Multi-GNSS Vertical Total Electron Content Estimates: Data

Analysis and Machine Learning with Python to Evaluate

Ionospheric Perturbations from Earthquakes

Derry Holding1

1Independent Researcher, Holding Engineering Consultancy, Frankfurt, Germany

July 29, 2017

Abstract

Today, Global Navigation Satellite System (GNSS) observations are routinely used to study the phys-ical processes that occur within the Earth’s upper atmosphere. Due to the experienced satellite signalpropagation effects the total electron content (TEC) in the ionosphere can be estimated and the derivedGlobal Ionosphere Maps (GIMs) provide an important contribution to monitoring space weather. Whilelarge TEC variations are mainly associated with solar activity, small ionospheric perturbations can alsobe induced by physical processes such as acoustic, gravity and Rayleigh waves, often generated by largeearthquakes.

In this study Ionospheric perturbations caused by four earthquake events have been observed andare subsequently used as case studies in order to validate an in-house software developed using the Pythonprogramming language. The Python libraries primarily utlised are Pandas, Scikit-Learn, Matplotlib, SciPy,NumPy, Basemap, and ObsPy. A combination of Machine Learning and Data Analysis techniques have beenapplied. This in-house software can parse both receiver independent exchange format (RINEX) versions 2and 3 raw data, with particular emphasis on multi-GNSS observables from GPS, GLONASS and Galileo.BDS compatibility is to be added in the near future.

Several case studies focus on four recent earthquakes measuring above a moment magnitude (MW) of 7.0and include: the 11 March 2011 MW 9.1 Tohoku, Japan, earthquake that also generated a tsunami; the 17November 2013 MW 7.8 South Scotia Ridge Transform (SSRT), Scotia Sea earthquake; the 19 August 2016MW 7.4 North Scotia Ridge Transform (NSRT) earthquake; and the 13 November 2016 MW 7.8 Kaikoura,New Zealand, earthquake.

Ionospheric disturbances generated by all four earthquakes have been observed by looking at the esti-mated vertical TEC (VTEC) and residual VTEC values. The results generated from these case studies aresimilar to those of published studies and validate the integrity of the in-house software.

1 Introduction

Natural hazards such as earthquakes, tsunamis andvolcanic eruptions pose grave threats to humans.Global Navigation Satellite Systems (GNSS) satel-lites can act as a primary sensor to identify charac-

teristic signatures caused by natural hazards. Thesesignatures come in the form of crustal deformationmeasurements and atmosphere-ionosphere coupling.At ionospheric altitudes the presence of neutral par-ticles and ions enables electron density fluctuations[17]. Empirical data retrieved from a high-end GNSS

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receiver can be utilized in such a way to manipulatethe observations and so producing geometry-free ob-servables that ultimately detect ionospheric distur-bances caused by seismic activity.

In recent years several severe tsunamis and earth-quakes have highlighted the necessity for effectiveand robust method modeling as well as providing astable observational system that identifies the char-acteristic of an impending tsunami or TEC pertur-bations in the ionosphere caused by seismic activity.

Measurement data obtained from GNSS receivers,configured to collate observables from BeiDou,Galileo, GLONASS and GPS, have proven to bea resourceful method for remote sensing the iono-sphere [4]. Many delays contribute to errors in GNSSpositioning, such as the receiver and clock offsets,and multipath. However one of the largest errorsin GNSS positioning is attributable to the delay inthe atmosphere. The GNSS signal from the satel-lite traverses through the vacuum of space until itreaches the Earth’s atmosphere. Upon reaching theEarth’s atmosphere, in particular the ionosphere, theGNSS signal experiences refraction, diffraction, anda decrease in the apparent speed. Subsequently thisinduces an apparent delay of the transit time of thesignal from the satellite to the receiver.

Computation of the differential phase of the codeand carrier measurements retrieved from a GNSS re-ceiver subsequently enables the calculation of theionospheric delay, in particular the TEC. Numer-ous studies have already been carried out investi-gating the ionospheric TEC perturbations followinga major seismic event by a dense network of ground-based GNSS receivers. Throughout history mankindhas regularly suffered from natural disasters such asthe devastation caused be earthquakes and tsunamis.The Sumatra tsunami of 2004 claimed the lives ofa staggering 228,000 people, and more recently thedeath toll following the Tohoku earthquake of 2011was approximately 16,000 [10].

On 11 March 2011 at 5:46:23 Universal Time (UT)a magnitude MW 9.0 earthquake struck off the coastof Japan causing widespread devastation affectingthe northern region of Tohoku as well as triggeringoff a major tsunami [11].

Several observations have already been published

demonstrating that earthquakes and tsunamis pro-duce gravity and acoustic waves that transcend upto the ionosphere influencing fluctuations in elec-tron density in the F region. Previous studies haveshown that atmospheric gravity waves generated bytsunamis may be detected as traveling ionosphericdisturbances (TIDs), which in turn can also be iden-tified via TEC measurements retrieved from GNSSobservations [11]. The ionospheric signature gener-ated by tsunamis has frequently been demonstratedwhereby remote observations are made. There arealso sources of TIDs that are not attributed totsunamis or earthquakes, but to significant tropo-spheric weather, geomagnetic and auroral activity.This makes detection of tsunami-driven TIDs in-creasingly more challenging [10].

In order to determine the effects of seismic ac-tivity and augment previous similar studies this re-search focuses on observations on the day of a seismicevent. By doing so the geomagnetic activity alongwith TEC perturbations can be observed. Differen-tiation between regular TIDs and those induced byseismic shocks can also to be determined.

When a GNSS satellite is positioned near to thelocal horizon, its signal will first propagate throughthe ionosphere, then through the troposphere, be-fore arriving at a receiver. A GNSS receiver con-figured to collect measurements with a 10◦ eleva-tion cut-off, and assuming a 350 km ionosphericshell height would have a distance between theionospheric pierce point (IPP) and the receiver of1900 km. For 15◦ elevation cut-off, this distance isapproximately 1300 km. Consequently the geome-try involved in producing the GNSS TEC measure-ments is such that a tsunami signature from a coast-line can be observed despite being hundreds of kilo-meters away from land. Current tsunami monitor-ing systems comprise tidle gauges, Deep-ocean As-sessment and Recording of Tsunamis (DART) sys-tems, and seafloor pressure recording sensors, how-ever GPS TEC observations can also assist signifi-cantly to these tsunami monitoring systems.

