of 7
ARTICLE
Localization of seismic waves with submarine
fi
ber
optics using polarization-only measurements
Luis Costa
1
, Siddharth Varughese
2
, Pierre Mertz
2
, Valey Kamalov
3
& Zhongwen Zhan
1
Monitoring seismic activity on the ocean
fl
oor is a critical yet challenging task, largely due to
the dif
fi
culties of physical deployment and maintenance of sensors in these remote areas.
Optical
fi
ber sensing techniques are well-suited for this task, given the presence of existing
transoceanic telecommunication cables. However, current techniques capable of inter-
rogating the entire length of transoceanic
fi
bers are either incompatible with conventional
telecommunication lasers or are limited in their ability to identify the position of the seismic
wave. In this work, we propose and demonstrate a method to measure and localize seismic
waves in transoceanic cables using only conventional polarization optics, by launching pulses
of changing polarization. We demonstrate our technique by measuring and localizing seismic
waves from a magnitude
M
w
6.0 earthquake (Guerrero, Mexico) using a submarine cable
connecting Los Angeles, California and Valparaiso, Chile. Our approach introduces a cost-
effective and practical solution that can potentially increase the density of geophysical
measurements in hard-to-reach regions, improving disaster preparedness and response, with
minimal additional demands on existing infrastructure.
https://doi.org/10.1038/s44172-023-00138-4
OPEN
1
Seismological Laboratory, California Institute of Technology, Pasadena, CA 91125, USA.
2
In
fi
nera Corporation, 9005 Junction Drive, Savage, MD 20701,
USA.
3
Valey Kamalov LLC, Gainesville, FL, USA.
email:
ldpcosta@gmail.com
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1
1234567890():,;
T
he lack of geophysical instrumentation on the ocean
fl
oor
imposes a bottleneck in our ability to study the Earth
s
structure and dynamics, impeding access to a wealth of
geophysical and oceanographic information in remote off-shore
regions. Overcoming this challenge would not only bene
fi
t fun-
damental research efforts, but also enable timely detection of off-
shore earthquakes and tsunamis, providing adequate warning to
nearby coastal areas.
Most technological developments for ocean
fl
oor vibration
sensing are either temporary installations or are associated with
high deployment and maintenance costs, which discourage their
wide-scale use
1
3
. One of the emerging alternatives, however,
proposes the use of optical signals propagating in existing tele-
communication optical
fi
bers for sensing, thus leveraging the
immense scale of the telecommunications industry and infra-
structure. By using in-land instruments and relying on the
existing
fi
ber cables (which cover an appreciable portion of the
sea
fl
oor and reach locations of high geophysical interest), these
methods aim to reduce deployment costs, ease maintenance, and
enable continuous monitoring of the sea
fl
oor.
Indeed, optical
fi
ber strain sensing technologies have proven
successful in geophysical mea
surements for both in-land and
near-shore applications
4
8
. Long-haul transoceanic cables,
however, introduce unique cha
llenges that cannot be tackled
using the prevailing techniques applied for in-land cables (i.e.,
distributed optical
fi
ber sensing
5
,
9
). These methods often rely on
weakly backscattered light, which
restricts their application to
the
fi
rst ~100 km of cable, makes them incompatible with
optical repeaters
10
, and elicits the use of high optical peak
powers (leading to optical non
linearities which compromise
coexisting data channels in the same
fi
ber strand
11
). These
limitations are often inconsequential for in-land or near-shore
deployments,asthetotalcablelengthsareshorterandthe
abundance of unused
fi
ber strands facilitates the use of dedi-
cated sensing
fi
bers, but constitute critical roadblocks for
transoceanic deployme
nts. Moreover, successfully overcoming
the instrumentation gap using transoceanic optical
fi
bers
demands an emphasis on scalability and compatibility with the
existing infrastructure, instead of the use of specialized instru-
ments and sources.
Recent demonstrations of optical
fi
ber sensing in subsea net-
work cables can be classi
fi
ed as either interferometric
12
,
13
or
