Patent Publication Number: US-11650340-B2

Title: Detection of seismic disturbances using optical fibers

Description:
BACKGROUND 
     Field 
     Various example embodiments relate to seismography and, more specifically but not exclusively, to detection of seismic disturbances using terrestrial and/or submarine optical fibers. 
     Description of the Related Art 
     This section introduces aspects that may help facilitate a better understanding of the disclosure. Accordingly, the statements of this section are to be read in this light and are not to be understood as admissions about what is in the prior art or what is not in the prior art. 
     Sparse seismic instrumentation in the oceans limits earthquake-detection capabilities. For example, the majority of seismic stations are located on land, with only a handful of seismographs being on the ocean floor. As a result, many underwater earthquakes remain under-detected, e.g., because land-based seismic stations are often too far away from the earthquakes&#39; epicenters. Similarly, most tsunami-detection equipment is on shore, which may not be optimal in terms of generating adequate tsunami warnings for the affected coastal communities. 
     SUMMARY OF SOME SPECIFIC EMBODIMENTS 
     Disclosed herein are various embodiments of an optical communication system that enables any deployed (e.g., long-haul, terrestrial or submarine) fiber-optic cable to function as an earthquake-detection sensor. In an example embodiment, a wavelength-division-multiplexing (WDM) optical transmitter of one network node is configured to transmit an optical-probe signal together with legacy data-carrying optical signals. At another network node, a low-complexity, low-latency coherent optical receiver is used to obtain time-resolved measurements of the Stokes parameters of the optical-probe signal. The signal-processing chain of the optical receiver employs digital filtering to select frequency components of the measurements streams corresponding to seismic disturbances of the fiber-optical cable connecting the nodes. The selected frequency components are then used to compute values of an earthquake indicator, which are reported to a network controller. Based on such reports from three or more nodes, the network controller can determine the epicenter and magnitude of the earthquake and, if warranted, generate a tsunami forecast. 
     An example embodiment can beneficially be implemented at a relatively small additional cost, with only small modifications of some of the network&#39;s WDM transceivers, and without any modifications of the existing fiber-optic-cable plant. 
     According to an example embodiment, provided is an apparatus to provide information on earthquakes, the apparatus comprising: an electronic analyzer connected to receive measurements of states of polarization of pairs of light beams, the light beams of each one of the pairs of light beams having traveled in opposite directions between a respective pair of network nodes via a respective optical fiber cable end-connecting the respective pair of network nodes, different ones of the pairs of light beams having traveled over different ones of the respective optical fiber cables; and wherein the electronic analyzer has circuitry configured to characterize one of the earthquakes based on the measurements of the states of polarization of a plurality of the pairs of light beams. 
     According to another example embodiment, provided is a machine-implemented method of providing information on earthquakes, the machine-implemented method comprising the steps of: (A) receiving measurements of states of polarization of pairs of light beams, the light beams of each one of the pairs of light beams having traveled in opposite directions between a respective pair of network nodes via a respective optical fiber cable end-connecting the respective pair of network nodes, different ones of the pairs of light beams having traveled over different ones of the respective optical fiber cables; and (B) processing, in electronic circuitry, the measurements of the states of polarization of a plurality of the pairs of light beams to characterize one of the earthquakes. 
     According to yet another example embodiment, provided is an apparatus, comprising: an optical wavelength demultiplexer having a plurality of pass bands to demultiplex optical signals received through an optical fiber; a first optical receiver connected to the optical wavelength demultiplexer to receive a data-modulated optical signal; and a second optical receiver connected to the optical wavelength demultiplexer to obtain time-resolved measurements of Stokes parameters of an optical-probe signal, both of the data-modulated optical signal and the optical-probe signal passing through one of the pass bands of the optical wavelength demultiplexer; and wherein the second optical receiver comprises a digital band-pass filter to filter streams of the time-resolved measurements to select frequency components of the streams corresponding to seismic disturbance of the optical fiber. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other aspects, features, and benefits of various disclosed embodiments will become more fully apparent, by way of example, from the following detailed description and the accompanying drawings, in which: 
         FIG.  1    shows a block diagram of one optical fiber line of an optical communication system in which some embodiments may be practiced; 
         FIG.  2    shows a block diagram of a wavelength-division-multiplexing (WDM) optical transceiver that can be used in the optical communication system of  FIG.  1    according to an embodiment; 
         FIG.  3    graphically illustrates certain spectral characteristics of the WDM optical transceiver of  FIG.  2    according to an embodiment; 
         FIG.  4    shows a block diagram of an optical receiver that can be used in the WDM optical transceiver of  FIG.  2    according to an embodiment; 
         FIG.  5    shows a graphical representation of a state of polarization (SOP) using the Poincare sphere; 
         FIG.  6    shows a block diagram of a digital signal processor (DSP) that can be used in the optical transceiver of  FIG.  4    according to an embodiment; 
         FIG.  7    shows a block diagram of a fiber-optic network in which some embodiments may be practiced; and 
         FIG.  8    shows a flowchart of an example signal-processing method that can be used in the fiber-optic network of  FIG.  7    according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Some embodiments may benefit from the use of apparatus, method, and some features disclosed in U.S. patent application Ser. No. 16/988,874, filed on 10 Aug. 2020, which is incorporated herein by reference in its entirety. 
     Although some example embodiments are described herein below in reference to submarine optical fibers and/or submarine fiber-optic cables, a person of ordinary skill in the art will readily understand, based on the provided description, how to make and use embodiments that employ terrestrial optical fibers and/or terrestrial fiber-optic cables. 
     Some embodiments may be used for detection of earthquakes and/or prediction of tsunami waves. 
       FIG.  1    shows a block diagram of an optical fiber line of a portion of an optical communication system  100  in which some embodiments may be practiced. System  100  is a long-haul submarine communication system comprising landing stations  102   1  and  102   2  connected by way of a wet cable plant  104 . Landing stations  102   1  and  102   2  are typically further connected to respective terrestrial networks (not explicitly shown in  FIG.  1   ). In an alternative embodiment, system  100  may have one or more additional landing stations connected to different wet cable plant(s), i.e., having a similar form to the wet cable plant  104 , as known in the pertinent art, e.g., using one or more branching units and/or completely different submarine fiber cable lines between the additional landing stations (not explicitly shown in  FIG.  1   ). 
     In an example embodiment, wet cable plant  104  comprises an undersea cable system that includes, inter alia, submersible optical repeaters  150   1 - 150   L  serially connected by spans  140  of optical fiber, e.g., as indicated in  FIG.  1   , where L is a positive integer. In the shown embodiment, each span  140   i  includes two optical fibers, which are labeled  140   ia  and  140   ib , respectively, where i=1, 2, . . . , L+1. The number L of optical repeaters  150  used in wet cable plant  104  depends on the particular embodiment and may be in the range, e.g., from 1 to ˜200. A typical length of a fiber span  140   i  may range from ˜50 km to ˜150 km, depending on the distance between landing stations  102   1  and  102   2 . In some embodiments, wet cable plant  104  may not have any optical repeaters between landing stations  102   1  and  102   2 . 
     In the shown embodiment, an optical repeater  150  comprises optical amplifiers (OAs)  160   ja  and  160   jb , where j=1, 2, . . . , L. Optical amplifier  160   ja  is configured to amplify optical signals traveling towards landing station  102   2 . Optical amplifier  160   jb  is similarly configured to amplify optical signals traveling towards landing station  102   1 . In an example embodiment, an optical amplifier  160  can be implemented as known in the pertinent art, e.g., using an erbium-doped fiber, a gain-flattening filter, and one or more laser-diode pumps. The laser diodes can be powered by a DC current from the corresponding shore-based power-feeding equipment (PFE, not explicitly shown in  FIG.  1   ), fed through the electrical conductor(s) of the corresponding submarine cable, which also typically contains optical fibers  140   ia  and  140   ib . In some embodiments, the electrical conductors (e.g., wires) may be located near the center of the submarine cable. In some other embodiments, the electrical conductors may have a generally tubular shape, e.g., with a ring-like cross-section in a plane orthogonal to the longitudinal axis of the submarine cable. 