Several networks of ground-based GNSS receiversexist that can produce TEC observations. TheGEONET network in the Japan region consists ofa highly dense network of GNSS receivers. This

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is in contrast to the sparse GNSS receiver cover-age currently established in the South Atlantic. Forthis report, seven sites have been selected for iono-spheric behavior analysis: the MIZU site in Japan;the KEPA and KRSA sites in the South Atlantic;the HOIK, KAIK, WEST, and LKTA sites in NewZealand. This report focuses on TEC analysis withthe dual-frequency technique, with emphasis on theanalysis on the acoustic as opposed to gravity waves.

Using the obspy [5] [19] package in Python, Figure1 has been generated for the four earthquakes out-lined in Table 2, which are focused on in this casestudy. Focal mechanism (beachball) maps are fre-quently employed by seismologists to demonstratethe magnitude, characteristic, and location of anearthquake.

2 Methodology

Determining the absolute VTEC values are useful inorder to understand the background ionospheric con-ditions when looking at the TEC perturbations, how-ever small-scale variations in electron density are ofprimary interest. Quality checking processed GNSSdata, applying carrier phase leveling to the measure-ments, and comparing the TEC perturbations with apolynomial fit creating residual plots are discussed inthis section. Finally this section ends with the typesof waves and fault motions involved during and fol-lowing seismic activity.

2.1 Data Collection and Data Manip-ulation

Time delay and phase advance observables can bemeasured from dual-frequency GNSS receivers toproduce TEC data.

There exists a globally distributed network ofGNSS receivers, which among other functions, ac-curately measure the ionosphere delay. The Inter-national GNSS Service (IGS) provides high-qualityGNSS data products in order to facilitate scientific,educational, and commercial application orientatedtowards the geodetic and space community. The IGSfederation is a non-profit organization comprising

more than 200 agencies, universities, and researchinstitutions, globally. The primary aim of the IGSis to provide a highly precise GPS data set in theform of an array of IGS products, that enable sci-entific advancement and public benefit. The IGScomprises a global network of GNSS ground sta-tions, data centers, and data analysis centers. Theavailable data and derived data products are utilizedin Earth science research; positioning, navigation,and timing (PNT) applications; and education. Thepresent IGS network comprises a global network of350 GNSS receivers. The coverage of the network iswidespread but sparse [10].

Other major regional GNSS station networks alsoexist, such as the GEONET network in Japan, whichconsists of over 1200 GPS stations. The South-ern California’s Plate Boundary Observatory (PBO)network consists of over 850 GPS stations in a verydense and local coverage [10].

For the purpose of this report, RINEX (ReceiverIndependent Exchange Format) files were collatedfrom seven different sites: MIZU at Mizusawa inJapan; and KEPA and KRSA at the King EdwardPoint Geodetic Observatory; HOIK, KAIK, WEST,LKTA all based in New Zealand. The MIZU datawere retrieved from the IGS Network and the KEPAand KRSA data were retrieved via the University ofLuxembourg network. Data retrieved from HOIK,KAIK, WEST, LKTA were made available courtesyof the GeoHazard Monitoring Department, GeoNet,New Zealand. The GNSS data comprises both obser-vation and ephemeris (navigation) data. The obser-vation and ephemeris data used were of the RINEXV2 and RINEX V3 formats. The data sampling rateof the RINEX files was 1 Hz, with the exception ofthe data retrieved from the New Zeland, which hasa data sampling rate of 30 Hz

The format of how the observations are given inthe RINEX V2 and RINEX V3 versions are differ-ent. Each different format is to be handled differ-ently, and so a unique method of parsing the datafor each format is required. Data processing of theRINEX V2 data was performed with the use of aPython RINEX parsing and VTEC calculation pro-gram. Two RINEX parsers support both the RINEXV2 and RINEX V3 formats. These parsers con-

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Figure 1: Global map focusing on four recent earthquakes measuring above a moment magnitude (MW) of7.0 for this case study. For clarity, the tectonic plate boundaries are shown here in red. Information givenin the grey boxes denote the location, magnitude, and date of the earthquake. SSRT refers to South ScotiaRidge Transform; NSRT is the North Scotia Ridge Transform. Note the difference in colors between thebeachballs, where orange represents between MW 6.0 and MW 7.9, and red represents greater than or equalto a magnitude of MW 8.0

solidate the data blocks into multidimensional ar-rays, then mathematically manipulate the subse-quent multidimensional arrays, in order to plot ver-tical TEC values (VTEC) against a timeline. Typ-ically a 12 MB file will take ∼1 min to process. Aprecondition for the RINEX V2 parsing was firstnecessary. This pre-step involves retaining the GPS(GLONASS, or Galileo) data and filtering out the re-maining GNSS and SBAS systems from the RINEXV2 file. To achieve this, UNAVCOs TEQC tool wasemployed [9].

In the case of manipulating Galileo data, TEQCwas employed to include the Galileo observables on asignal-by-signal basis into a RINEX file, thus prepar-ing the RINEX data in order to be processed by thePython RINEX parsing tool.

2.2 Total Electron Content

Electromagnetic waves are influenced by refractivemediums in terms of the distance the wave traverses.

Fermat’s principle states that the path the wave tra-verses is the path that can be traversed in the quick-est time. This results in the GNSS signal’s pathbeing arched, see Figure 2.

