Geophysical Research Letters

Supporting Information for

Rate-and-state Model Casts New Insight into Episodic Tremor and Slow-slip Variability in Cascadia

Yingdi Luo1, 2*, Zhen Liu 2

Affiliations:1 JIFRESSE, University of California, Los Angeles, CA 90095 2 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91125

*Correspondence to: Yingdi Luo (luoyingd@jpl.nasa.gov)

Contents of this file

Text S1 to S3Figures S1 to S3Table S1

Introduction

This supporting material includes Text S1 summarizing previous efforts on modeling tremors and ETS; Text S2 introducing our numerical earthquake simulator QDYN; Text S3 describing the “1.5D” approximation we used in the model. Figure S1 shows additional slip rate information during one ETS gap; Figure S2 and S3 provide two additional sets of ETS variability model. Table S1 shows the model parameters we used for models presented in the main text.

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Text S1.Previous efforts on modeling tremors and ETS

Over the past decade significant amount of modeling efforts has been made to capture the physics of ETS. Despite the progress, our understanding of ETS, especially its physical mechanism is still incomplete. Models of ETS or tremor in general fall into three groups. First group consists of mathematical models to reproduce collective tremor signal characteristics and scaling relations but not actual ETS events and propagation patterns. For example, Ide and Maury (2018) used a stochastic Brownian slow earthquake model to explain tremor/LFE signals and their scaling relations. Second group aims to reproduce ETS and tremor occurrence but without prescribing any actual tremor asperities. For example, Ben-Zion (2012) developed a discrete rate-and-state model with critical fault of zero-weakening to produce first-order features of tremors. Similarly, Colella et al., (2012) proposed discrete rate-and-state near-critical ETS model that generates both forward and backward along-strike tremor propagation, but with similar propagation velocities in both directions. Both Ben-Zion and Colella’s models are inherently discrete for computational efficiency thus simulated tremor activities are stochastic in nature, i.e., tremor does not arise from particular tremor asperities. Third group of models consider actual tremor asperities (small seismogenic patches) from which tremors naturally originates. e.g. Ariyoshi et al., (2012) and Ando et al., (2012) proposed asperity-in-matrix models that partially captures the tremor migration feature but the propagation velocity of backward tremor migration is not faster than the forward migration, in contrast to the observations in Cascadia. Furthermore, Luo (2018), Luo and Ampuero (2018) developed two end-member models of heterogeneous fault with competent tremor asperities. Their asperity-in-matrix models are supported by the plentiful geological observations of exhumed subduction fault zone materials consisting of competent phacoid embedded in incompetent background matrix (Fagereng et al., 2010). Their models are able to produce ETS features that are consistent with observations in Cascadia such as large-scale forward migration and sparsely distributed RTRs. But the models fail to reproduce other ETS features such as ETS gap and halt. Moreover, the origin of RTRs was not thoroughly studied. Key ingredients in their models are the differential pore pressure (effective normal stress) between the tremor asperity and the background matrix. These are supported by high pore pressure environment in the seismic-aseismic transition region of subduction zone and heterogeneous porosity and permeabilities of fault materials and contact conditions of fault gouge (Osborne and Swarbrick, 1997; Sibson, 2014; Fagereng and Hartog, 2017; Fagereng et al., 2010; Sibson 2017; Rittenhouse, 1971). In previous models, the effective normal stress of the tremor asperities and background are kept constant along strike, respectively, while observations suggest strong stress-dependent ETS behaviors in Cascadia (Peng and Gomberg, 2010; Wech and Creager, 2011; Mulargin and Bizzarri, 2015). Thus in this study we relax such constraint and allow the stress and relative strength to vary along strike and study their effects on ETS patterns.

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Text S2.Numerical MethodWe simulate fault behaviors using our rate-and-state friction earthquake simulator QDYN (Quasi-DYNamic earthquake simulator), an open-source code developed by Luo (Luo et al., 2017) and has been benchmarked against other rate-and-state friction simulators in the community (https://www.scec.org/workshops/2018/cvws-seas). More details can be found at the QDYN website (https://github.com/ydluo/qdyn).