polarization-based approaches
14
,
15
. Earlier demonstrations used
the full span of the cable as a single sensor (unable to localize the
point of perturbation), by employing either ultrastable lasers for
long-haul interferometry
12
or observing the change of the state of
polarization (SOP) at the output of the
fi
ber
14
,
15
. Full-span
methods, however, have multiple disadvantages: without locali-
zation capabilities, multiple cables or sensors must be used for
epicenter localization, which is further complicated by the long
gauge length. Furthermore, by measuring the cumulative effects
of environmental noise sources over the whole cable length
against the localized perturbations of interest, these methods will
necessarily suffer from higher noise
fl
oors.
In a recent demonstration of localization, interferometric
measurements were able to pinpoint measurements to a span of
cable between consecutive repeaters (typically spaced every 50 to
100 km) by measuring the return light re
fl
ected from high-loss
loop back (HLLB) paths placed at each repeater
13
. Nonetheless,
this approach still required specialized laser sources of much
greater coherence length (and cost) than conventional tele-
communication transponders, restricting its wide deployment.
On the other hand, polarization-based methods bene
fi
t from less
stringent hardware requirements but have thus far been unable to
localize the seismic wave to a single-span. The non-commutative
nature of birefringence operations has limited these methods to
full-cable measurements or, at most, to the localization of a single
dominant perturbation occurring along the cable.
In this work, we propose and demonstrate a method that relies
only on a series of SOP measurements to localize geophysical
measurements to within a single span of an ampli
fi
ed transo-
ceanic
fi
ber cable, with minimal alterations to conventional
optical transponders
16
. We detect, measure and localize a mag-
nitude
M
w
6.0 earthquake that happened in Guerrero, Mexico, on
the 11th of December 2022. The earthquake was detected on a
transoceanic
fi
ber cable that connects Los Angeles (California) to
Valparaiso (Chile). The proposed method (hereby dubbed the
eigenvalue method) demands only incoherent polarization mea-
surements and can coexist with co-propagating data channels in
the same
fi
ber strand.
Results
Single-span localization
. Our method employs a laser emitting
light pulses of
fi
xed polarization, which are then passed through a
programmable polarization controller and launched into the
fi
ber
under test (FUT). At the receiver end, a polarimeter is used to
measure the state of polarization (SOP) of the
N
re
fl
ections that
originate from each HLLB paths present at every repeater in the
majority of modern submarine cables (as shown in Fig.
1
a).
We express the SOP of the re
fl
ection originating from the
m
th
repeater,
^
y
ð
m
Þ
, as a normalized Stokes vector given by:
^
y
ð
m
Þ
¼
A
ð
m
Þ
^
s
;
ð
1
Þ
where
^
s
is the normalized Stokes vector representing the SOP of
the input pulse, and
A
(
m
)
is the real-valued rotation (orthogonal)
matrix that describes the cumulative birefringence effects of the
complete round-trip to and from the
m
th repeater (Fig.
1
a).
The matrices
A
(
m
)
can be measured by probing the
fi
ber with
multiple inputs
^
s
i
spanning the full Stokes space, instead of a
single input SOP. This is optimally achieved by cycling the input
SOP between three states forming an orthogonal Stokes basis,
^
s
i
where
i
=
{1, 2, 3} (e.g., horizontal, vertical, and left-circularly
polarized light), assuming that the
fi
ber remains stationary over
the three acquisitions, but can be achieved with any choice of 3
vectors that spans the full Stokes space.
Each matrix
A
(
m
)
can be decomposed into the birefringence
contribution from the laser to the
m
th repeater
A
fwd
ð
m
Þ
(forward
path) and the birefringence contribution from the
m
th repeater to
the receiver through the HLLB path
A
bkd
ð
m
Þ
(backward path):
A
ð
m
Þ
¼
A
bkd
ð
m
Þ
A
fwd
ð
m
Þ
:
ð
2
Þ
If we now de
fi
ne the matrices encoding only the local
birefringence of the
fi
ber span between repeater (
m
1) and
(
m
)as
X
fwd
ð
m
Þ
and
X
bkd
ð
m
Þ
(for the forward propagation and backward
propagation, respectively), we can rewrite Eq. (
2
) as:
A
ð
m
Þ
¼
A
bkd
ð
m

