Supporting Information of

The potential of distributed acoustic sensing (DAS) in teleseismic

studies from the Goldstone experiment

Chunquan Yu1*, Zhongwen Zhan1, Nathaniel J. Lindsey2,3, Jonathan B. Ajo-Franklin3, Michelle

Robertson3

1 Seismological Laboratory, California Institute of Technology, Pasadena, CA, USA2 Earth and Planetary Science Department, University of California, Berkeley, CA, USA

3 Energy Geosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA* Now at Department of Earth and Space Sciences, Southern University of Science and Technology, Guangdong,

China

This file includes

Text S1

Table S1

Figures S1-S4

Text S1 Azimuthal dependence of strain for plane-wave incidence

The azimuthal dependence of strain for plane-wave incidence has already been documented (e.g.

Benioff, 1935). Here, we summarize the key points. For a plane wave incidence shown in Figure

S1, strain in the horizontal x⃑ direction can be formulated as

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ε xx=−p cos φ u̇x (S1)

where,p=cos δ

v is the horizontal slowness of the incident wave, δ the dip angle of the incident

wave,v the wave speed. φ is the azimuthal angle between cable orientation x⃑ and the horizontal

wave propagation direction r⃑.

For P and SV wave incidence,

ε xxP =−pα cos2 φu̇r (S2)

ε xxSV=−pβ cos2φ u̇r (S3)

For SH wave incidence,

ε xxSH=− pβ cosφ sin φ u̇t (S4)

where, u̇r and u̇t are the radial- and tangential-component particle velocities, respectively. pα and

pβ are horizontal slowness for P and S waves, respectively.

It is clear from eqns. S2 and S3 that the amplitude of strains in different azimuths is modulated

by a factor of cos2φ for both P and SV wave incidences. Since cos2φ is non-negative, the phases

of horizontal strains are always the same, and are 180° from radial particle velocity. In contrast,

strains for SH wave incidence change polarity at every 90° horizontally (eqn. S4).

Another interesting property of horizontal strain is that the summation of two orthogonal

components is angle independent (Lindsey et al., 2017; Martin et al., 2018). Assuming that y⃑ is

in the horizontal plane and is perpendicular to x⃑, we can derive from eqns. S2-S4

ε xxP +ε yy

P =−pα u̇r (S5)

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ε xxSV +ε yy

SV=−pβ u̇r (S6)

ε xxSH+ε yy

SH=0 (S7)

The summation of two horizontal orthogonal components eliminates all SH-type particle

motions, and is equivalent to strain recorded in the horizontal wave propagation direction r⃑.

For teleseismic incidence, the wavelength is usually much longer than the typical DAS gauge

length, thus the above equations are applicable to DAS strains.

Table S1 3 events with Mw>=6.5 recorded by the GOLFS experiment.

Event

#

Origin Time

(UT)*

Lat.

(oN)

Lon.

(oE)

Depth

(km)

Magnitude

(Mw)

Distance (o)

(to GSC)

1 2017/11/04,09:00:19.4 -15.32 -173.17 10 6.8 73.5

2 2017/11/13,02:28:23.7 9.51 -84.49 19 6.5 39.1

3 2018/01/10,02:51:33.3 17.48 -83.52 19 7.5 34.5

* Earthquake catalogue from US National Earthquake Information Center (NEIC)

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Figure S1 Geometry of plane wave incidence at the receiver.

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Figure S2 DAS and GSC waveforms for two other teleseismic events. (a), (b) are for event 1, and

(c), (d) are for event 2 in Table S1, respectively. The left column shows event waveforms on all

DAS channels. The channel spacing is 4 m. The right column is the waveform comparison

between selected DAS strain (stacked in the black box of left columns) and GSC particle

velocities.

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Figure S3 (a) Estimated orientations of DAS channels by cross correlating them with the nearby

GSC station. (b) Calculated orientations of the DAS cable using its surface markers.

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Figure S4 Estimated time delays of body waves between DAS channels and the GSC station. (a)

is for the PP phase and (b) for the S phase.

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