining sufficient information to understand the source, 112

while making the total data count sufficiently small that inversion methodologies are 113

tractable. In this study, we require that the data be split whenever a box had a variance in 114

LOS displacement greater than 40% of the total. We assign the location of each of the 115

resulting data points to the ‘center of mass’ of coherent pixels. Because the second pass 116

follows one day after the event, any postseismic signal is likely to remain small. 117

Furthermore, because most observations of early afterslip occur primarily up-dip of the main 118

rupture along subduction zones (e.g. Hsu et al., 2006; Malservisi et al., 2015), we suspect the 119

land-based data to be more representative of coseismic rupture. 120

We incorporate the rapidly determined sea-surface deformation calculated from the 121

full wave tsunami source estimated by Tang et al. (2016) and using unit sources developed 122

by Gica et al. (2008). The Tang et al. (2016) full wave estimation of the tsunami inverts 123

open-ocean signals from nearby DART gauges assuming the linear superposition of 124

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regionally located, pre-computed rectangular slip patches, 50 km wide by 100 km long, with 125

fault geometries coarsely representing the subduction zone in the region. Their published 126

solution uses five patches with slip coefficients ranging from 0.8 to 7.3 m of pure thrust 127

(Figure 3). Both the Tang et al. (2016) and this study incorporate the Method of Splitting 128

Tsunami (MOST) model to compare observed and modeled slip with DART gauges (Titov 129

and Synolakis, 1998; Titov and Goznales, 1997). The MOST model is a finite-difference 130

numerical code based on the long-wave approximation for tsunami waves in deep water. 131

When constrained to the use of only land-based instruments such as GPS and InSAR, 132

the shallow subduction zone region is generally too far offshore to be resolvable using 133

distributed-slip inversions. While seafloor geodetic instruments are feasible, they are often 134

cost prohibitive, causing many communities forgo their use (Newman, 2011). This leads to 135

the possibility of underestimating slip in this highly hazardous, but in these cases poorly 136

resolved, zone. By supplementing this dataset with ocean-based observations, like tide gauge 137

or pressure gauge mareograms, spatial resolvability of the offshore region increases 138

substantially, allowing for better control on the problem (see Model Resolution section, 139

below). 140

2.2 Model Geometry 141

The two-dimensional curvi-planar fault geometry used here has a constant strike of 142

N5°E, with dip that increases with depth, approximating the Slab 1.0 profile (Figure 4) 143

(Hayes et al., 2012), which exhibits almost no along-strike variability across the coseismic 144

region area in this study. The modeled fault plane is discretized into a 450 x 200 km surface, 145

consisting of a regular 18x8 grid, with individual patches about 25 km x 25 km. 146

7

Green functions are calculated for both the vertical seafloor and InSAR LOS 147

displacements through an analytic solution to the elastodynamic equations for rectangular 148

dislocations in an elastic half space (Okada, 1985). The code uses here, GTdef Chen et al. 149

(2009), uses a bounded and weighted linear least squares algorithm for slip inversions. We 150

regularize our solution using a two-dimensional Laplacian smoothing factor, which requires 151

an interdependence between adjacent slip patches, which trade-off with misfit (Harris and 152

Segall, 1987). Here, the misfit is determined as the root mean square of the weighted-residual 153

sum of squares (Jónsson et al., 2002), while the roughness term is the degree of two-154

dimensional spatial smoothing. The preferred model is then determined by subjectively 155

choosing the best trade-off between the two parameters. 156

2.3 Model Resolution 157

We approximate the spatial resolvability of our model using a checkerboard test, 158

consisting of 50 km by 50 km blocks with alternating predefined uniform slip magnitudes 159

between 0 and 1 meter. Using these patches as input, we predict deformation at each data 160

point (InSAR, Seafloor, and both) as determined by our Quadtree decomposition. We 161

subsequently invert these synthetic data with our observed data variance, and compare our 162

inverted with our initial models (Figure 5). In areas where the checkerboard is retained, we 163

have high resolvability, which includes the area of most predicted slip (Figure 1). However, 164

we lose resolution towards the edges of our spatial domain, where our Quadtree methodology 165

severely reduces sampling, due to lack of signal change. 166

If only tsunami data are used, resolution is unsurprisingly limited to the offshore 167

environment, while using InSAR data alone allows for resolvability primarily under land, 168

extending modestly offshore (approximately 50 km), but not to the trench. The size of 169