     In an alternative embodiment, optical repeaters  150  can be designed for two, three, four, or more pairs of optical fibers  140  connected thereto at each side thereof. For example, an optical repeater  150  designed to be compatible with a four-fiber-pair submarine cable typically includes eight optical amplifiers  160  arranged in four amplifier pairs, each pair being similar to the pair of optical amplifiers  160   ja  and  160   jb . 
     Optical repeater  150   j  may also comprise a supervisory optical circuit (not explicitly shown in  FIG.  1   ) that enables monitoring equipment (ME) units  120   1  and  120   2  located at landing stations  102   1  and  102   2 , respectively, to monitor the operating status of the optical repeaters. Some embodiments of the supervisory optical circuit are disclosed, e.g., in European Patent Application Nos. EP17305569.0 and EP17305570.8, which are incorporated herein by reference in their entirety. 
     In an example embodiment, each of ME units  120   1  and  120   2  is configured to use dedicated supervisory wavelengths (labeled λ 1  and λ 2 ) for respective supervisory signals that can be sent through the corresponding fiber(s)  140  towards the remote landing station  102 . The supervisory optical circuit of each optical repeater  150   j  is configured to loop back, in the opposite direction, at least a portion of a supervisory optical signal. As a result, ME unit  120   1  can receive a looped-back supervisory optical signal comprising the portions of the original supervisory optical signal returned to that ME unit by the different supervisory optical circuits of different optical repeaters  150   1 - 150   N . Similarly, ME unit  120   2  can receive a looped-back supervisory optical signal comprising the portions of the corresponding supervisory optical signal returned to that ME unit by the different supervisory optical circuits of different optical repeaters  150   1 - 150   N . The looped-back supervisory optical signals received by ME units  120   1  and  120   2  can be processed and analyzed to determine the present operating status and/or certain operating characteristics of at least some or all of optical repeaters  150   1 - 150   N  in wet cable plant  104 . The determined parameters may include but are not limited to: (i) input and output signal levels and the gains of some or all individual optical amplifiers (OAs)  160   ja  and  160   jb ; (ii) non-catastrophic faults in individual optical fibers  140   i , such as any gradual loss increases therein; and (iii) catastrophic failures in individual optical repeaters  150   j  and/or optical fibers  140   i . 
     Landing station  102   1  comprises a submarine line terminal equipment (SLTE) unit  110   1  and ME unit  120   1  connected to wet cable plant  104  by way of an optical wavelength multiplexer (MUX)  130   1  and an optical wavelength demultiplexer (DMUX)  136   1  as indicated in  FIG.  1   . In an example embodiment, SLTE unit  110   1  includes a wavelength-division-multiplexing (WDM) transceiver (not explicitly shown in  FIG.  1   ; see  FIG.  2   ) configured to transmit and receive payload-carrying optical data signals using carrier wavelengths λ 3 -λ n , where n generally denotes the number of WDM channels in system  100 . The number n can be in the range, e.g., between ˜10 and ˜150. 
     In an example embodiment, carrier wavelengths λ 1 -λ n  can be selected in accordance with a frequency (wavelength) grid, such as a frequency grid that complies with the ITU-T G.694.1 Recommendation, which is incorporated herein by reference in its entirety. The frequency grid used in system  100  can be defined, e.g., in the frequency range from about 184 THz to about 201 THz, with a 100, 50, 25, or 12.5-GHz spacing of the channels therein. While typically defined in frequency units, the parameters of the grid can equivalently be expressed in wavelength units. For example, in the wavelength range from about 1528 nm to about 1568 nm, the 100-GHz spacing between the centers of neighboring WDM channels is equivalent to approximately 0.8-nm spacing. In alternative embodiments, other fixed or flexible (flex) frequency grids can be used as well. 
     In operation, MUX  130   1  multiplexes the optical signals of wavelengths λ 3 -λ n  generated by SLTE unit  110   1  and the one or more supervisory optical signals of wavelengths λ 1  and λ 2 , and applies the resulting multiplexed optical signal to optical fiber  140   1a . DMUX  136   1  de-multiplexes a multiplexed optical signal received from optical fiber  140   1b  into two portions. The first portion has optical signals of wavelengths λ 3 -λ n  and is directed to SLTE unit  110   1 . The second portion has the looped-back supervisory optical signals of the one or more wavelengths λ 1  and λ 2  and is directed to ME unit  120   1 . 
     In an example embodiment, ME unit  120   1  comprises an optical time-domain reflectometer (OTDR, not explicitly shown in  FIG.  1   ) configured to optically probe wet cable plant  104  using wavelengths λ 1  and λ 2 . For example, ME unit  120   1  can be designed to perform OTDR measurements by detecting and processing the looped-back supervisory optical signals received from optical repeaters  150   1 - 150   N . In general, ME unit  120   1  can be configured to use any suitable OTDR method. 
     Landing station  102   2  is generally analogous to landing station  102   1  and comprises an SLTE unit  110   2 , ME unit  120   2 , a MUX  130   2 , and a DMUX  136   2 . The analogous elements/components of the two landing stations are labeled in  FIG.  1    using the same numerical labels, but with different respective subscripts. The descriptions of SLTE unit  110   1 , ME unit  120   1 , MUX  130   1 , and DMUX  136   1  of landing station  102   1  given above generally apply to SLTE unit  110   2 , ME unit  120   2 , MUX  130   2 , and DMUX  136   2 , respectively, of landing station  102   2  and are not repeated here. 
     In various embodiments, each of landing stations  102   1  and  102   2  may further include one or more of the following conventional elements/components: (i) power feeding equipment; (ii) system supervisory equipment; (iii) network management equipment; (iv) cable termination boxes; (v) network protection equipment; and (vi) various interface circuits. 
     When an earthquake occurs in relative proximity to system  100 , mechanical disturbances  190 , such as shock waves and seismic waves caused thereby, travel from the epicenter through the Earth&#39;s crust to eventually reach wet cable plant  104 . Given a sufficiently strong earthquake in sufficiently close proximity to at least some of the optical fibers  140 , mechanical disturbances  190  may cause optical-signal perturbations therein detectable by landing stations  102   1  and  102   2 , e.g., as described below. Appropriate signal processing can then be used, e.g., to accurately estimate the distances D 1  and D 2  from the incidence point at which mechanical disturbances  190  first reach the corresponding optical fibers  140  to the landing stations  102   1  and  102   2 , respectively. 
       FIG.  2    shows a block diagram of a WDM optical transceiver  200  that can be used in SLTE unit  110   1  according to an embodiment. The transmit and receive optical channels corresponding to transceiver  200  are illustratively referred to as being the “uplink” (or U) channels and “downlink” (or D) channels, respectively. The indexing of the optical channels in  FIG.  2    is consistent with the indexing used in  FIG.  1   , wherein SLTE unit  110   1  uses the wavelengths λ 1 -λ n , and ME unit  120   1  uses wavelengths λ 1 -λ 2 . A block diagram representing an embodiment of a WDM optical transceiver that can be used in SLTE unit  110   2  can be obtained by flipping the U and D notations in  FIG.  2   . 
     Optical transceiver  200  comprises a plurality of individual-channel optical data transmitters  210   3 - 210   n  and an optical-probe transmitter  220 . Optical-probe transmitter  220  comprises a laser  222 . In some embodiments, laser  222  can be a directly modulated laser. In some other embodiments, laser  222  can be a continuous-wave (CW) laser. Optical transmitters  210   3 - 210   n-1  are directly connected to the corresponding optical input ports (labeled  3 , . . . , n−1) of an optical MUX  230 . Optical transmitters  210   n  and  220  are, in the illustrated example, connected to a common corresponding optical input port (labeled n) of optical MUX  230  via an optical combiner (e.g., a 3-dB optical coupler)  214 , but in other embodiments, the optical transmitter  220  may connect to a separate optical input port of the corresponding optical MUX (not shown). Optical MUX  230  operates in a conventional manner to wavelength-multiplex optical signals  216   3 - 216   n  applied to optical input ports  3 , . . . , n thereof to generate an optical output signal  232  at an optical output port  0  thereof. Optical output signal  232  can be directed to optical MUX  130   1  and further uplink (also see  FIG.  1   ). In an example embodiment, all of optical signals  216   3 - 216   n  are spectrally within the amplification band(s) of optical repeaters  150   1 - 150   N . 