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Figure 2: Wave bending in a refractive medium

The refractive index, n, is defined as the ratio ofthe speed of light, c, in a vacuum and the velocity ofthe wave, v, in the medium:

n =c

vwith v =

1√εµ

(1)

where:

ε permittivity of the mediumµ permeability of the mediumc is 299,792,458 ms−1

For an increment of time, dt, and distance, dS,the velocity can be shown as v = dS/dt. Using v =dS/dt with (1), then the traversed time t of a signalfrom the GNSS satellite s to receiver r is given by:

t =

s∫r

dt =

s∫r

1

vdS =

1

c

s∫r

n dS (2)

The difference between the measured range S andthe geometrical range ρ gives the delay (or advance)D, and using (2) can be shown as [15]:

D = S − ρ = c∆t

=

s∫r

n dS −s∫

r

dρ

=

s∫r

(n− 1) dρ

︸ ︷︷ ︸delay

+

s∫r

n dS −s∫

r

n dρ

︸ ︷︷ ︸bending effect

(3)

As the GNSS signal propagates through the iono-sphere, this delay is known as the ionosphere delayor ionospheric refraction. To first order, the refrac-tive index of a frequency, f, can be approximated to

nph = 1− 40.3 Ne

f2ngr = 1 +

40.3 Ne

f2(4)

and

Dph = −40.3

f2

∫Ne dρ Dgr =

40.3

f2

∫Ne dρ (5)

where:

nph phase refractivity index,ngr group refractivity index,Dph phase delay,Dgr group delay,Ne electron density.

The ionized gas disperses electromagnetic waveswithin the ionosphere, and so the refractive indexis dependent on the frequency and electron density.Dispersion in terms of pseudorange measurementsof group and phase are equal in magnitude but op-posite in sign. Since ngr > nph, it logically followsthat vgr < vph, so that the different velocities inducethe carrier phase advance and modulated code delay.In terms of GNSS, the observed code measurementsthat propagate with the group velocity are delayedand the observed carrier phase measurements thatpropagate with phase velocity are advanced. Com-paring these measurements with the geometric dis-tance between the satellite and the receiver, the code

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pseudoranges are measured too long, while the phasepseudoranges are measured too short [1].

The number of free electrons along the path of asignal from the satellite to receiver influences a radiosignal’s propagation speed. The number of free elec-trons within a tube, with cross section 1m2 extend-ing from the satellite to the receiver can be definedas the Total Electron Content (TEC) or Slant TotalElectron Content (STEC)

STEC =

R∫S

Ne dρ (6)

where Ne is the variable electron density alongthe path of the signal, and integration is along thesignal path from the satellite to receiver, dρ [21].Substituting STEC into (5) gives

Dph = −40.3

f2STEC Dgr =

40.3

f2STEC (7)

as a final representation of ionospheric refraction(ionospheric delay) to first order given in terms ofTEC, in metres. TEC is often denoted in TEC units(TECU) where [14]

1 TECU = 1016 el m−2 (8)

Navigation systems are vulnerable to TEC fluc-tuation events, where one TECU corresponds to arange delay of approximately 0.16 m and 0.54 ns onthe GPS L1 frequency [6]. The nominal range is be-tween 1016 to 1019 electrons per m2 with minimumdensity occurring at local midnight and maximumdensity at local afternoon [27].

2.3 Determining TEC from Dual-Frequency Obervables

Depending on the geographic location of the earth-quake and tsunami the station of interest can beselected. Using the Python tool, RINEX files areparsed and an STEC time series can be generated.The timeframe selected from the RINEX data is cho-sen encompassing the period just before and after theearthquake event.

Quantifying TEC is challenging simply becauseTEC depends on the electron density, which in turndepends on temporal and spatial (observation site)variations, line of sight (LOS) of the signal, andsunspot activity. This makes it difficult to find anappropriate formula to model the effects of the iono-sphere. The most efficient method to eliminate theeffect of the ionosphere is by using signals whosefrequencies differ. Primarily for this reason spacegeodetic techniques require GNSS satellites to trans-mit in at least two different frequencies [1]. A dual-frequency GNSS receiver can estimate ionosphericgroup delay and phase advance from the measure-ments. The dispersive nature of the ionosphere act-ing on GNSS signals enables elimination of the iono-spheric refraction of the observables. This assumeshowever that the second and higher order terms areneglected. The elimination of the ionospheric refrac-tion is performed by taking the ionosphere-free linearcombination of pseudorange and carrier phase mea-surements.

GPS dual-frequency carrier phase and code delayobservations are combined to obtain observables thatrelate to the TEC values along the GNSS signal’sLOS. The procedure for determining first order iono-spheric effects in GNSS measurements is performedby the geometry-free linear combination.

The geometric distance between the receiver andsatellite, and introducing an error term gives [24]

P = ρ+c(δR−δS)+c(BR−bS)+I+T+MPR+ε (9)

whereIdeally the true range of the satellite ρ, is to be

determined. Instead it is the biased and noisy mea-surement of ρ, that is, the pseudorange PS

R that isobtained. Elaborating the terms in (9) a little fur-ther:

• ρ: the true geometric range is considered tobe the geometric distance between the satel-lite’s antenna electrical phase center and the re-ceiver’s electrical phase center. The actual lo-cation of the antenna’s electrical phase centeris dependent on antenna hardware, the carrier

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ρ true geometric range between the satelliteand receiver;

δS satellite clock error due to the differencein the arbitrary timescale;

δR receiver clock error due to the differencein the arbitrary timescale;

BR code biases induced by receiver hardwaredelay;

bS code biases induced by satellite hardwaredelay;

I signal delay of the ionosphere;T signal delay of the troposphere;MPR code multipath error caused by

reflected signals;ε all unmodelled effects and receiver noise.

frequency, the azimuth and elevation of the sig-nal. The true geometric range also compensatesfor all relevant displacements, including but notlimited to ocean tide loading, earth body tides,atmospheric loading, and plate tectonics [24],

• BR and bS : GNSS satellites modulate differ-ent codes and navigation messages onto differ-ent carrier frequencies. The dispersive propertyof the ionosphere means that these codes, navi-gation messages and carrier frequencies are alsodispersed differently. The GNSS signal is imper-fectly synchronized as a result of the differentdigital and analog signal paths that correspondto each individual signal. This leads to the satel-lite biases. The receiver biases are induced bythe analog hardware and by-pass filters,

• I: the electromagnetic GNSS signal is dispersivewhen traversing through the ionosphere. Thisultimately leads to the delay of the signal. Iono-sphere delay principles are discussed in great de-tail throughout this research,

• T : the tropospheric delay comprises a dry andhydrostatic component that is dependent of thelocal atmosphere. Tropospheric refraction un-like that of the ionospheric signal delay does notdepend on the frequency of the carrier for fre-quencies used in the GNSS frequency range,

• M : The path of a GNSS signal not only takesthe route of direct line of sight, but may alsoreflect from objects in the surrounding environ-ment, such as trees or within urban canyons.The GNSS signal arrives at the GNSS receiverantenna through different paths, resulting inmultipath. The effect of multipath is muchlarger for pseudorange than for carrier phase.