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onshore resolvable slip patches also increases with the depth of the underlying fault, 170

somewhat smoothing subduction megathrust models below land. 171

172

3. Results 173

Our preferred model result for the spatial extent of slip along the megathrust (Figure 174

1), has a maximum of 15 m of thrust near to the trench, and averaging just over 2 m across 175

the model domain, corresponding to a seismic moment for the thrust component of 5.3x1021 176

Nm (Mw 8.38) assuming rigidity of 30 GPa. Slip extends from the coastal interior up-dip 177

towards the shallow portion of the fault, near the trench. Because seafloor model inputs are 178

vertical, and the orientation of the satellite track is only about 15° off a longitudinal path, the 179

data have little information along-strike for our model geometry. As such, though along-180

strike motion is inverted, we limit our discussion to the thrust-only component. 181

Over- and under- smoothed results are included in Figure 6 as well as the roughness 182

versus misfit tradeoff curve for modeled smoothness parameters, κ. While some features on 183

the edges of our model change with the changing κ, the overall features in our resolvable 184

zone do not change significantly past the degree imposed by smoothing. 185

We validate our results through a comparison with both the original unwrapped 186

Sentinel-1 interferogram and observed waveforms at DART gauges. For the InSAR data we 187

find that we are able to recreate the general shape and overall magnitude of static offset seen 188

in the observed image (Figure 7), though the model underpredicts surface deformation 189

immediately to the south of the event, and modestly overpredicts deformation to the north 190

along the coast, where model resolution is low. 191

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For the forward tsunami model, we use the ETOPO1 global relief model with a 192

bathymetric data density of 1 arc minute. In order to satisfy the Courant-Friedrichs-Lewy 193

(CFL) condition for the tsunami wave propagation model, a computational time step of six 194

seconds is imposed. Additionally, we impose a reflective coastline as a spatial boundary 195

condition, however we do not quantify inundation levels or wave amplitudes outside of the 196

deep-ocean because of the limited resolution of ETOPO1 data. Observations from DART 197

gauges are processed with a high-pass butterworth filter (wave period> 2 hours) to removed 198

tidal signals. We compare the results from our forward model with the waveforms at the 199

three nearest and regionally located DART gauges (Figure 8; location shown in Figure 1). 200

We also include the rapidly derived results from the Tang et al. (2016) study as a 201

comparison. Our model is in good agreement with the observed waveforms, as it accurately 202

reproduces both the initial positive and negative waves at DART gauge 32402, as well as 203

most of the following wave train. Additionally, our computed wave heights for the initial 204

positive peak are in general agreement with the observed data. Model tsunami time series are 205

shifted forward in time by 140 seconds, similar to the time delay in Heidarzadeh et al. 206

(2015), while results from Tang et al. (2016) are shifted forward 72 seconds. We explore a 207

possible reason for this time shift below. 208

4. Discussion 209

The large thrust along the shallow megathrust environment is responsible for the 210

majority of tsunami excitation. This is likely a leading role in why the Illapel earthquake 211

generated a tsunami that is disproportionally large when compared to events like the larger 212

MW 8.8 2010 Maule earthquake, and the slightly smaller MW 8.1 2014 Iquique earthquake 213

(Figure 1). There are a number of reasons for this. Firstly, and quite obviously, larger slip 214