       FIG.  3    graphically illustrates spectral characteristics of optical MUX  230  and optical output signal  232  according to an embodiment. More specifically, dashed lines  310   3 - 310   n  graphically show spectral pass bands of optical MUX  230 . Spectral pass band  310   3  corresponds to the optical path between optical input port  3  and optical output port  0  of optical MUX  230 . Spectral pass band  310   4  corresponds to the optical path between optical input port  4  and optical output port  0  of optical MUX  230 , and so on. Spectral pass band  310   n-1  corresponds to the optical path between optical input port n−1 and optical output port  0  of optical MUX  230 . Spectral pass band  310   n  corresponds to the optical path between optical input port n and optical output port  0  of optical MUX  230 . 
     Optical signals  216   3 - 216   n  are spectrally aligned with the spectral pass bands  310   3 - 310   n , respectively, as indicated in  FIG.  3   . For example, for each of optical signals  216   3 - 216   n-1 , a center frequency of the signal is approximately spectrally aligned with the center frequency of the corresponding one of the spectral pass bands  310   3 - 310   n-1 . In an example embodiment, the center frequencies f 3 , . . . , f n-1  of optical signals  216   3 - 216   n-1  may correspond to wavelengths λ 3 , . . . , λ n-1  of  FIG.  1   . In some embodiments, the wavelengths λ 3 , . . . , λ n-1  may be carrier wavelengths. In some other embodiments, e.g., employing carrier-suppressed modulation, the wavelengths λ 3 , . . . , λ n-1  may approximately be the center wavelengths of the corresponding spectral envelopes. 
     Optical signal  216   n  comprises two components, labeled  212  and  224 , respectively (also see  FIG.  2   ). Optical signal  212  is generated by optical transmitter  210   n  and is generally analogous to any of the above-described optical signals  216   3 - 216   n-1 . The center frequency of optical signal  212  is the frequency f n , which is approximately spectrally aligned with the center frequency of the spectral pass band  310   n . In an example embodiment, optical signal  224  is a continuous-wave (CW) signal generated by laser  222  and has a much narrower spectral width than that of optical signal  212 . As such, in  FIG.  3   , optical signal  224  is represented by a spectral line at the frequency f s . The frequency f s  is near the roll-off edge of the spectral envelope of optical signal  212 , but is still within the spectral pass band  310   n . In other embodiments, modulated optical signals may be used to implement optical signal  224  as long as the modulation does not cause one or more modulation sidebands to spectrally overlap with optical signal  212 . 
     In the illustrated example embodiment, the frequency f s  is shown to be in the last optical channel of the corresponding WDM-channel multiplex. In various alternative embodiments, the frequency f s  may be placed within any other selected optical channel in a similar manner. In some embodiments, the frequency f s  can be at any spectral location within the EDFA gain region such that the frequency f s  is also within a spectral pass band of the corresponding MUX/DMUX. For example, if a selected payload channel is not used, then the frequency f s  can be placed near the center frequency of the corresponding pass band of the corresponding MUX/DMUX. 
     Referring back to  FIG.  2   , optical transceiver  200  further comprises a plurality of individual-channel optical data receivers  260   3 - 260   n  and an optical-probe receiver  270 . Optical receivers  260   3 - 260   n-1  are directly connected to the corresponding optical output ports (labeled  3 , . . . , n−1) of an optical DMUX  280 . Optical receivers  260   n  and  270  are connected to a common corresponding optical output port (labeled n) of optical DMUX  280  via an optical splitter  264 , but in other (not-shown) embodiments, may be connected to separate optical output ports of the corresponding optical DMUX. Optical DMUX  280  operates in a conventional manner to wavelength-demultiplex an optical input signal  282  received at an optical input port  0  thereof, e.g., from optical DMUX  136   1  (also see  FIG.  1   ). The resulting demultiplexed optical signals  266   3 - 266   n  are directed from optical output ports  3 , . . . , n of DMUX  280  to optical receivers  260   3 - 260   n-1  and optical splitter  264 , respectively. Optical splitter  264  operates to split optical signal  266   n  into optical signals  262  and  274 , which are then applied to optical receivers  260   n  and  270 , respectively. 
     In an example embodiment, optical DMUX  280 , optical input signal  282 , and optical signals  266   3 - 266   n  may have spectral characteristics analogous to those shown in  FIG.  3   . In some embodiments, optical DMUX  280  may be implemented using a nominal copy of optical MUX  230 , but configured to transmit signals in the opposite direction, i.e., from port  0  to ports  3 , . . . , n. 
       FIG.  4    shows a block diagram of optical receiver  270  according to an embodiment. As shown in  FIG.  4   , optical receiver  270  comprises an optical local-oscillator (OLO) source (e.g., laser)  406 , polarization beam splitters (PBS&#39;s)  410   1  and  410   2 , optical couplers  420   1  and  420   2 , photodiodes  430   1 - 430   4 , transimpedance amplifiers (TIAs)  440   1  and  440   2 , analog-to-digital converters (ADCs)  450   1  and  450   2 , and a digital signal processor (DSP)  460 . The photodiodes in each of photodiode pairs  430   1 / 430   2  and  430   3 / 430   4  are electrically connected in a differential (e.g., balanced) configuration as indicated in  FIG.  4   . 
     In operation, PBS  410   1  receives optical signal  274  (also see  FIG.  2   ) and splits the received light into two relatively orthogonal polarization components, labeled  274   X  and  274   Y , respectively. PBS  410   2  receives an OLO signal  408  generated by OLO source  406  and similarly splits the received light into two relatively orthogonal polarization components, labeled  408   X  and  408   Y , respectively. In an example embodiment, OLO signal  408  is a CW optical signal that may have a fixed linear polarization and an optical-carrier frequency f LO . The frequency difference Δf between the frequencies f LO  and f s  ( FIG.  3   ) can be expressed as Δf=|f LO −f s |. In some embodiments, f LO  may be larger than f s . In other embodiments, f LO  may be smaller than f s . 
     Optical coupler  420   1  operates to mix optical signals  274   X  and  408   X  to generate mixed optical signals  428   1  and  428   2 , the mixed optical signals being light mixtures with different (e.g., by approximately 180 degrees) relative phase shifts between optical signals  274   X  and  408   X . Photodiode pair  430   1 / 430   2  then converts optical signals  428   1  and  428   2  into a corresponding electrical signal  432   1 . Electrical signal  432   1  is amplified using TIA  440   1  and optionally filtered, e.g., low-frequency filtered, and the corresponding amplified electrical signal is converted into a digital electrical signal  452   1  using ADC  450   1 . 
     Optical coupler  420   2  similarly operates to mix optical signals  274   Y  and  408   Y  to generate mixed optical signals  428   3  and  428   4 . Photodiode pair  430   3 / 430   4  converts optical signals  428   3  and  428   4  into a corresponding electrical signal  432   2 . Electrical signal  432   2  is amplified using TIA  440   2  and optionally filtered, e.g., low-frequency filtered, and the corresponding amplified electrical signal is converted into a digital electrical signal  452   2  using ADC  450   2 . 
     Digital electrical signals  452   1  and  452   2  are applied to DSP  460 , wherein these signals can be processed, e.g., as described below in reference to  FIG.  6    and Eqs. (3)-(16), to determine the state of polarization (SOP) of optical signal  274 . In response to certain SOP characteristics exhibited by optical signal  274 , DSP  460  may further operate to generate control messages, warnings, and/or alarms  462  indicating an occurrence of mechanical disturbances  190  (also see  FIG.  1   ). 
     In an alternative embodiment, optical receiver  270  may be implemented using a coherent optical receiver disclosed in the above-cited U.S. patent application Ser. No. 16/988,874. 
     In optics, polarized light can be represented by a Jones vector, and linear optical elements acting on the polarized light and mixtures thereof can be represented by Jones matrices. When light crosses such an optical element, the Jones vector of the output light can be found by taking a product of the Jones matrix of the optical element and the Jones vector of the input light, e.g., in accordance with Eq. (1): 
                     [           E   x   r               E   y   r           ]     =       J   ⁡     (     θ   ,   ϕ     )       ⁡     [           E   x   t               E   x   t           ]               (   1   )               
where E x   t  and E y   t  are the x and y electric-field components, respectively, of the Jones vector of the input light; E x   r  and E y   r  are the x and y electric-field components, respectively, of the Jones vector of the output light; and J(θ,ϕ) is the Jones matrix of the optical element given by Eq. (2):
 