The range between the satellite and the receivercan also be determined through the carrier phaseof the signal. The total number of carrier cyclesplus the fractional cycle both at the receiver and thesatellite, then multiplied by the carrier wavelength,results in the range. Ranges determined by the car-rier are more accurate compared to those obtainedfrom the pseudoranges, since the wavelength of thecarrier phase is much smaller than that of the codes.

Carrier phase measurement can be expressed as[27]:

L = ρ+ c(δR − δS) + c(DR − dS)

− I + T + P +MCP + λN + ε (10)

where

L phase measurement in unit of lengths;DR phase biases induced by receiver hardware

delay for the carrier wave;dS phase biases induced by satellite hardware

delay for the carrier wave;P phase wind-up effect;MCP phase multipath error caused by reflected

signals;λ carrier phase wavelength;N initial integer ambiguity;ε all unmodelled effects and receiver noise.

Note that the negative sign in the above equationfor the ionospheric delay. This is because for thecarrier phase traversing the ionosphere, the signalis advanced, not delayed as is the case for the codemeasurements.

The phase and pseudorange measurements, likethat in (10) and in (9) can be expressed in termsof a frequency, i, giving

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Pi = ρ+ c(δR − δS) + c(BR − bS)

+ Ii + T +MPRi + ε (11)

Li = ρ+ c(δR − δS) + c(DR − dS)

− Ii + T +MCPi + λiNi + ε (12)

where i is equal to 1, 2, and denotes the differ-ent frequencies. Corrections related to relativisticeffects, phase wind-up effect, and antenna phase cen-ter deviations are omitted from (11) and (12).

The Linear Combination (LC) enables dual-frequency receivers to measure the ionospheric delayvia its dual-frequency observations. The pseudocoderanges are determined from the measurements of thesignals P1 and P2 that are modulated on the two car-rier frequencies L1 and L2. The ionospheric termsI1 and I2 are thus identical to (7).

By combining the measurements, L1 and L2, theionospheric delay can be removed from the mea-surements and provide the LC solution. The fol-lowing observable equations comprise the dimensionof length; multipath terms and noise are not explic-itly expressed; higher-order ionospheric terms are ne-glected:

L1 = ρ− I1 + λ1N1

L2 = ρ−(f21f22

)I1 + λ2N2

P1 = ρ+ I1

P2 = ρ+

(f21f22

)I1

(13)

Where ρ is non dispersive delay and consists ofLOS, clocks and tropospheric biases; I1 is the dis-persive delay on the first frequency; and N1, N2 areinteger ambiguities on L1 and L2. For GPS the satel-lites operate on two different frequencies, f1 and f2,which are derived from the fundamental frequencyf0, of 10.23 MHz

f1 = 154× f0 = 1575.42 MHz

f2 = 120× f0 = 1227.60 MHz(14)

Since it assumed that the L1 and L2 observablestraverse along the same path through the ionosphere,then the difference in ionosphere delays betweenthese frequencies can be measured with use of a dual-frequency GPS receiver. This leads to the obtainedgroup delay as being

P2 − P1 = 40.3× TEC(

1

f22− 1

f21

)(15)

Where P1 and P2 are group path lengths corre-sponding to the f1 and f2 frequencies, respectively.Using (15) results in the TEC to be derived as

TEC =1

40.3

(f1f2f1 − f2

)(P2 − P1) (16)

where P1 and P2 are the pseudoranges measuredin L1 and L2, respectively [27] [22]. In terms ofrepresenting (16) for the GPS L1 and L2 carriers,this becomes

TEC = 9.519970× (P2 − P1) (17)

For GLONASS, determining (17) is dependent onthe frequency and so is dependent on the satellitenumber. GLONASS satellites use Frequency Di-vision Multiple Access (FDMA) modulation tech-niques unlike that of GPS and Galileo, which usesCode Division Multiple Access (CDMA).

2.4 Phase and Group Delay

Since the ionosphere is dispersive, the time delay at-tributed to the ionosphere is dependent on the sig-nal’s frequency. The dispersive nature of the iono-sphere means that the codes – which are the modu-lations on the carrier wave – are dispersed differentlycompared to the carrier phase along the signal’s paththrough the ionosphere. In terms of GPS, this meansthat the P, C/A codes and navigation message areslowed down and affected by the group delay. How-ever the carrier wave itself appears to speed up inthe ionosphere and so affected by the phase delay.Calling this increase in speed a delay is counter in-tuitive and so this term is also referred to as thephase advancement.

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Using data retrieved from the Center of Orbit De-termination in Europe (CODE) site (ftp://ftp.unibe.ch/aiub/CODE), the differential code biasesare subtracted from the ionospheric observables [18]

The geometry-free linear combination is employedto determine the ionosphere delay in terms of elec-tron density (STEC) and instrumental biases DCBC1 − C2. Currently the DCB C1 − C2 formats arenot available as a final product and so for this re-port the DCB C1 − C2 has been determined usingCODE’s products as outlined in (18)

SDCBtheoC1C2 = −SDCBP1P2 + SDCBP1C1

− SDCBP2C2 (18)

where SDCBtheoC1C2 is the theoretical value for

SDCB C1-C2. SDCBP1P2, SDCBP1C1, andSDCBP2C2 are all instrumental biases retrievedfrom CODE for SDCB P1-P2, SDCB P1-C1, andSDCB P2-C2, respectively [18].