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causes greater disturbances of the entire environment. When this slip occurs very near the 215

seafloor, there is very little spatial smoothing of deformation from the very thin over-riding 216

plate, as such the displacement field will be larger and more focused than for deeper slips of 217

equivalent magnitude. This larger slip may be aided by both the lack of a substantial 218

overriding elastic layer, and by the absence of a bounded, and slip limited, fault tip at the 219

trench. Lastly, slip-generated vertical motions near the trench occur, almost by requirement, 220

in the deepest parts of the oceans. As such they affect the largest column of ocean, and 221

initiate propagation at higher speeds (tsunami speed, 𝑉" = 𝑔ℎ, where g and h are gravity 222

and ocean depth, respectively). The results become devastating as initial waves slow near the 223

coastlines, and increase in amplitude due to conservation of momentum. 224

Earthquake rupture speeds normally are around 3km/s for most subduction zone 225

earthquakes (e.g. Bilek and Lay, 1999). However, in the case of slow, tsunami earthquakes, 226

rupture can be substantially reduced, down to as little as 1 km/s, greatly extending the 227

duration of rupture, and substantially diminishing the propagated energy, as was the case in 228

the 1996 Chimbote, Peru earthquake (Figure 1) (Kanamori, 1972; Newman and Okal, 1998). 229

The slowed rupture is attributed to slip in the shallowest portion of the interface near the 230

trench (e.g. Bilek and Lay, 1999; Polet and Kanamori, 2000). Based on teleseismic energy 231

back-projections, Yin et al. (2016) identified a substantial and slow delayed rupture 232

component to the 2015 Illapel earthquake, extending between 80 and 130 s from the initial 233

rupture, with the patch occurring up-dip of the initial nucleation, and very near the trench. 234

Using a teleseismic inversion of the spectral contributions from the Illapel earthquake, Lee et 235

al. (2016) similarly found a two-stage rupture process, but with moderately longer durations, 236

11

the first lasting 100 s, and the second not terminating until about 250 s after the rupture 237

initiation. 238

Examination of the real-time radiated energy growth, automatically ran at Georgia 239

Tech using RTerg (Convers and Newman, 2011), also shows that this earthquake has some 240

features of a complex and possibly slow rupture that are discernable within the high-241

frequency cumulative time series (Figure 9). While the automated algorithm estimated 242

rupture duration, TR, at 135 s using the cross-over between the rapid initial growth and the 243

later slow-growth of high-frequency energy (between 0.5 and 2 Hz), careful examination 244

shows two near linear trends in the data, one terminating near 83s, and the second at about 245

146s. These windows correspond well with the two periods found by Yin et al (2016). The 246

second stage grows more slowly—such slow rupture is a character also seen in slow tsunami 247

earthquakes using this algorithm (Convers and Newman, 2011; Newman et al., 2011). 248

Finally, the total high-frequency energy is deficient at about 3.0e15 J (corresponding to 249

energy magnitude, Me-hf =7.8), a feature similarly seen as deficient for tsunami earthquakes in 250

Newman and Okal (1998). The corroborating evidence from each the back-projections of 251

Yin et al. (2016), the spectral analysis of Lee et al. (2016) and the earthquake energy 252

determinations following Convers and Newman (2011) strongly support the likelihood of a 253

slow and tsunamigenic rupture in the near-trench region. Finally, the delayed rupture of the 254

tsunamigenic near-trench region, can explain most of the time-shift necessary to best 255

describe the tsunami waveforms recorded at nearby DART stations (Figure 8). 256

This mode of shallow-slip and tsunamigenesis is in contrast to other recent 257

megathrust events along the Peru-Chile trench. After an extended foreshock sequence, the 258

2014 MW 8.1 Iquique earthquake ruptured both further down dip and under a shallower 259

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column of water, with between 4 to 7 m of thrust occurring between 25-35 km depth (Schurr 260

et al., 2014; Gusman et al., 2015). The location of early aftershocks also indicate little 261

activity near the trench (Hayes et al., 2014). The lower amplitude slip and deeper rupture led 262

to less tsunami excitation, as observed at local and regional tide gauges along the South 263