                     J   ⁡     (     θ   ,   ϕ     )       =     [           cos   ⁡     (   θ   )               -     e       -   j     ⁢           ⁢   ϕ         ⁢     sin   ⁡     (   θ   )                     e     j   ⁢           ⁢   ϕ       ⁢     sin   ⁡     (   θ   )               cos   ⁡     (   θ   )             ]             (   2   )               
where 2θ and ϕ are the elevation and azimuth polarization rotation angles, respectively, the values of which can be used to define the SOP. For clarity, the above example of a Jones matrix does not include effects of optical attenuation and/or amplification.
 
       FIG.  5    shows a graphical representation of an SOP using the Poincare sphere. Herein, the Poincare sphere is a sphere of radius P centered on the origin of the three-dimensional Cartesian coordinate system, the mutually orthogonal axes S 1 , S 2 , and S 3  of which represent the corresponding Stokes parameters of the optical field. The radius P represents the optical power and is expressed by Eq. (3):
 
 P =√{square root over ( S   1   2   +S   2   2   +S   3   2 )}  (3)
 
For a given optical power P, different SOPs can be mapped to different respective points on the surface of the Poincare sphere. For example, the vector S shown in  FIG.  5    represents one of such SOPs. An SOP rotation can then be visualized as a corresponding rotation of the vector S.
 
     In some cases, it is convenient to use a unity-radius Poincare sphere, for which P=1. The unity-radius Poincare sphere can be obtained by normalizing the Stokes parameters with respect to the optical power P. For the unity-radius Poincare sphere, the angles θ and ϕ are related to the normalized Stokes parameters S 1 ′, S 2 ′, and S 3 ′ as follows: 
     
       
         
           
             
               
                 
                   
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     As used herein, the term “polarization tracking” refers to time-resolved measurements of the SOP of an optical signal. In some embodiments, such polarization tracking may include determination, as a function of time, of the angles θ and ϕ. In some other embodiments, such polarization tracking may include determination, as a function of time, of the Stokes parameters S 1 ′, S 2 ′, and S 3 ′ of the normalized Stokes vector S′=(1 S 1 ′ S 2 ′ S 3 ′) T , where the superscript T means transposed. In yet some other embodiments, such polarization tracking may include determination, as a function of time, of the Stokes parameters S 0 =P, S 1 , S 2 , and S 3  of the non-normalized Stokes vector S=(S 0  S 1  S 2  S 3 ) T . 
     In an example embodiment, DSP  460  ( FIG.  4   ) may be programmed based on the following simplified model of the optical channel corresponding to the probe light of frequency f s  in system  100  (also see  FIGS.  2 - 3   ). 
     For simplification, let us assume that the downlink optical signal  224  generated by SLTE unit  110   2  ( FIG.  1   ) has a fixed linear polarization, which can be denoted as the X polarization. In this case, the Jones vector of the downlink optical signal  224  at SLTE unit  110   2  can be expressed as (E x   t  0) T , where E x   t  is given by Eq. (5):
 
 E   x   t   =A ·exp( j φ)  (5)
 
where A is a constant amplitude; and φ is the phase of signal  224 . After propagating through wet cable plant  104 , the downlink optical signal  224  is received by optical receiver  270  of SLTE unit  110   1  as downlink optical signal  274  (also see  FIG.  2   ). Using Eqs. (1)-(2), the Jones vector (E x   r  E y   r ) T  of this downlink optical signal  274  can be expressed as follows:
 
 E   x   r =cos(θ)· A ·exp( j φ)  (6a)
 
 E   y   r =sin(θ)· A ·exp( jφ+j ϕ)  (6b)
 
The Jones vector (E x   LO  E y   LO ) T  of the OLO signal  408  can be expressed as follows:
 
 E   x   LO   =E   y   LO   =B ·exp( jδ+j 2π·Δ f·t )  (7)
 
where B is a constant amplitude; δ is the phase of signal  408 ; Δf is the frequency difference between the frequencies f LO  and f s  as already indicated above; and t is time.
 