2.5 Determining VTEC: Thin ShellMapping Function

Accurate monitoring of the ionosphere has profoundimplications in most areas of the GNSS community.The thin shell mapping function is one of the first as-sumptions to consider when ionospheric correctionsare estimated and applied from GNSS data. In manyGNSS applications the typical assumption is to con-sider a fixed mapping function constant, that is pro-jected onto a 2D distribution of electron content ata given effective height.

The main contributor to TEC variations occursat around the height whereby the ionization withinthe ionosphere is at a maximum. This maximumoccurs in the F2 layer, and so this enables a simplis-tic thin shell encompassing the Earth when model-ing the ionosphere. The thin shell mapping functionassumes that all electrons are compressed into thisspherical shell of infinitesimal thickness surroundingthe Earth. The point of intersection along the lineof sight is referred to as the ionospheric pierce point(IPP). The propagation of TIDs are represented bysubionospheric points (SIP), which are a projection

of the ionospheric pierce point (IPP) as in Figure 3,and for example in Figure 11.

Since the GNSS signal’s path length depends onthe satellite’s position in the sky, this also has aneffect on the TEC: the lower the satellite elevation,the longer the path of the signal and so the higherthe TEC value [27] [3] [7] [23] [2] [16].

Assuming no lateral electron gradients exist, TECis calculated by mapping the slant of the path sig-nal to its corresponding vertical path. So STEC isdefined as the sum of electron density Ne, along theray path, as defined in (6).

Figure 3: Propagation path through the ionosphere

The slant or obliquity factor (OF) as is known inthe Klobuchar model is applied to the TEC valueto obtain the Vertical TEC, or VTEC. The VTECvalue however does not correspond to the locationof the GNSS receiver, and due to the thin shell as-sumption it instead refers to the SIP, as shown inFigure 3. The mapping process depends on the el-evation angle, e, and its complement zenith angle,z, of the satellite. Calculating the elevation angle isperformed by the parameters given in the BroadcastEphemeris and depends on the type of GNSS un-der analysis. The method employed for the satelliteorbit determination, which in turn is used to deter-mine the elevation and azimuth for GPS, Galileo,

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and BeiDou follows a very similar process with oneanother. For GLONASS the process employed usesthe Runge–Kutta 4th order technique [8] [24].

The lower the elevation angle between a particularreceiver-satellite pair, the higher the absolute STECvalues as well as increased amplitude variations inSTEC. This is because the integration of TEC per-turbation is over a longer signal ray path at a lowerelevation angle than that of a shorter ray path at ahigher elevation angle, with the highest elevation be-ing when the satellite is located at zenith. Thereforeexaggerated fluctuations of STEC are observed atlower elevation angles than at higher ones. This doesnot however imply that seismic-driven TEC pertur-bations are deemed invalid when considering STECobservations made at lower elevation angles, howevercaution should be taken since the amplitudes of theseTEC perturbations may be artificially amplified [10].

The ionospheric shell height, H, used in ionospheremodeling has been open to debate for many yearsand typically ranges from 300 – 400 km, which cor-responds to the maximum electron density withinthe ionosphere. The mapping function compensatesfor the increased path length traversed by the sig-nal within the ionosphere. Figure 4 demonstratesthe impact of varying the IPP height on the TECvalues.

At zenith angle, z, VTEC can be translatedto STEC respective of path lengths through theionospheric shell by

MF (z) =STEC

V TEC=

1

cosz’=

1√1− sin2z′

with sinz′ =R

RO +Hsinz

(19)

where:The mapping function increases with increasing

zenith angle z to the satellite. For small elevationangles TEC can reach up to three times the value ofVTEC, as can be seen by Table 1.

Figure 4 shows how increasing the IPP value from300 km in increments of 50 km impacts the calcu-lated VTEC via the mapping function. This vari-ation can be seen to differ whereby the resulting

Figure 4: Impact on TEC values from varying IPPheights. The height of the thin shell, H, is increasedin 50 km increments from 300 to 500 km.

MF(z) thin shell mapping function;z, z’ respective geocentric zenith angles at

the height of the GNSS receiver and theionospheric pierce point at the thinshell;

R, RO respective radius to the GNSS receiverand the mean radius to the Earth(approximately 6,371 km);

H height of the thin shell above the Earth’smean surface.

VTEC difference is not linear, but is also depen-dent on the elevation angle. Note the relativelyconsistent VTEC differences (between adjacent IPPheights) till ∼6.5 UT, thereafter the VTEC differ-ences between each IPP altitude until ∼7.9 UT be-come greater. Figure 5 shows the elevation angle forthe corresponding satellite (G21) for Figure 4. Thegreater variation observed after ∼6.5 UT can be ex-plained by the decreasing elevation angle from 31◦to2◦towards the end of the recorded measurements. Atlow elevations the GNSS signal has a greater pathlength to traverse through the ionosphere.

By rearranging (19) it can be derived that an in-

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Figure 5: Elevation angle on 11 March 2011 for G21at MIZU.

crease in H decreases sinz′ which entails an increasein cosz′. Hence an increase in the height of the thinshell in the mapping function results in an increasein the VTEC value.

Table 1: Mapping Function, MF, comparisons. Firstthree columns units in degrees (Source [24]).

Elevationangle

z z’ MF Distance(km)

90 0 0 1.00 060 30 28 1.13 21530 60 55 1.73 60320 70 62 2.14 87310 80 68 2.66 13445 85 70 2.87 1712

Values of mapping functions range from 1 in thezenith direction to approximately 3 at an elevationangle of 5◦. It should be noted that the thin layermodel currently deployed in the GPS domain con-sists of discrepancies, resulting from STEC to VTECconversions. Within the mid-latitude regions theelectron density is small and so in these geographiclocations the conversion induces small errors. At

low-latitudes where electron density is greater, thenobvious errors become more apparent [27].