American Pacific coast (Figure 1). 264

Slip inversions for the 2010 MW 8.8 Maule earthquake, including Lorito et al. (2011) 265

and Yue et al. (2014), found peak slips of between 16 to 20 m between 15 and 20 km depth. 266

The models show two broad patches of substantial (>5m slip) extending along-strike for 267

about 450 km, and up-dip from the coastline about 80 km toward the trench, leaving little 268

modeled slip in the last 60 to 90 km closest to the trench. Though the rupture extent of the 269

Maule earthquake was much greater than the most recent Illapel event, the tsunami heights 270

were comparable, and actually smaller in most locales (figure 1). 271

Thus, though the Maule earthquake was more than six times larger than the Illapel 272

event (as measured by seismic moment), it is clear that size alone is not the deciding factor in 273

tsunami generation, but where the slip occurs in relation to the trench. Such near-trench slip 274

is also likely why both the much smaller MW 7.5 1996 Chimbote tsunami earthquake 275

(Newman and Okal, 1998; Bourgeois et al., 1999) and the much larger MW 9.5 1960 Valdivia 276

earthquake were so efficient at generating destructive tsunami waves (Plafker and Savage, 277

1970). 278

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5. Conclusion 279

We conduct trans-coastal joint inversion of regional surface deformation to solve for 280

coseismic slip along the subduction megathrust using tsunami-derived vertical seafloor 281

deformation and Sentinal-1 InSAR data following the 2015 Illapel earthquake. By 282

supplementing the traditional land-based geodetic slip inversion with a tsunami derived 283

dataset, key vertical deformation information about the region between the trench and the 284

coast can be incorporated, substantially increasing the resolution domain for megathrust 285

events. Our preferred result has a large concentration of slip rupturing the shallowest portion 286

of the megathrust near the trench. Our model is in very good agreement with tsunami time 287

series recorded at 3 nearby DART gauges. A necessary time shift is possibly due to delayed 288

and slow rupture of the shallow portion of the fault. The shallow rupture of this event and its 289

large tsunami, along with other recent and notable tsunamigenic earthquakes in the region 290

highlight that the Peru-Chile trench has significant tsunamigenic potential from earthquakes 291

with substantial near-trench rupture. This includes giant earthquakes like Valdivia in 1960, 292

slow rupturing tsunami earthquakes like Chimbote in 1996, and hybrid events like Illapel 293

2015. 294

295

6. Acknowledgements 296

This research was supported through State Funds through Georgia Tech to AVN. Figures 297

were generated using Generic Mapping Tools from Wessel et al. [2013]. We appreciate the 298

openly available and processed Sentinal-1 InSAR data and open ocean tsunami waveform 299

datasets that were made accessible by the European Space Agency and the US National 300

Oceanic and Atmospheric Administration, respectively. We are extremely grateful of Y. Wei 301

and V. Titov’s support of ALW’s training in use of the MOST tsunami modeling software. 302

303

304

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434 435

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436Figure 1. Regional map of past tsunamigenic earthquakes and their generated tsunamis. The 437epicenter of the 1960 and centroid location for later events (Esktröm et al., 2012) with the 438approximate rupture area are shown by colored stars and transparent polygons beneath 439(Bourgeouis et al., 1999; Lorito et al., 2011; Hayes et al., 2014). For each event, the regional 440tsunami wave height measured by local tide gauges and deep-water pressure sensors (green 441triangles) are shown as columnar bars (1960 is augmented by eyewitness accounts (gray tops, 442and are all divided by 4 to stay on scale) (NGDC, 2016). Observations at Juan Fernandez 443Island (~34°S) are offset for clarity. The Nazca plate motion relative to a stable South 444American plate is also shown (black arrows) (DeMets et al., 2010). (Inset) Surface projection 445of our preferred model from a tsunami-InSAR joint inversion (location shown as black box 446with model in main map). Gray lines indicate depth contours derived from Slab 1.0 (Hayes, 4472012). 448