1
Þ
X
bkd
ð
m
Þ
X
fwd
ð
m
Þ
A
fwd
ð
m

1
Þ
:
ð
3
Þ
Measuring the local birefringence matrix
X
fwd
ð
m
Þ
X
bkd
ð
m
Þ
is not
possible, since the previously described strategy of probing the
fi
ber with pulse triplets allows us only to measure the cumulative
A

1
ð
m

1
Þ
and
A
(
m
)
. However, it is possible to retrieve partial
information about
X
fwd
ð
m
Þ
X
bkd
ð
m
Þ
from the measured
A
(
m
)
matrices by
performing the following operation:
A

1
ð
m

1
Þ
A
ð
m
Þ
¼
U

1
X
bkd
ð
m
Þ
X
fwd
ð
m
Þ
U
;
ð
4
Þ
where
U
¼
A
fwd
ð
m

1
Þ
can be any (unknown) unitary matrix. The
resulting matrix from Eq. (
4
) is similar to
X
fwd
ð
m
Þ
X
bkd
ð
m
Þ
and therefore
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has the same eigenvalues:
eig
X
fwd
ð
m
Þ
X
bkd
ð
m
Þ
no
¼
eig
A

1
ð
m

1
Þ
A
ð
m
Þ
no
:
ð
5
Þ
The two complex eigenvalues represent the local angle of
rotation of polarization around the unknown birefringence vector
(see Fig.
1
c), and are thus proportional to the birefringence
strength along a single, localized span. A change in the local
birefringence that affects the overall magnitude of the rotation of
SOP in the Stokes space can be measured by computing the angle
of the eigenvalue at time
t
for every
m
th re
fl
ection, and
comparing it to a previous reference measurement at time
t
ref
.
Hence, a measurement
μ
(
m
,
t
) can be de
fi
ned as:
μ
ð
m
;
t
Þ¼
eig
A

1
ð
m

1
Þ
A
ð
m
Þ
no
ð
t
Þ


eig
A

1
ð
m

1
Þ
A
ð
m
Þ
no
ð
t
ref
Þ

ð
6
Þ
Figure
1
visually depicts the information encoded in each of the
A
(
m
)
and
X
(
m
)
involved in the calculation, the method for recovering
the
A
(
m
)
matrix, and a depiction of the measurement concept.
Measurement and post-processing
. After measuring the SOP of
3 consecutive probe pulses of orthogonal SOP (Fig.
1
b), the
obtained
A
(
m
)
(
t
) matrices are generated by stacking the normal-
ized stokes vectors as:
A
ð
m
Þ
ð
t
Þ¼
.
.
.
.
.
.
.
.
.
^
y
ð
m
Þ
ð
t