     Using Eqs. (6)-(7), the electric fields E 1 -E 4  of the mixed optical signals  428   1 - 428   4 , respectively, can be expressed as follows:
 
 E   1 =cos(θ)· A ·exp( j φ)+ B ·exp( jδ+j 2π·Δ f·t )  (8a)
 
 E   2 =cos(θ)· A ·exp( j φ)− B ·exp( jδ+j 2π·Δ f·t )  (8b)
 
 E   3 =sin(θ)· A ·exp( jφ+j ϕ)+ B ·exp( jδ+j 2π·Δ f·t )  (8c)
 
 E   4 =sin(θ)· A ·exp( jφ+j ϕ)− B ·exp( jδ+j 2π·Δ f·t )  (8d)
 
The electrical signals  432   1  and  432   2  can then be expressed as follows:
 
 H   x   =|E   1 | 2   −|E   2 | 2   (9a)
 
 H   y   =|E   3 | 2   −|E   4 | 2   (9b)
 
where H x  denotes the electrical signal  432   1 ; H y  denotes the electrical signal  432   2 ; and the expressions for E 1 -E 4  are given by Eqs. (8a)-(8d), respectively. For simplification, the optical-to-electrical conversion coefficient is omitted (i.e., is set to one). Expansion of Eqs. (9a) and (9b) with Eqs. (8a)-(8d) reveals that each of H x  and H y  has two spectral components located at the frequencies +Δf and −Δf, respectively. The negative-frequency components of H x  and H y  can be rejected, e.g., using a suitable SSB filter (see, e.g.,  610 ,  FIG.  6   ), which will only pass the positive-frequency components I x  and I y  of signals H x  and H y , respectively, for further processing. Herein, SSB stands for “single sideband.” It can be verified using Eqs. (8)-(9) that I x  and I y  can be expressed as follows:
 
 I   x =SSB( H   x )=2 AB ·cos(θ)·exp( jφ+jδ+j 2π·Δ f·t )  (10a)
 
 I   y =SSB( H   y )=2 AB ·sin(θ)·exp( jφ+jϕ+jδ+j 2π·Δ f·t )  (10b)
 
Using Eqs. (4a)-(4c) and (10a)-(10b), it can further be verified that the non-normalized Stokes vector S=(S 0  S 1  S 2  S 3 ) T  of optical signal  274  can be computed as follows:
 
 S   0   =|I   x | 2   +|I   y | 2   (11a)
 
 S   1   =|I   x | 2   −|I   y | 2   (11b)
 
 S   2 =2 Re( I   x ·( I   y )*)  (11c)
 
 S   3 =−2 Im( I   x ·( I   y )*)  (11d)
 
where the “*” symbol in the superscript denotes complex conjugation. The normalized Stokes vector S′=(1 S 1 ′ S 2 ′ S 3 ′) T  can then be computed by dividing the components of the resulting non-normalized Stokes vector S by the value of S 0  computed using Eq. (11a).
 
     In an example embodiment, ADCs  450   1  and  450   2  can be clocked to operate at a relatively high sampling rate, e.g., 10 9  samples/second or higher. As a result, the Stokes parameters can be updated by DSP  460  at a fast rate to enable polarization tracking with a relatively high time resolution, thereby providing a sufficient volume of SOP-tracking data for accurately extracting therefrom the relevant characteristics of the SOP dynamics and/or kinetics. 
     Mechanical disturbances  190  typically cause the SOP to be modulated with characteristic frequencies in the range between approximately 0.1 Hz and approximately 2 Hz. The amplitude of the corresponding frequency components may be related to the amplitude of mechanical disturbances  190 . For example, in one possible approximation, a linear dependence of the amplitude of such frequency components on the magnitude of the corresponding earthquake may be assumed for a fixed distance to the epicenter. The attenuation of mechanical disturbances  190  with an increase of the distance to the epicenter may also be incorporated into the signal processing, e.g., as known in the pertinent art. 
       FIG.  6    shows a block diagram of DSP  460  according to an embodiment. Digital signals  452   1  and  452   2  and control signal  462  are also shown in  FIG.  6    to better illustrate the relationship between the circuits of  FIGS.  4  and  6   . 
     As shown in  FIG.  6   , DSP  460  comprises SSB filters  610   1  and  610   2  connected to receive digital signals  452   1  and  452   2 , respectively. In an example embodiment, each of SSB filters  610   1  and  610   2  operates to convert the received real-valued digital signal  452   i  into a corresponding complex-valued digital signal  612   i , where i=1, 2. For a real-valued time-dependent signal a(t), the transfer function L(⋅) of the SSB filter can be related to the Hilbert transform {tilde over (H)} as follows: 
                     L   ⁡   (     a   ⁡   (   t   )     )     =       1   2     [       a   ⁡   (   t   )     +     j   ⁢       H   ~     (     a   ⁡   (   t   )     )         ]             (   12   )               
A spectral transfer function of the SSB filter  610   i  is approximately the Heaviside step function having the 0-1 transition thereof at the zero frequency.
 
     DSP  460  further comprises squaring circuits  620   1  and  620   2 , a conjugation circuit  624 , an SOP circuit  630 , a band-pass filter  640 , and a signal analyzer  650 . 
     Squaring circuit  620   i  operates to compute a square of the absolute value of each complex value provided by digital signal  612   i , thereby generating a corresponding real-valued digital signal  622   i . 
     Conjugation circuit  624  outputs a conjugated value in response to each complex value provided by digital signal  612   2 , thereby generating a corresponding complex-valued digital signal  626 . 
     SOP circuit  630  uses the received digital signals  612   1 ,  622   1 ,  622   2 , and  624  to compute three streams of digital values, which are labeled in  FIG.  6    as S 1 ′, S 2 ′, and S 3 ′, respectively. Each of those digital values is proportional to the corresponding one of the Stokes parameters S 1 ′, S 2 ′, and S 3 ′ of the normalized Stokes vector S′=(1 S 1 ′ S 2 ′ S 3 ′) T  In one example embodiment, this computation can be performed in SOP circuit  630  in accordance with Eqs. (4) and (11). In another example embodiment, this computation can be performed in SOP circuit  630  in accordance with Eqs. (11b)-(11d). The latter embodiment can be used, e.g., when laser  222  is a relatively stable CW laser generating optical signal  224  having a substantially constant output power. 
     Band-pass filter  640  operates to digitally filter digital signals S 1 ′, S 2 ′, and S 3 ′ to pass through only the frequency components  642   1 - 642   3  of these signals that are spectrally located within the pass band of the filter. In an example embodiment, the pass band of filter  640  may be between approximately 0.1 Hz and approximately 2 Hz. In some embodiments, band-pass filter  640  may be tunable, e.g., capable of controllably changing one or both of the upper and lower boundaries of the pass band thereof. 
     Signal analyzer  650  operates to process digital signals  642   1 - 642   3  to generate control signal  462 . In an example embodiment, the signal processing implemented in signal analyzer  650  may include the steps of: (i) computing an earthquake indicator P(t) in response to digital signals  642   1 - 642   3 ; (ii) comparing the earthquake indicator with a threshold value; (iii) recording and time-stamping the instances in which the earthquake indicator P(t) exceeds the threshold value; (iv) determining a maximum value of the earthquake indicator P(t) over a time interval; and (iv) reporting observations and measurements to an appropriate control entity (e.g.,  710 ,  FIG.  7   ) via control signal  462 . 
     In an example embodiment, signal analyzer  650  may be programmed to compute the earthquake indicator P(t) as follows:
 
 P ( t )=| F   1 ( t )|+| F   2 ( t )|+| F   3 ( t )|  (13)
 
where F 1 (t) represents the band-pass-filtered digital signal S 1 ′; F 2 (t) represents the band-pass-filtered digital signal S 2 ′; F 3 (t) represents the band-pass-filtered digital signal S 3 ′; and t is time. The maximum value of the earthquake indicator P(t) can be used, e.g., to estimate the magnitude of the corresponding earthquake, e.g., as described below in reference to  FIGS.  7 - 8   .
 