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449Figure 2. Regional InSAR derived displacements in the direction of satellite line-of-sight 450with Quadtree discretization (white boxes). 33 points, one per box, mark the average value 451within each box, and its location is determined as the ‘center of mass’ of the coherent data. 452The size of each point corresponds to the degree of error, calculated as the overall variance 453within each box. These points, their shown magnitudes and weights define the InSAR data 454used for model inversions. 455

−72˚ −71˚ −70˚

−33˚

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−29˚

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−25 0 25 50 75 100 125 150Observed LOS Displacement [cm]

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456Figure 3. (a) Rapidly determined fault plane solution using near-field tsunami waveforms 457derived by Tang et al. (2016). The block dimensions and geometry were described in Gica et 458al (2008). (b) Vertical seafloor deformation predicted using the Tang et al. unit sources, 459following Okada (1985). (c) Quadtree decomposition of vertical seafloor deformation, 460yielding 45 boxes total, limited to the region off-shore of central Chile. 461 462

463

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Figure 4. (a) Surface projection of fault discretization. Each patch (outlined in red) is 25 km2 464in area. Gray north-south trending lines indicate the approximate depth of the plate interface 465as derived in Slab 1.0 (Hayes et al., 2012). (b) Trench-normal cross-section showing our 466model geometry (red line), and three profiles representing the 25th, 50th, and 75th percentile of 467the fault length (gray lines). The zero datum, and location of the approximate location of the 468trench (as defined by the southern extent of our model geometry) are shown as vertical and 469horizontal solid black lines, respectively. 470

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471Figure 5. “Checkerboard” resolution test showing: (a) the initial synthetic slip model; (b) 472results of a joint inversion of both tsunami and InSAR datasets, with the area of highest 473resolvability (red dashed box). We also show results for (c) a tsunami-only test, and (d) an 474InSAR-only test, highlighting the spatial sensitivity of the individual data. 475

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476Figure 6. Model results for a number of smoothness-based dampening choices, where higher 477κ values correspond to increased dampening (and decreased roughness). The three shown 478solutions (a) κ = 4,000, (b) κ = 10,000, and (c) κ = 16,000, represent an under-479damped, our preferred, and over-damped models, respectively. (d) The trade-off between 480model roughness, and model misfit is shown for our example cases, as well as other tested 481models. Our preferred solution represents a subjective choice,that attempts to minimize both 482roughness and model misfit. 483

484

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485Figure 7. Comparison of InSAR line-of-sight (LOS) change for data and our preferred 486model. (a) Observed LOS displacement, repeated from Figure 2. (b) LOS projection of the 487optimal model results. (c) Residual LOS displacement, determined by removing the predicted 488(b) from the observed (a) signal. 489

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Figure 8. Comparison between observed waveforms at regional DART gauges (black line), 490results produced in Tang et al. (2016) (blue line) and our preferred model (red line). For each 491location, our model is shifted 140 seconds forward in time and the results produced in Tang 492et al. (2016) are shifted forward 72 seconds in time. 493

494

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e He

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Figure 9. The cumulative high-frequency energy radiated from the Illapel earthquake is 495shown (red line) using data from 41 seismic stations available in real-time (red triangles in 496map) and automatically processed following Convers and Newman (2011). The automated 497rupture duration, TR (dashed gray line), two near-linear periods of growth (denoted by thick 498blue lines) and their termination times relative to the earthquake nucleation (dashed black 499lines). The cumulative energy is converted to a high-frequency energy magnitude, which 500appears deficient for this event, similar but more moderate than slow-rupturing tsunami 501earthquakes. 502 503