2.6 Carrier Phase Leveling

Single-frequency GPS users can utilise models of theionosphere such as the Klobuchar Model, also knownas the GPS Broadcast Model. The Klobuchar Modelis constructed using ionospheric parameters givenin the GPS broadcast message and is representedby a third degree polynomial. The coefficients ofthis third degree polynomial are transmitted as partof the broadcast message header [22]. Using thismethod enables ionospheric parameters such as TECto be extracted.

For dual-frequency GNSS users however TEC val-ues can be retrieved with the use of dual-frequencymeasurements by applying calculations like that in(16). Calculation of TEC by applying (16) for pseu-dorange measurements in practice produces a noisyoutcome and so the relative phase delay between twocarrier frequencies – which produces a more preciserepresentation of TEC fluctuations – is preferred.Since the actual number of phase cycles is unknown,obtaining the differential carrier phase yields a pre-cise measure for only the relative TEC; the absoluteTEC values are thus only determined if the pseu-dorange measurements are also used. Therefore thepseudorange measurements are used to obtain theabsolute scale of the TEC values and the carrierphase measurements are then used to provide in-creased precision of the TEC values [22]. As pre-viously mentioned the noise level of the pseudorangemeasurements is high and so produces TEC valueswith greater uncertainty whereas the noise level ofthe carrier phase measurements is significantly lowerthan that of the pseudorange. To circumvent theeffect of pseudorange noise on TEC data, GNSSpseudorange measurements can be smoothed by car-rier phase measurements, with the use of the car-rier phase smoothing technique, which is often re-ferred to as carrier phase leveling [22]. The carrierphase smoothing technique is essentially a combi-nation of the noisy code pseudorange measurementswith the comparatively smooth carrier phase mea-surements. These comparatively smaller measure-

11

ment errors seen in the carrier phase measurementsas opposed to the pseudorange measurement errorsenable the determination of STEC through smooth-ing the pseudoranges [22]. The steps applied withinthe carrier phase leveling technique are outlined be-low:

1. The phase measurements given in units of phasecycles are multiplied by the wavelength of thecarrier to obtain values in units of length. Thegeometry free linear combination is given by[25]:

L4 = L1 − L2

=

(1− f21

f22

)I1 + (λ1N1 − λ2N2)

(20)

The resulting phase derived slant delay calcu-lated from the geometry free linear combination,L4 (20), is scaled to zero for the relative rangeat the first epoch. This step enables the elim-ination of the integer ambiguity, N, if no cycleslips are present [22]. This results in

L4 =

(1− f21

f22

)I1 (21)

2. The code multipath effect typically seen at lowelevation angles or at either end of the path ofthe signal was eliminated by fitting the codedifferential delay at the higher elevation angles.The parser tool used to plot ionospheric delayfrom the RINEX data has been developed insuch a way to seek out the highest elevationangle for each individual satellite, then at thisparticular epoch identifying the correspondingdifferential delay value and defining this valueas the shift value. This shift value was subse-quently added to the relative phase values andso fitting the data to the code differential de-lay. Consequently the absolute differential de-lay was determined and any remaining noise wasregarded as negligible [22]. This procedure isshown in Figure 6.

3. The smoothed differential delay was then con-verted to absolute STEC by multiplying witha constant (as in Equation 21) then using themapping function as in Equation 19 the conver-sion from STEC to VTEC was finally made [22].

Figure 6: Phase smoothed code differential delay

This report is primarily – although not exclusively– focused on only the observations of small-scale vari-ations in the electron density, which implies just thechanges in TEC values as opposed to the absoluteTEC values [10]. The slant TEC (STEC) values aremapped to the vertical using the mapping functionand so producing estimates for VTEC [10]. Never-theless for completeness the plots shown in the Re-sults section are given in absolute TEC values, asdescribed in the above carrier phase leveling proce-dure. Longer periodic variations in the TEC time se-ries, such as diurnal and seasonal trends, are avoidedby selecting time series data sets typically of the 3 –4 hour range.

The IPP geographic location is defined as the ge-ographic location where the LOS between the GNSSsatellite and the GNSS receiver penetrates the Fregion of the ionosphere at its peak electron den-sity. For the Tohoku event, Galven et al [10] de-termined the F region peak density altitude byusing JPL’s Global Assimilative Ionosphere Model(GAIM). The GAIM process ingests ground-based

12

GPS as well space-based radio-occulation TEC mea-surements from the COSMIC constellation. Thissubsequently generates an electron density profileas a function of altitude. This particular profilewas determined for the location above the Tohokuearthquake epicenter. Using the GAIM profiles overJapan resulted in an F region peak of 300 km alti-tude. The IPP altitude in this report – based onthese findings – has applied an F region peak of300 km altitude.

2.7 Residual Determination

For the purpose of this study the monitoring ofsmall-scale variations in ionospheric electron densityfrom the ionospheric observables are of particular in-terest.

Longer period variations can be associated withdiurnal alterations, and changes in the receiver-satellite elevation angles. In order to remove theselonger period variations in the TEC time series aswell as to monitor more closely the small-scale vari-ations in ionospheric electron density, a higher-orderpolynomial is fitted to the TEC time series. Thishigher-order polynomial fit is then subtracted fromthe observed TEC values resulting in the residuals.The variation of TEC due to the TID perturbationare thus represented by the residuals. For this reportthe polynomial order applied was typically greaterthan 4, and was chosen to emulate the nature of thearc for that particular time series. The order numberselected is dependent on the nature of arcs displayedupon calculating the VTEC values after an initialinspection of the VTEC plots [10].

2.8 Waves and Fault Motion

Earthquakes are generally categorized by their faultmotion and are commonly consisting of one or moretypes of a fault motion. The reverse motion is pre-dominantly caused by the uplifting at the surfacewhereby vertical co-seismic crustal displacement isa standard feature. Normal motion (also known asthrust motion) is caused by the subsidence at thesurface. The third type of motion, the strike-slip mo-tion (SSM) is predominantly characterised by hor-

izontal motion and so generates little vertical dis-placement [4].