     Let us assume that the earthquake indicator P U (t) that is being computed at the uplink optical receiver  270  (located at landing station  102   2 ,  FIG.  1   ) reaches or exceeds the threshold value P 0,U  (i.e., P U (t)≥P 0,U ) at the time stamp to (i.e., at t=t U ). Then, the time t 0  at which mechanical disturbances  190  hit the corresponding fiber span  140  can be estimated as follows: 
                     t   0     =       t   U     -         n   f     ·     D   2       c               (   14   )               
where n f  is the effective refractive index of the fiber; D 2  is the fiber length between landing station  102   2  and the location at which the mechanical disturbances  190  first hit the fiber (also see  FIG.  1   ); and c is the speed of light. Similarly, at the downlink optical receiver  270  (located at landing station  102   1 ,  FIG.  1   ), the time to can be estimated as follows:
 
                     t   0     =       t   D     -         n   f     ·     D   1       c               (   15   )               
where t D  is the time stamp at which the earthquake indicator P D (t) that is being computed at the downlink optical receiver  270  reaches or exceeds the threshold value P 0,D  (i.e., P D (t)≥P 0,D ); and D 1  is the fiber length between landing station  102   1  and the location at which the mechanical disturbances  190  first hit the fiber (also see  FIG.  1   ). Combining Eqs. (14) and (15), one obtains the following equation:
 
                     t   0     =       1   2     ⁢     (       t   D     +     t   U     -         n   f     ·   Z     c       )               (   16   )               
where Z is the total length of optical fiber between landing stations  102   1  and  102   2  at different or opposite ends of the same optical fiber link. Since all quantities in the right-hand part of Eq. (16) are observable or known, Eq. (16) can be used to determine to. Eqs. (14) and (15) can then be used to determine the lengths D 1  and D 2 .
 