Text S3.The “1.5-D approximation” We model the Cascadia subduction fault in a 1-D along-strike setting embedded in 2-D media. We employ a 1.5-D approximation to account for the effect of fault width (perpendicular to along-strike direction). The model has periodic boundary conditions and the QDYN code employs the Fast Fourier Transform for computation efficiency. We consider the Fourier transform ~K of the kernel which connects the displacement (Δ δ) to stress transfer (Δ τ) of the fault (Δ τ=∫~K Δ δ). For an infinite fault in 3-D, the stress transfer kernel ~K is given by Eq. 20 of Andrews (1981). Here in analogy to the expression of 1-D fault, we use~K (k )=G

2|k| (S1)

where k is the spatial wave number. For a 2-D fault~K (k x , k y)=G

2 √k x2+k y

2 (S2)

where k x and k y are wave numbers of the along-strike and along-dip directions. In the 1.5-D approximation we assume that along-dip distribution of slip does not change along strike, and is approximated by a sinusoidal function with wavelength equal to the width of the fault (W). k y=2π /W (S3)Combining (S2) and (S3) gives the “1.5-D” spectral domain kernel adopted in our QDYN simulations for periodic faults:~K (k x , k y)=~K (k x )=G

2 √k x2+( 2 π

W)

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(S4)

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Figure S1. Space-time evolution of tremor and slow slip during the 2011 ETS gap. Figure subpanel layout is similar to Figure 1b. In main subpanel, background color shows transient slip rate from kinematic network slip inversion using continuous GPS data (Liu et al., 2015), (see also Bartlow et al., 2014). There is strong spatiotemporal correlation between slow slip and tremor activity. During the ETS gap tremor activity completely stops while the SSE continues but with reduced slip rate and propagation velocity. Bottom and right plots are corresponding binned tremor activity as a function of time and location (Latitude) during the 2011 ETS event.

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Figure S2. Rate-and-state modeling of ETS variability using 10 km variation zone. Rate-and-state simulations of northern Cascadia ETS based on the “baseline” model with variation region at along-strike location X = -10 km to + 0 km (marked with horizontal red strip) of asperities with different effective normal stress. Similar panel layout as Figure 3. (a) Rb=1. The variation region of asperities with lowest effective normal stress displays “ETS gap” phenomenon. (b) Rb=10. The variation region of asperities with low effective normal stress has low tremor activity and ETS without RTR. (c) Rb=20. The variation region of asperities with moderate effective normal stress shows ETS with RTR; (d) Rb=40. The variation region of asperities with high effective normal stress has increased tremor activity and “ETS halt” phenomenon. The result is very similar to the one with 20 km variation region (Figure 3).

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Figure S3. Rate-and-state modeling of ETS variability using 40 km variation zone. Rate-and-state simulations ETS based on the “baseline” model of northern Cascadia ETS with variation region at along-strike location X = -10km to + 30 km (marked with horizontal red strip). Similar panel layout as Figure 3. (a) Rb=1. The variation region of asperities with lowest effective normal stress act as a barrier to stop the propagation of ETS. (b) Rb=10. The variation region of asperities with low effective normal stress has low tremor activity and ETS without RTR. (c) Rb=20. The variation region of asperities with moderate effective normal stress displays ETS with RTR. (d) Rb=40. The variation region of asperities with high effective normal stress has increased tremor activity and “ETS halt” phenomenon. The model with 40 km variation region is similar to the 20 km variation region model counterpart except that the ETS stoppage instead of gap is observed for the very low stress case.

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Table S1. Physical and numerical properties used in rate-and-state baseline model and models with local stress variations.

physical properties value

fault total length with VS boundary Lall 250 km

fault length L 200 km

fault width W 110 km

shear modulus G 30 GPa

shear wave velocity V s 3000 m/s

reference friction coefficient μ¿ 0.6

Tectonic loading rate V pl 10−9m/s

asperity / background area ratio 1/4

matrix strength ¿ - direct effect 12 KPa

matrix strength ¿ - indirect effect 10 KPa

asperity strength ¿ - direct effect 180 KPa

asperity strength ¿ - indirect effect 200 KPa

asperity strength inside variation area ¿ - direct effect 9~360 KPa

asperity strength inside variation area ¿ - indirect effect 10~400 KPa

asperity criticalness dx / Lc 0.02~0.6

Numerical properties value

cell size dx 61.0352 m (250 km / 212)

solver accuracy 10−14

tremor detecting threshold V th 104 V pl

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References for Supporting Information

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