Geophysical Research Letters

Supplementary Information for

Triggering of the Mw 7.2 Hawaii earthquake of May 4, 2018 by a dike intrusion

Kejie Chen1, Jonathan D Smith2, Jean-Philippe Avouac1, Zhen Liu3, Y. Tony Song3 and Adriano Gualandi3

1 Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, 91125, USA

2 Department of Earth Sciences, University of Cambridge, Madingley Rise, Cambridge, CB3 0EZ, UK.

3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, 91109, USA

Contents of this file

Text S1 to S3Figures S1 to S8Tables S1 to S2

Introduction

This supplementary document contains supporting text and figures on the data adopted, inversion/modelling method and results.

Text S1 details how the co-seismic rupture is jointly inverted based on GPS, strong motion and teleseismic data, together with the tsunami validation. Text S2 and Text S3 summarize the modelling of the pre-intrusion creep and dyke intrusion, respectively. Figures S1-S8 show co-seismic rupture slip distribution along with data fits at different hypocenter depths, pre-intrusion rift opening, InSAR data fits of dyke intrusion modeling and related coulomb stress change. Finally, Table S1 and S2 contain velocity structure model and variance reduction corresponding to different hypocenter depths.

Text S1, co-seismic rupture inversion

We perform a joint inversion of the static GPS displacements, the strong motion and broadband seismic waveforms using the code Mudpy originally developed by

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Melgar and Bock (2015) . To estimate the co-seismic GPS offsets, we used the raw GPS data (30 s sampling interval) recorded on May 4, 2018 at 57 stations across Hawaii downloaded from UNAVCO (available at ftp://data-out.unavco.org/pub/rinex/) and then employ precise point positioning (PPP) to estimate epoch-wise solutions. The satellite orbits, Earth rotation parameters and satellite clocks for PPP are from CODE (Center for Orbit Determination in Europe). We follow the data processing strategies of Chen et al. (2016). The co-seismic positions are expressed in the International Terrestrial Reference Frame 2008 (ITRF08) and transformed into a local north, east, up frame.

The strong motion records are downloaded from the Incorporated Research Institutions for Seismology (IRIS) data management center, and only strong motion sensors within 45 km from the hypocenter (see their distribution in Fig. 2) are included for the joint inversion. Three components of raw accelerators are first integrated into velocity waveforms, then bandpass filtered with (0.02,0.2) corner frequency and decimated to 1 Hz. The velocity waveforms are trimmed to be 80 s long, starting at the origin time of the earthquake. We also performed inversion using a bandpass filter of (0.02 0.4), but find a remarkable decrease in strong motion waveform fits, indicating a refined 3-D velocity structure would be required for higher frequency Greens’ function synthesis.

P-wave records from 40 broadband seismic stations with high signal-to-noise ratios are selected and downloaded from IRIS (http://ds.iris.edu/wilber3/find_event). The stations have epicentral distances ranging from 30° to 90° and provide a good azimuthal coverage (see their distribution in Figure S1). Instrument responses are deconvolved to get displacement waveforms, which are then filtered with a bandpass filter with corner frequencies of 0.005 to 0.4 Hz and decimated to 1 Hz. A 60-s-long time window is extracted from the raw data, starting 6 s prior to the clearest first arrival of the P waves, and the P wave initial motions are aligned manually to the theoretical arrival time predicted by velocity model of preliminary reference earth model (PREM) (Dziewonski and Anderson, 1981).

The fault plane is parameterized by 25 along strike and 8 along dip sub-faults with 4 x 4 km2 patch size. In terms of strike and rake angles, we assign their initial values based on global centroid moment tensor solutions (strike angle 245, rake angle 120). During the inversion procedure, we vary them by ± 10° with 1 ° step. For the dip angle, we follow the estimation by Lay et al. (2018) , allowing it vary from 3 to 8. In addition, the hypocenter depth varies from 5 km to 9 km with 1 km step length. For each fault, two orthogonal vectors are used and non-negative least square inversion is employed to account for the rake-varying slip. The source time function is parameterized with 5 symmetric triangles with 3 second half-durations staggered by 1.5 sec each. Furthermore, we test a series of rupture speeds increasing from 1.0 km/s to 2.8 km/s. Besides, we employ the first-order Laplacian regularization (Hartzell and Heaton, 1983) to ensure a stability of the inversion result.

The frequency-wavenumber integration method (Zhu and Rivera, 2002) is adopted to compute Green’s functions for near field GPS and strong motion stations using the 1-D layered velocity model of Klein et al.(1987) (Table S1). The teleseismic Green’s functions are generated by propagator matrix approach

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(Kikuchi and Kanamori, 1982), velocity model by Klein et al. (1987) is used for the source side and PREM (Dziewonski and Anderson, 1981) is used for the receiver side. Besides, the same bandpass filter used for the waveforms is applied to the Green functions.