Following an earthquake are atmospheric waves,which appear as one of three types: (1) acousticwaves occurring in close proximity to the epicenter;(2) gravity waves generated by a tsunami; (3) sec-ondary acoustic waves caused by the Rayleigh sur-face wave originating from the epicenter [17]. Thesecoseismic TIDs have been identified as having prop-agation speeds of ∼1000 ms-1, ∼3.4 km s-1, and upto ∼200 ms-1 (triggered by a fault slip earthquakefollowed by an impending tsunami with a depth of5000 m) for acoustic, Rayleigh, and gravity waves,respectively [28].

2.8.1 Acoustic Waves

Co-seismic vertical motion of the ground perturbsthe ionosphere and is referred to as co-seismic iono-spheric disturbances (CID). The sudden impulsiveforce of the ground or sea induces atmospheric pres-sure waves that propagate skyward into the tro-posphere and ionosphere. This affect is detectableusing remote sensing techniques that detect iono-spheric disturbances.

These atmospheric waves can occur as an acousticwave or as a Rayleigh wave, both of which demon-strating different propagation velocities. The ver-tical component of the co-seismic crustal deforma-tion is analogous to a piston-like movement and isattributable to the source of the primary acousticwaves [4]. Acoustic waves are described as beingsound waves induced by longitudinal compression inthe propagation’s direction. These acoustic wavesare typically generated by earthquakes and propa-gate through the atmosphere at the speed of sound.In a region where the fault line is located under-neath a large body of water such as an ocean, thisdisplacement of the seafloor and ultimately the over-lying body of water is responsible for the generationof a tsunami [4].

Depending on the region of the atmosphere tra-versed by the acoustic wave, the speed can varybetween several hundreds of ms-1 at sea level to1000 ms-1 at 400 km altitude. Therefore a durationof between 10 to 15 min is typical for a wave to affect

13

the F region and to observe TEC perturbations. Theacoustic wave generated by a seismic event at theepicenter traverses isotropically in the atmosphere,whereby the horizontal and vertical components ofthe propagation velocity are identical [10].

2.8.2 Rayleigh Waves

Earthquakes also generate Rayleigh waves. Thesewaves transverse solid Earth waves propagatingalong the surface with a horizontal velocity of about3.4 km s-1. These solid Earth (Rayleigh) waves alsoproduce acoustic waves within the immediate at-mosphere. These newly generated acoustic wavesinduce a corresponding electron density fluctuationtraversing in the ionosphere that is also consistentwith the moving horizontal 3.4 kms-1 Earth wave.Not all submarine earthquakes produce tsunamis,and so tsunami-driven ionospheric disturbances maynot necessarily be observed. Earthquake-drivenionospheric disturbances would exist regardless, andso care needs to be taken when differentiating thesource of the ionospheric disturbance [10].

2.8.3 Gravity Waves

As a tsunami begins to traverse the ocean a grav-ity wave is generated, propagating obliquely into theatmosphere with both horizontal and vertical com-ponents. In the case of gravity waves, the Earth’ssurface rises and falls generating vertical transverseoscillations of pockets of air. These oscillations theninduce buoyancy waves and are observed as the inter-nal gravity waves. These waves propagate verticallywith velocities in the region of 40 to 50 ms-1, reachingthe F region in over 2 hours [10]. As the gravity wavepropagates towards higher altitudes, the amplitudeof the wave also increases as a result of the exponen-tial decline of atmospheric density with increasingheight. The wave amplitude continues to increaseas the propagation altitude through the ionospherealso increases. The end effect is waves with muchlarger amplitudes are observed in the F as opposedto the E region. Gravity waves could be powerfulenough to perturb the E region and subsequently bedetected in TEC observations, however these per-

turbations would pale into insignificance comparedto the ensuing F region TEC perturbations. Thisfurther advocates the reasoning behind the assump-tion that tsunami-driven waves will be observed assignificant TEC perturbations at an altitude of 300to 400 km where peak electron density occurs [10].

The TIDs caused by tsunamis can be easily dif-ferentiated from the TIDs caused by other naturalsources (such as geomagnetic activity, ionosphericstorms, tropospheric weather) by the period, veloc-ity and propagation direction of the tsunamis thatgenerated these TIDs [17].

3 Results

For this analysis four earthquake events have beenselected with either an IGS or private GNSS sta-tion with near proximity to the epicenter. Thissection describes the seismological characteristics ofeach event, as well as the ionospheric perturbationassociated with each of these events.

Table 2: Earthquake main parameters. Seismologi-cal parameters were taken from the Earthquake Haz-ards Program of the U.S. Geological Survey (USGS)website (http://earthquake.usgs.gov)

Date Name MwTime(UT)

Location(lat; lon)

Depth(km)

11/03/11 Tohoku 9.0 5:46:24 38.30;142.37

29.0

17/11/13 ScotiaSea

7.7 9:04:55 -60.27;-46.4

10.0

19/08/16 SouthGeorgia

7.4 7:32:22 -55.29;-31.88

10.0

13/11/16 Kaikoura 7.8 11:02:56 -42.76;173.08

25.0

3.1 Tohoku Earthquake

The sampled data was retrieved from the IGS sta-tion, MIZU, located at Mizusawa, Japan. The MIZUsite is 39N 08’ 06.61” and 141E 07’ 58.18”. The

14

location of the data collection site, MIZU, and theearthquake epicenter can be seen in Figure 7.

Figure 7: MIZU IGS station and Tohoku earthquakeepicenter.

Figure 8 displays the ionospheric delay in terms ofvertical TEC (VTEC), in units of TECU (1 TECU =1016 el m-2). The plot is split into two smaller sub-plots, the upper section displaying the ionosphericdelay (VTEC) in units of TECU, the lower display-ing the residuals. The vertical grey-dashed lined cor-responds to the epoch of the earthquake at 05:46:23UT (2:46:23 PM local time) on March 11 2011.

In the upper section of the plot, the blue line corre-sponds to the absolute VTEC value calculated fromthe observations, in this case L1 and L2 on GPS,whereby the carrier phase leveling technique was ap-plied to the data set. The VTEC values are mappedfrom the STEC values which are calculated from theLOS between MIZU and the GPS satellite PRN 18(on Figure 8 denoted G18). For this particular dataset as seen in Figure 8, a polynomial fit of five degreeswas applied, which corresponds to the red-dashedline. As an alternative to polynomial fitting, band-pass filtering can be employed when TEC pertur-

bations are desired. However for the scope of thisreport polynomial fitting to the time series of TECdata was the only method used [11].