       FIG.  7    shows a block diagram of a portion  700  of a fiber-optic network in which some embodiments may be practiced. Network  700  comprises landing stations LS 1 , LS 2 , and LS 3 . Landing stations LS 1  and LS 2  are connected via a fiber-optic link  740   A . Landing stations LS 2  and LS 3  are connected via a fiber-optic link  740   B . Network  700  further comprises an electronic (e.g., digital) analyzer  710  connected to landing stations LS 1 , LS 2 , and LS 3  via control links  720   1 ,  720   2 , and  720   3 , respectively. In case of an earthquake, network  700  can be used to determine the geo-location E of the earthquake epicenter and to estimate the magnitude of the earthquake, e.g., using method  800  ( FIG.  8   ). For example, the resulting pressure or displacement waves may spherically radiate from the epicenter, as illustrated, but terrestrial surface features may cause the radiating waves to have differently shaped wave-surfaces, which could be taken into account in an embodiment of method  800  ( FIG.  8   ). In an example embodiment, each of landing stations LS 1 , LS 2 , and LS 3  may be analogous to the above-described landing station  102   i  ( FIG.  1   ). In some embodiments, electronic analyzer  710  may be located at a corresponding control entity (e.g., a network controller)  708 . In alternative embodiments, other locations of electronic analyzer  710  may also be possible, including distributed configurations in which different parts of the electronic analyzer are placed at two or more different, relatively distanced locations. 
     In an example embodiment, electronic analyzer  710  has appropriate circuitry, e.g., a digital processor  712 , configured to process the received SOP measurements to characterize an earthquake. 
     In some embodiments, the corresponding fiber-optic network may comprise additional landing stations LS and/or additional fiber-optic links  740  (not explicitly shown in  FIG.  7   ). For example, the two or more optical fiber links used to sense an earthquake may not share a landing station as in  FIG.  8    so that measurements at four or more landing stations may be used to characterize an earthquake using method  800  ( FIG.  8   ). Depending on the relative location of the earthquake epicenter E and the network topology, a suitable subset of the landing stations LS and fiber-optic links  740  may be selected for executing method  800  or other suitable method. For example, a triangulation method may be used when the selected subset of fiber-optic links  740  has three or more links. 
       FIG.  8    shows a flowchart of an example signal-processing method  800  that can be used in network  700  according to an embodiment. Method  800  is described below with continued reference to  FIG.  7   . The execution of method  800  can be triggered, e.g., by mechanical disturbances  190  emanating from the epicenter E of a sufficiently strong earthquake (also see  FIGS.  1  and  7   ). 
     At step  802  of method  800 , optical receivers  270  located at landing stations LS 1 , LS 2 , and LS 3  detect an event in which the corresponding earthquake indicators P(t) (see, e.g., Eq. (13)) exceed the relevant threshold(s) in response to the mechanical disturbances  190  reaching the fiber-optic links  740   A  and  740   B . 
     At step  804 , landing stations LS 1 , LS 2 , and LS 3  use control links  720   1 ,  720   2 , and  720   3 , respectively, to provide the relevant measurements of the event to electronic analyzer  710 . In an example embodiment, landing stations LS 1 , LS 2 , and LS 3  may collectively provide to electronic analyzer  710  the following measured parameters: (i) the time stamps t U  and t D  corresponding to fiber-optic link  740   A ; (ii) the maximum value P UA  of the earthquake indicator P(t) observed for the uplink direction of fiber-optic link  740   A ; (iii) the maximum value P DA  of the earthquake indicator P(t) observed for the downlink direction of fiber-optic link  740   A ; (iv) the time stamps t U  and t D  corresponding to fiber-optic link  740   B ; (v) the maximum value P UB  of the earthquake indicator P(t) observed for the uplink direction of fiber-optic link  740   B ; and (vi) the maximum value P DB  of the earthquake indicator P(t) observed for the downlink direction of fiber-optic link  740   B . 
     At step  806 , electronic analyzer  710  uses the time stamps provided thereto at step  804  to determine the locations of points A and B along the fiber-optic links  740   A  and  740   B , respectively (also see  FIG.  7   ). More specifically, point A is the location along the fiber-optic link  740   A  that is hit first by the mechanical disturbances  190 . Similarly, point B is the location along the fiber-optic link  740   B  that is hit first by the mechanical disturbances  190 . The location of point A can be determined, e.g., using Eqs. (14)-(16) and the received time stamps t U  and t D  corresponding to the fiber-optic link  740   A . The location of point B can similarly be determined, e.g., using Eqs. (14)-(16) and the received time stamps t U  and t D  corresponding to the fiber-optic link  740   B . 
     At step  808 , electronic analyzer  710  uses the geo-locations of the points A and B inferred from the processing performed at step  806  and the map of network  700  to determine the geo-location of the epicenter E. In the shown example, the geo-location of the epicenter E is determined as the intersection of lines  702   A  and  702   B , wherein the line  702   A  is locally orthogonal to the fiber-optic link  740   A  at point A, and the line  702   B  is locally orthogonal to the fiber-optic link  740   B  at point B. 
     In alternative embodiments of step  808 , electronic analyzer  710  may use the geo-locations of the points A, B, and one or more analogous points corresponding to additional fiber-optic links  740  to determine the geo-location of the epicenter E by triangulation. 
     At step  810 , electronic analyzer  710  uses the maximum values P DA , P UA , P DB , and P UB  of the earthquake indicators P(t) to estimate the Richter scale magnitude of the earthquake. In an example embodiment, step  810  may comprise the sub-steps of: (i) scaling the maximum values P DA , P UA , P DB , and P UB  by the respective scaling factors representing the estimated attenuation of the seismic waves along the respective propagation paths from the epicenter E determined at step  808  to the incidence points A and B determined at step  806 ; (ii) averaging the scaled maximum values computed at sub-step (i); and (iii) converting the average value computed at sub-step (ii) into the corresponding Richter scale magnitude. In an example embodiment, sub-step (iii) can be performed, e.g., using a look-up table compiled based on previous earthquake observations for which the Richter scale magnitudes were also measured by conventional seismological means. 
     At step  812 , the geo-location of the epicenter E determined at step  808  and the Richter scale magnitude determined at step  810  are used, in a conventional manner, to forecast the expected tsunami magnitudes for the affected costal communities. If a significant tsunami wave is being forecast, then appropriate tsunami warnings may be issued, e.g., by way of network controller  708 . 
     According to an example embodiment disclosed above, e.g., in the summary section and/or in reference to any one or any combination of some or all of  FIGS.  1 - 8   , provided is an apparatus to provide information on earthquakes, the apparatus comprising: an electronic analyzer (e.g.,  710 ,  FIG.  7   ) connected (e.g., via  720 ,  FIG.  7   ) to receive measurements of states of polarization of pairs of light beams, the light beams of each one of the pairs of light beams having traveled in opposite directions between a respective pair of network nodes (e.g., LS 1 , LS 2 ,  FIG.  7   ) via a respective optical fiber cable (e.g.,  740 ,  FIG.  7   ) end-connecting the respective pair of network nodes, different ones of the pairs of light beams having traveled over different ones of the respective optical fiber cables; and wherein the electronic analyzer has circuitry (e.g.,  712 ,  FIG.  7   ) configured to characterize one of the earthquakes based on the measurements of the states of polarization of a plurality of the pairs of light beams. 
     In some embodiments of the above apparatus, the electronic analyzer is configured to estimate a region (e.g., A,  FIG.  7   ) of first receipt of seismic waves (e.g.,  190 ,  FIG.  7   ) of an earthquake at one (e.g.,  740   A ,  FIG.  7   ) of the optical fiber cables based on the measurements of states of polarization of the light beams received at both network nodes (e.g., LS 1 , LS 2 ,  FIG.  7   ) end-connected by the one of the optical fiber cables. 
     In some embodiments of any of the above apparatus, the first receipt is identified by a measure of state of polarization (e.g., P(t), Eq. (13)) having an above-threshold frequency component spectrally below about 1 Hertz. 
     In some embodiments of any of the above apparatus, the electronic analyzer is configured to estimate a time (e.g., t 0 , Eq. (16)) of the first receipt of seismic waves of the earthquake at the one of the optical fiber cables based on the measurements of states of polarization of the light beams received at the both network nodes. 
     In some embodiments of any of the above apparatus, the electronic analyzer is configured to identify an epicenter (e.g., E,  FIG.  7   ) of the earthquake by estimating regions (e.g., A, B,  FIG.  7   ) of first receipt of the seismic waves of the earthquake at two or more of the optical fiber cables (e.g.,  740   A ,  740   B ,  FIG.  7   ) based on the measurements of states of polarization of the light beams traveled over the two or more of the optical fiber cables. 
     In some embodiments of any of the above apparatus, the electronic analyzer is configured to estimate a time of first receipt of seismic waves of an earthquake at one of the optical fiber cables based on the measurements of states of polarization of the light beams received at both network nodes end-connected by the one of the optical fiber cables. 
     In some embodiments of any of the above apparatus, each of the measurements of a particular one of the received light beams measures mixtures of the particular one of the light beams with light of an optical local oscillator (e.g.,  408 ,  FIG.  4   ). 
     In some embodiments of the above apparatus, the apparatus further comprises one or more filters (e.g.,  640 ,  FIG.  6   ) to remove from the measurements frequency components spectrally higher than about 1 Hertz. 
     In some embodiments of any of the above apparatus, each particular pair of the network nodes is configured to optically communicate data therebetween via optical wavelength channels different from a wavelength channel carrying the light beams between the particular pair of optical nodes. 
     In some embodiments of any of the above apparatus, the light beams are not modulated to carry data streams. 
     According to another example embodiment disclosed above, e.g., in the summary section and/or in reference to any one or any combination of some or all of  FIGS.  1 - 8   , provided is a machine-implemented method of providing information on earthquakes, the machine-implemented method comprising the steps of: (A) receiving (e.g., at  804 ,  FIG.  8   ) measurements of states of polarization of pairs of light beams, the light beams of each one of the pairs of light beams having traveled in opposite directions between a respective pair of network nodes (e.g., LS 1 , LS 2 ,  FIG.  7   ) via a respective optical fiber cable (e.g.,  740 ,  FIG.  7   ) end-connecting the respective pair of network nodes, different ones of the pairs of light beams having traveled over different ones of the respective optical fiber cables; and (B) processing (e.g., at  806 - 812 ,  FIG.  8   ), in electronic circuitry (e.g.,  712 ,  FIG.  7   ), the measurements of the states of polarization of a plurality of the pairs of light beams to characterize one of the earthquakes. 