Each kind of data are first normalized by their own norm and then different weighting factors are tested. The relative weighting of the different dataset is determined by trial and error so that residuals are in the noise level, and we find that an equal weighting among GPS offsets, strong motion and P waves can fit all datasets well.

Furthermore, to validate our preferred model, we derive seafloor displacements from the preferred model to drive tsunami simulations using open-source code GeoClaw (Leveque et al., 2011) and compare them with observations. Publicly available topography and bathymetry data sets with 15 arcsecond resolution (Becker et al., 2009) are adopted for six hours’ tsunami propagation simulations. For the roughness of the seafloor, the Manning coefficient is fixed at 0.025. Tsunami records at tide gauge HILO2 (see its distribution in Figure 2) are collected from Global Sea Level Observing System (http://www.ioc-sealevelmonitoring.org/index.php).

Text S2, pre-intrusion deformation modelling

We use daily GPS position timeseries provided by Nevada Geodetic Laboratory (available at ftp://gneiss.nbmg.unr.edu/rapids/tenv/) to estimate pre-seismic deformation evolution in south flank of Hawaii. The time series data are 24-hour rapid solutions, expressed in the IGS08 reference system, from June 2012 to April 20, 2018, before the start of the magmatic intrusion. To remove the background tectonic movement, we measure displacements relative to a station which located in the saddle between Mauna Kea and Mauna Loa that is far from seismicity and volcano inflation (deflation). Furthermore, we correct the steps in timeseries due to GPS antenna change.

The time evolution of a deformation source can be derived by inverting the displacement data available at each epoch. Such an approach is computationally expensive for large datasets, and would not impose any coherent time evolution of the source, since it would yield independent models at each epoch. We use a variational Bayesian independent component analysis (vbICA) (Gualandi et al., 2016) to overcome these limitations by decomposing the data into a set of linearly mixed statistically independent components, each associated with its own spatial and temporal function. The spatial function for each of these independent components can then be inverted separately for fault slip, and combined with the time functions and amplitudes to determine the slip history. Three independent components fit ~98% of the original data variance. In addition, the scaling factors for the three components are 24.7 mm, 2.7 mm, 0.95 mm, which demonstrates that the first component contributes almost 90% of the overall deformation and the related stress change. The time function

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associated with that component (see Figure 3) is nearly linear. This component represents the pre-intrusion deformation. The remaining two components are small temporal variations (including possible slow slip events in 2015 which are not accounted for by the first component). The Green’s functions are calculated assuming an elastic half-space (Okada, 1985) with an assumed rigidity of 30 GPa and Poisson coefficient of 0.25. We get the final static offsets for source inversion by multiplying spatial, temporal and scaling factors of the first component, and the static offsets field clearly imply at least three deformation sources, i.e., Mogi sources (Mogi, 1958) for Mauna Kea and Mauna Loa summits, fault creep beneath the south flank, and a possible fourth deformation source: magma intrusion to the dike in ERZ. Resolving Mogi volume change and location simultaneously is a nonlinear optimization problem. Here we employ grid search (grid steps of longitude, latitude, depth are 0.005, 0.005 and 0.5 km, respectively) to find the favorable locations of Mogi sources. With respect to the aseismic creep, we assume it is on the south west extension of the Mw 7.2 rupture plane, i.e., strike angle as 245, dip angle as 5, central depth as ~10 km, consistent with décollement geometry inferred from seismic reflection (Morgan et al., 2003). The creep area is 52 km long and 28 km wide, with sub-patch size as 44 km2. The creep zone of the best model extends beyond the coastline, while some previous studies (Cayol et al., 2000; Segall et al., 2006) had inferred that it was restricted to the onshore area. If we force creep not to extend beyond the coastline the creep fault shrinks to be 20 km wide, but the fit to GPS data get significantly worse (variance reduction of GPS displacements in south flank drops from 82% to 57%). For the dike geometry, we assume a vertical plane with strike angle 70 inferred from the locations of craters (see Figure S6). The dike is 20 km long and extends from earth surface to 9 km depth, it is subdivided into 180 sub-faults with 1 x 1 km2 patch size, 20 along strike and 9 along dip. To ensure the inversion stability, we regularize the creep and dike intrusion by employing smoothing (using the Laplacian operator) and positivity constraints.

To find a set of optimal deformation source models and identify whether the dike intrusion source is needed, we run two groups of inversions separately, one group omits dike opening and the other includes it. Each group has 640 iterations with the gradual change of Mogi source location and smoothing factor. Our preferred results for the two groups of inversions, which are chosen based on overall data misfits and solution roughness of detachment creep and dike opening, are shown in Figure 3.