1
Þ
^
y
ð
m
Þ
ð
t
Þ
^
y
ð
m
Þ
ð
t
þ
1
Þ
.
.
.
.
.
.
.
.
.
2
6
6
6
4
3
7
7
7
5
:
ð
7
Þ
Before processing, each of the recovered
A
(
m
)
(
t
) matrices is
denoised by
fi
nding the closest unitary matrix, in the Frobenius
norm sense. This is achieved by performing the singular value
decomposition of the
A
(
m
)
(
t
) matrix (
A
ð
m
Þ
ð
t
Þ¼
U
m
Σ
m
V
T
m
), and
keeping the denoised matrix
^
A
ð
m
Þ
ð
t
Þ¼
U
m
V
T
m
.
We then perform the operation described in Eq. (
4
) for each
repeater using the denoised matrices. We store the angle of the
complex eigenvalue of the positive argument, and calculate the
difference in the measured angle to that of the
fi
rst acquisition.
The complete processing stack is illustrated in the Supplementary
Information, Supplementary Note 1.
Experimental results
. On December 11, 2022, at 14:31:29 UTC, a
magnitude 6.0 earthquake occurred in Guerrero, Mexico, which
we captured on the Curie transoceanic
fi
ber cable, which connects
Los Angeles (California) to Valparaiso (Chile) (Fig.
2
b). The cable
contains 110 repeaters with HLLB paths, each comprising a high-
splitting ratio directional coupler and a Bragg grating re
fl
ector.
The interrogation setup (situated in the Los Angeles terminal) is
depicted in Fig.
2
a, and includes a telecommunication
transponder
17
used to send linearly polarized optical pulses
through a polarization synthesizer on the emitter side, and a
polarimeter on the receiver side, which is used to evaluate the
state of polarization of the received re
fl
ections.
By observing the changes in the SOP of the re
fl
ections
coming from the HLLB paths when using constant input
polarization (hereby called direct SOP measurements), the
earthquake was visible on span 41 and all following spans (due
to the cumulative nature of this method). We observe an initial
arrival about 153 s after the earthquake origin time. Given that
the 41st span is about 532 km away from the earthquake
epicenter (Fig.
3
a), this arrival time is consistent with a
dominant seismic phase Sg wave in oceanic crust. The observed
earthquake is predominantly visible in the 0.25
0.35 Hz band,
and its duration is about 10 min (Fig.
3
b).Thisisconsistent
Without Perturbation
SOP at input of span
Different Birefringence Strength
With Perturbation
2
Pulsed
Laser
Polarization
Synthesizer
1
2M-1
M
N
Polarimeter
a.)
c.)
b.)
m
Propagation through
perturbed span
Propagation through
unperturbed span
1
m
m
m
m
Repeater
Input SOP
Acquisition
1
0
1
2
3
4
5
2
3
M
N
...
...
...
...
...
...
...
...
...
...
...
...
...
...
Fig. 1 Measurement concept. a
Representation of the sections of
fi
ber modeled by each of the matrices. The
A
(
m
)
matrix models the blue colored
fi
ber
path, the
A
(
m
1)
matrix models the green
fi
ber path, and the local
X
(
m
)
matrix models the purple
fi
ber path.
b
Illustration of the acquisition of an
A
(
m
)
matrix, from three consecutive acquisitions. Each acquisition recovers
N
re
fl
ections, each originating from a speci
fi
c repeater in the cable. The
A
(
m
)
matrix
is constructed by combining the Stokes vectors from the 3 consecutive re
fl
ections originating from the same (
m
th) repeater in a matrix, when probing the
fi
ber with different SOP.
c
Conceptual visualization of the information obtained about the local birefringence using our proposed approach. Propagation
through a span of
fi
ber is modeled as a rotation of the Stokes vector representing the SOP at the span input (red arrow) around the effective birefringence
vector of the span (green arrow), tracing the path in represented in the purple circles. A perturbation acting on the
fi
ber affects the orientation and strength
of the birefringence vector (bottom, left and right). The change in angle of the rotation around the birefringence vector, which we measure, is propor
tional
to a change in the birefringence strength.
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3
with previous reports of direct SOP measurements performed
over the full-span of the cable for similar events
14
.
We tested the localization abilities of our proposed eigenvalue
method by plotting the signal power in the earthquake band (0.25
to 0.35 Hz) over 60-s-long time windows, depicted in Fig.
3
c, left.
The earthquake signal is
fi
rst visible in the 41st span, in accordance
with the direct SOP measurements (Fig.
3
c, right). However, while
the earthquake signal is visible in every span following the 41st
when using the direct SOP approach, our eigenvalue method
localizes the measurement to a single span with minimal crosstalk
(de
fi
ned as the increase in signal noise power in the earthquake
frequency band to subsequent
fi
ber locations). We observe a
median value of ~1 dB of crosstalk (Fig.
3
d).
We also used the eigenvalue method to observe the seismic
wave move out. Besides span 41, we can observe the earthquake
signal in span 43 (673 km away from the epicenter), starting ~40 s
after the wave recorded in span 41 (532 km away from the
epicenter), as shown in Fig.
3
e. Notably, however, most
neighboring spans to the 41st do not display a clear earthquake