     According to yet another example embodiment disclosed above, e.g., in the summary section and/or in reference to any one or any combination of some or all of  FIGS.  1 - 8   , provided is an apparatus comprising: an optical wavelength demultiplexer (e.g.,  280 ,  FIG.  2   ) having a plurality of pass bands (e.g.,  310 ,  FIG.  3   ) to demultiplex optical signals received through an optical fiber (e.g.,  140 ,  FIG.  1   ;  740   A ,  FIG.  7   ); a first optical receiver (e.g.,  260   n ,  FIG.  2   ) connected to the optical wavelength demultiplexer to receive a data-modulated optical signal (e.g.,  262 ,  FIG.  2   ); and a second optical receiver (e.g.,  270 ,  FIG.  2   ) connected to the optical wavelength demultiplexer to obtain time-resolved measurements of Stokes parameters of an optical-probe signal (e.g.,  274 ,  FIG.  2   ), both of the data-modulated optical signal and the optical-probe signal passing through one of the pass bands of the optical wavelength demultiplexer; and wherein the second optical receiver comprises a digital band-pass filter (e.g.,  640 ,  FIG.  6   ) to filter streams of the time-resolved measurements to select frequency components of the streams corresponding to seismic disturbance of the optical fiber. 
     In some embodiments of the above apparatus, the apparatus further comprises a plurality of third optical receivers (e.g.,  260   3 - 260   n-1 ,  FIG.  2   ) connected to receive respective data-modulated optical signals (e.g.,  266   3 - 266   n-1 ,  FIG.  2   ) through different respective ones of the pass bands of the optical wavelength demultiplexer. 
     In some embodiments of any of the above apparatus, each of the first optical receiver and the third optical receivers is configured to recover data encoded in a corresponding one of the data-modulated optical signals. 
     In some embodiments of any of the above apparatus, a carrier frequency (e.g., f s ,  FIG.  3   ) of the optical-probe signal is different from a center frequency (e.g., f n ,  FIG.  3   ) of the data-modulated optical signal. 
     In some embodiments of any of the above apparatus, a carrier frequency (e.g., f s ,  FIG.  3   ) of the optical-probe signal is spectrally located at a spectral edge of the data-modulated optical signal (e.g., as shown in  FIG.  3   ). 
     In some embodiments of any of the above apparatus, a carrier frequency (e.g., f s ,  FIG.  3   ) of the optical-probe signal is spectrally located outside a spectral envelope (e.g.,  212 ,  FIG.  3   ) of the data-modulated optical signal (e.g., as shown in  FIG.  3   ). 
     In some embodiments of any of the above apparatus, the second optical receiver comprises an optical local oscillator (e.g.,  406 ,  FIG.  4   ) for coherently detecting the optical-probe signal. 
     In some embodiments of any of the above apparatus, the second optical receiver is configured to: compute an earthquake indicator (e.g., P(t), Eq. (13)) based on the selected frequency components of the streams; and record and time-stamp a value of the earthquake indicator if said value exceeds a fixed threshold value. 
     In some embodiments of any of the above apparatus, the apparatus further comprises an electronic analyzer (e.g.,  710 ,  FIG.  7   ) connected (e.g., via  720   1 ,  FIG.  7   ) to receive the time-stamped value of the earthquake indicator from the second optical receiver and further connected to receive (e.g., via  720   2 ,  FIG.  7   ) another time-stamped value of the earthquake indicator from a network node (e.g., LS 2 ,  FIG.  7   ); and wherein the optical wavelength demultiplexer and the network node are end-connected to opposite ends of the optical fiber (e.g.,  740   A ,  FIG.  7   ). 
     In some embodiments of any of the above apparatus, the electronic analyzer is configured to determine (e.g.,  808 ,  FIG.  8   ) a geo-location (e.g., E,  FIG.  7   ) of an earthquake epicenter based on said received time-stamped values of the earthquake indicator. 
     In some embodiments of any of the above apparatus, the electronic analyzer is configured to estimate (e.g.,  810 ,  FIG.  8   ), based on said received time-stamped values of the earthquake indicator, a Richter-scale magnitude of an earthquake. 
     In some embodiments of any of the above apparatus, the electronic analyzer is configured to generate (e.g.,  812 ,  FIG.  8   ) a forecast of tsunami waves based on said received time-stamped values of the earthquake indicator. 
     In some embodiments of any of the above apparatus, the optical-probe signal is a continuous-wave optical signal. 
     In some embodiments of any of the above apparatus, the digital band-pass filter has a pass band between 0.1 Hz and 1 Hz. 
     In some embodiments of any of the above apparatus, the digital band-pass filter is tunable. 
     While this disclosure includes references to illustrative embodiments, this specification is not intended to be construed in a limiting sense. Various modifications of the described embodiments, as well as other embodiments within the scope of the disclosure, which are apparent to persons skilled in the art to which the disclosure pertains are deemed to lie within the principle and scope of the disclosure, e.g., as expressed in the following claims. 
     Unless explicitly stated otherwise, each numerical value and range should be interpreted as being approximate as if the word “about” or “approximately” preceded the value or range. 
     It will be further understood that various changes in the details, materials, and arrangements of the parts which have been described and illustrated in order to explain the nature of this disclosure may be made by those skilled in the art without departing from the scope of the disclosure, e.g., as expressed in the following claims. 
     The use of figure numbers and/or figure reference labels in the claims is intended to identify one or more possible embodiments of the claimed subject matter in order to facilitate the interpretation of the claims. Such use is not to be construed as necessarily limiting the scope of those claims to the embodiments shown in the corresponding figures. 
     Although the elements in the following method claims, if any, are recited in a particular sequence with corresponding labeling, unless the claim recitations otherwise imply a particular sequence for implementing some or all of those elements, those elements are not necessarily intended to be limited to being implemented in that particular sequence. 
     Reference herein to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the disclosure. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments necessarily mutually exclusive of other embodiments. The same applies to the term “implementation.” 
     Unless otherwise specified herein, the use of the ordinal adjectives “first,” “second,” “third,” etc., to refer to an object of a plurality of like objects merely indicates that different instances of such like objects are being referred to, and is not intended to imply that the like objects so referred-to have to be in a corresponding order or sequence, either temporally, spatially, in ranking, or in any other manner. 
     Unless otherwise specified herein, in addition to its plain meaning, the conjunction “if” may also or alternatively be construed to mean “when” or “upon” or “in response to determining” or “in response to detecting,” which construal may depend on the corresponding specific context. For example, the phrase “if it is determined” or “if [a stated condition] is detected” may be construed to mean “upon determining” or “in response to determining” or “upon detecting [the stated condition or event]” or “in response to detecting [the stated condition or event].” 
     Also for purposes of this description, the terms “couple,” “coupling,” “coupled,” “connect,” “connecting,” or “connected” refer to any manner known in the art or later developed in which energy is allowed to be transferred between two or more elements, and the interposition of one or more additional elements is contemplated, although not required. Conversely, the terms “directly coupled,” “directly connected,” etc., imply the absence of such additional elements. 
     As used herein in reference to an element and a standard, the term compatible means that the element communicates with other elements in a manner wholly or partially specified by the standard, and would be recognized by other elements as sufficiently capable of communicating with the other elements in the manner specified by the standard. The compatible element does not need to operate internally in a manner specified by the standard. 
     The described embodiments are to be considered in all respects as only illustrative and not restrictive. In particular, the scope of the disclosure is indicated by the appended claims rather than by the description and figures herein. All changes that come within the meaning and range of equivalency of the claims are to be embraced within their scope. 
     The description and drawings merely illustrate the principles of the disclosure. It will thus be appreciated that those of ordinary skill in the art will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the disclosure and are included within its spirit and scope. Furthermore, all examples recited herein are principally intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the disclosure and the concepts contributed by the inventor(s) to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the disclosure, as well as specific examples thereof, are intended to encompass equivalents thereof. 
     The functions of the various elements shown in the figures, including any functional blocks labeled as “processors” and/or “controllers,” may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software. When provided by a processor, the functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared. Moreover, explicit use of the term “processor” or “controller” should not be construed to refer exclusively to hardware capable of executing software, and may implicitly include, without limitation, digital signal processor (DSP) hardware, network processor, application specific integrated circuit (ASIC), field programmable gate array (FPGA), read only memory (ROM) for storing software, random access memory (RAM), and non volatile storage. Other hardware, conventional and/or custom, may also be included. Similarly, any switches shown in the figures are conceptual only. Their function may be carried out through the operation of program logic, through dedicated logic, through the interaction of program control and dedicated logic, or even manually, the particular technique being selectable by the implementer as more specifically understood from the context. 
     As used in this application, the term “circuitry” may refer to one or more or all of the following: (a) hardware-only circuit implementations (such as implementations in only analog and/or digital circuitry); (b) combinations of hardware circuits and software, such as (as applicable): (i) a combination of analog and/or digital hardware circuit(s) with software/firmware and (ii) any portions of hardware processor(s) with software (including digital signal processor(s)), software, and memory(ies) that work together to cause an apparatus, such as a mobile phone or server, to perform various functions); and (c) hardware circuit(s) and or processor(s), such as a microprocessor(s) or a portion of a microprocessor(s), that requires software (e.g., firmware) for operation, but the software may not be present when it is not needed for operation.” This definition of circuitry applies to all uses of this term in this application, including in any claims. As a further example, as used in this application, the term circuitry also covers an implementation of merely a hardware circuit or processor (or multiple processors) or portion of a hardware circuit or processor and its (or their) accompanying software and/or firmware. The term circuitry also covers, for example and if applicable to the particular claim element, a baseband integrated circuit or processor integrated circuit for a mobile device or a similar integrated circuit in server, a cellular network device, or other computing or network device. 
     It should be appreciated by those of ordinary skill in the art that any block diagrams herein represent conceptual views of illustrative circuitry embodying the principles of the disclosure. Similarly, it will be appreciated that any flow charts, flow diagrams, state transition diagrams, pseudo code, and the like represent various processes which may be substantially represented in computer readable medium and so executed by a computer or processor, whether or not such computer or processor is explicitly shown. 
     “SUMMARY OF SOME SPECIFIC EMBODIMENTS” in this specification is intended to introduce some example embodiments, with additional embodiments being described in “DETAILED DESCRIPTION” and/or in reference to one or more drawings. “SUMMARY OF SOME SPECIFIC EMBODIMENTS” is not intended to identify essential elements or features of the claimed subject matter, nor is it intended to limit the scope of the claimed subject matter.