Text S3, dike intrusion modelling

We use hourly GPS displacement timeseries and InSAR measurements to retrieve the dike intrusion kinematics. We only select 14 GPS stations that are close to the rift zone (see their distribution in Figure 4). The 1-hour sampled GPS timeseries are decimated from NGL’s rapid solutions with 5 min interval (available at ftp://gneiss.nbmg.unr.edu//rapids_5min/kenv/2018), ranging from (UTC) 0h 20 April to (UTC) 22h 4 May (about half an hour before the main shock ruptured). The SAR single-look-complex (SLC) images were provided by the European Space Agency’s Sentinel-1 satellite. The interferogram pair was acquired on 20 April 2018 and 2 May 2018 from ascending track 124 and processed using JPL/Caltech InSAR Scientific Computing Environment software. 30m SRTM DEM was used for removing topography phase and geocoding. Original resolution of InSAR interferogram is 30 m. To reduce computational cost, we applied a quadtree method (Jónsson et al., 2002) to subsample the interferogram, and totally 3535 InSAR samples were included for the inversion.

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The InSAR data is included as a temporally sparse dataset, and is not included in the Independent Component Analysis. Instead, they are used as a sparse constraint on the dike opening (or closing). The outline to this processing procedure is detailed in the PCAIM users’ manual at http://www.tectonics.caltech.edu/resources/pcaim/. We demonstrate that two components are sufficient to reconstruct the GPS displacement timeseries (variance reduction =93%), with scaling factors of 5.7 mm and 1.34 mm.

The dike geometry has the same strike, dip and depth as it is in Text S2, but the length is extended much north based on the InSAR measurements. Its overall dimension is 459 km2 with 11 km2 sub-fault patch size (see its projection in Figure 4). Regularization is achieved by Laplacian smoothing, with smoothing parameter determined by roughness against misfit.

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Figure S1. Co-seismic slip inversion results at 8 km hypocenter depth. a) Tile view of slip distribution, isochrones of rupture front location in 5 s intervals are indicated by grey dashes. b) Moment rate release function, c) Teleseismic station distribution, d) P wave observations and fits, e) Strong motion observations and fits. Stars in a) and c) denote the epicenter, black and red lines in d) and e) are observations and synthetics, respectively. The numbers at right indicate the maximum amplitude values for each waveform with 10-6 m and m/s as units for teleseismic and strong motion datasets.

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Figure S2. Co-seismic slip inversion results at 5 km hypocenter depth. a) Map view of slip distribution and GPS data fits, red beach ball is the focal mechanism of the 2018 M 6.9 event. b) Moment rate release function, c) Tile view of slip distribution, d), e) and f) are tsunami, strong motion and P wave observations and fits.

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Figure S3. Co-seismic slip inversion results at 6 km hypocenter depth. a) Map view of slip distribution, b) Moment rate release function, c) Tile view of slip distribution, d), e) and f) are tsunami, strong motion and P wave observations and fits.

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Figure S4. Co-seismic slip inversion results at 7 km hypocenter depth. a) Map view of slip distribution, b) Moment rate release function, c) Tile view of slip distribution, d), e) and f) are tsunami, strong motion and P wave observations and fits.

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Figure S5. Co-seismic slip inversion results at 9 km hypocenter depth. a) Map view of slip distribution, b) Moment rate release function, c) Tile view of slip distribution, d), e) and f) are tsunami, strong motion and P wave and observations and fits.

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Figure S6. Top: Projection of basal thrust fault (red dashed line) and pre-intrusion rift plane (red solid line). Blue star and red points are epicenter and summits, respectively. Bottom: Rife opening model.

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Figure S7. InSAR synthetics (top) and residuals (bottom). Dashed pink line is the surface projection of the dyke plane.

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Figure S8. Coulomb failure stress changes (CFS) on the rupture plane with 8 km hypocentral depth. a) CFS due to basal fault creep a, b) CFS due to dyke intrusion, c) and d) are CFS due to Kilauea summit and Mauna Loa inflation, respectively. Color bar scales are saturated.

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Table S1. 1-D velocity model for Green’s function computation

Depth (km)

P-velocity (km/s)

S-velocity(km/s)

Density (g/cm3) QP QS

1.00 3.80 2.00 2.10 1000 5003.00 6.00 3.20 2.40 1000 5006.00 7.30 4.20 2.80 1000 500

15.00 7.60 4.60 3.05 1000 500237.00 8.20 4.79 3.45 360 140

Table S2. Variance reduction (%) and moment for different epicentral depths and a 20 dipping fault plane (the last row)

Depth (km) GPS Strong motion P wave

Moment (1019 Nm)

5 82 29 58 8.86 84 29 61 8.37 83 27 60 7.78 82 26 60 7.39 79 23 56 7.38 74 21 44 6.9

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