signal, likely due to a combination of the earthquake radiation
pattern of S waves, the relative orientation of the
fi
ber, variations
in mechanical coupling to the sea
fl
oor, and the complicated
response of birefringence to different types of stimulus.
Discussion
In this work, we proposed and demonstrated a scalable approach
to sense and localize perturbations affecting the birefringence of
ampli
fi
ed telecommunication
fi
ber cables. Our method is com-
patible with telecommunication-grade sources and detectors,
requiring only the addition of a polarization synthesizer to con-
ventional transponders. With about 500 operational cables
worldwide, mostly with HLLB re
fl
ectors, each of 50
100 spans,
our measurements can be extended to 25,000
50,000
fi
ber spans
without touching wetplant infrastructure.
We successfully accomplished the localization of a seismic
wave, identifying its location to a single span of
fi
ber between two
optical repeaters. The ability to localize the seismic wave to within
a span enables the observation of the seismic wave move-out (as
demonstrated in Fig.
3
e), and may lead to further bene
fi
ts, such as
the determination of the epicenter of a seismic event using a
single
fi
ber, and reduced in
fl
uence of environmental noise com-
pared to cumulative approaches. Our approach displayed mini-
mal crosstalk to subsequent spans as a ~1 dB increase in noise-
fl
oor in the earthquake band. The physical origin of the crosstalk
is likely linked to the non-stationarity of the
fi
ber over the pulse
triplet required to make a measurement (as demonstrated
numerically in the Supplementary Information, Supplementary
Note 4), suggesting that it may be improved by increasing the rate
of measurement pulses (limited by the polarization synthesizer in
our implementation).
Regarding the detection limit of the two tested approaches, we
observed similar SNR between the eigenvalue method and direct
SOP measurements. Notably, both approaches failed to detect the
earthquake at spans closer to the epicenter than the 41st. This
suggests that the dominant contribution to the detection limit in
any SOP-based method could originate from the complex sensi-
tivity of the local birefringence to different environmental stimuli
(e.g., bends
18
, twists
19
, or other effects
20
), the non-linear nature of
SOP-based measurements, variations in mechanical coupling
along the cable, or the geometry/layout of the cable with respect
to the induced deformation by the seismic wave
21
.
Nonetheless, it is not easy to draw a direct comparison between
the detection limit of both approaches, given the fundamental
differences between the eigenvalue and direct-SOP methods: on
the one hand, the detection limit when using direct-SOP methods
with HLLB will likely be in part determined by the accumulated
length of cable up to the interrogated span and the environmental
noise acting on the cable (due to the cumulative nature of
environmental noise). On the other hand, the eigenvalue meth-
od
s insensitivity to changes to the birefringence vector orienta-
tion suggests potentially lower sensitivity in some scenarios,
where the net effect along the span predominantly rotates the
birefringence vector, without a great net effect on birefringence
strength.
A possible future research direction would be to focus on
analyzing lower frequency events. Spectral features in the mHz
range are of particular interest for measurement of tsunami
and infragravity waves. Per-span resolution of tsunami
wave propagation measurement in the open sea using polar-
ization measurements has some advantages when compared to
phase-based approaches
13
, by being immune to laser phase
noise due to measuring the relative dynamics of two electric
fi
eld vectors.
Additionally, the sensitivity of the eigenvalue technique may
potentially be improved by using a Jones receiver or by recovering
the full Muller matrix. Currently, by acquiring three sets of Stokes
2x800G ICE6
Subcarriers
Pulsed Tones
Ch.1
Ch.2
2x800G ICE6
Subcarriers
Ch.1
Ch.2
MUX
1
2
3
4
5
6
Polarization
Synthesizer
Polarimeter
Filter
1.5 GHz
ROADM
ASE
1
2
3
4
...
N
MUX
1
2
3
4
5
6
ASE
ROADM
1
2
3
4
...
N
2
...
FUT
.
.
.
N
1
HLLB
30°S
30°N
150°W
120°W
90°W
60°W
30°W
2000 mi
5000 km
Longitude
Latitude
a.)
b.)
Fiber Bragg Grating
Erbium Doped Fiber Amplifier
Fig. 2 Experimental setup and layout of the interrogated
fi
ber cable. a
Diagram of the experimental setup. The emitter part of our interrogation system is
color-coded red, and the detector part of our interrogator system is color-coded green. The
fi
ber under test (FUT) is color-coded yellow. All the relevant
boxes use a dashed outline. The blue color-coded boxes represent parts of the telecommunication link that are not fundamental parts of the proposed
measurement technique (ASE ampli
fi
ed spontaneous emission, MUX multiplexer, ROADM recon
fi
gurable optical add-drop multiplexer).
b
Map of the FUT
(map generated using MATLAB
s
geoplot
function).
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