In the lower section of Figure 8 the residualsare plotted. The residuals are simply the phasesmoothed delay values (the blue line) minus the poly-nomial fit line (the red-dashed line).

All ionosphere delay plots follow the same layoutpattern and all time data is represented in UT (UT= GPS - 15 leap seconds, whereby 15 leap secondscorrespond to the amount of leap seconds at the timeof the seismic event). The time series shown for theionosphere delay plots are given in terms of decimalof the hour, so that the format follows hh.hh.

Figure 8: VTEC and residual plot for G18 at MIZUon March 11 2011

In Figure 8 it can be seen that the resulting resid-uals resemble a quasi damped sine wave signaturewith ∼11 min periods commencing ∼12 min after theearthquake event.

Acoustic waves in the atmosphere propagate omni-directionally at the speed of sound, which at 300 kmaltitude (F peak region) is 1000 ms-1. The VTECperturbations seen in the plots are consistent with apropagation velocity of an acoustic wave generatedby the earthquake [11]. Compared to the velocityof the tsunami traveling horizontally this velocitywould be 200 – 300 ms-1 away from the epicenter. A

15

(a) (b)

(c) (d)

Figure 9: VTEC and residual plots at MIZU on March 11 2011. The blue curve in the upper portion of theplot is the observed VTEC value and the red-dashed curve is the polynomial fitting applied to the curve.The vertical grey-dashed line signifies the earthquake epoch. The lower portion of the plot demonstrates theresiduals, which have been calculated from the observed VTEC values minus the polynomial fit values. Theplots are from perspective of the GNSS receiver at MIZU for four GPS satellites (a) G05 (b) G09; (c) G15;(d) G18. The y-axes for absolute VTEC values have been adjusted and so are not consistent between eachplot. The residuals y-axes for each plot however are consistent and are limited to ±1.8 TECU. The timescales (x-axes) are dependent on when the satellite was tracked between 5.00 UT and 8.00 UT, and so mayalso vary.

16

(a) (b)

(c) (d)

Figure 10: VTEC and residual plots at MIZU on March 11 2011. The plots are from the perspective of theGNSS receiver at MIZU for four GPS satellites (a) G21 (b) G26; (c) G27; (d) G28.

17

gravity wave would subsequently be generated prop-agating obliquely upward from the tsunami wave-front [11]. The vertical speed of the gravity waveis 50 ms-1 and is significantly lower than that of theacoustic wave. Consequently, this implies the initialTEC perturbations seen from Figure 8 are highlylikely to have been induced by the acoustic wavesgenerated from the earthquake. The gravity waveshowever are expected to be seen at a later stage [11].In order to establish a higher degree of confidencewhether a TEC perturbation has been caused by asurface disturbance, such as from seismic activity,not one but multiple satellite-receiver pair time se-ries are to be analysed.

The initial TEC fluctuations seen in the residualplots for G05, G09, G15, G18, G21, G26, G27, andG28 are congruent with a propagation velocity ofan acoustic wave ( 1000 ms-1) and so therefore likelyto have been caused from such acoustic waves gen-erated from the earthquake. In order to diminishany ambiguity regarding the origin of TEC pertur-bations – such as those caused at the surface (likethat of an earthquake or tsunami) or another sourcesuch as from a geomagnetic disturbance – not justone but several receiver-satellite pair time series wereassessed [11].

Figure 11: Geometry of the satellites, groundtrack and IPP. GNSS satellites orbit the Earth at∼20000 km altitude. The IPP is set to 300 km alti-tude. If a GNSS satellite were imagined to be or-biting instead of at 20000 km, at the IPP altitude of300 km along the satellite-receiver LOS, then its pro-jected ground track on the surface of the Earth atIPP is represented by the blue line. The focal mech-anism (beach ball) corresponds to the epicenter ofthe earthquake; the red stars (located on the bluelines) represent the location of this imaginary GNSSsatellite upon the IPP at the exact time an earth-quake strikes. The orange lines represent tectonicplate boundaries.

The residual plots in Figure 9 and Figure 10show significant variations with amplitudes rangingfrom 0.6 TECU (G09, G15, G21, G26, G27, G28)to 1.2 TECU (G05). The amplitude with the leastvariation (0.6 TECU) with greatest background ab-solute TEC (21.2 TECU) is observed for G21. Thiscorresponds to an observed variation of ∼2.8%. Con-versely the greatest amplitude variation of 1.2 TECUand background absolute TEC of ∼14 TECU is seenfor G05. In this case the observed variation is∼8.6%.The initial TEC perturbations in each of the residualplots occurs at ∼15 min after the earthquake event,with a disturbance still present even after ∼1.5 h

18

(G18). If these TEC perturbations at ∼15 min afterthe earthquake were caused by gravity waves gener-ated by the tsunami then this would imply a velocitymuch faster than the typical 50 ms-1 consistent withthe velocity of gravity waves. At 50 ms-1 with anF region peak of 300 km, the resulting time takenwould be ∼1.7 h from sea level. Following on fromthese estimates the TEC perturbation signatures ob-served were very unlikely to have been generatedfrom a tsunami-driven gravity wave. TEC pertur-bation was observed ∼15 min after the earthquakeoccurred. Consequently it is much more probablethat the TEC perturbation observed is the result ofacoustic waves generated by the earthquake itself.Such acoustic waves would exist regardless of thegenerated tsunami being present or not.

3.2 Scotia Sea Earthquake

Two large seismic events in the South Scotia regionare under analysis in this report. The first eventoccurred on the 17 November 2013 with a magnitudeof 7.7 MW at 9:04:55 UT with a depth of 10 km.A seismic event struck in the South Georgia IslandRegion with a magnitude of 7.4 MW at 7:32:22 UTon 19 August 2016, at a depth of 10.0 km.

The University of Luxembourg, along with theUnited Kingdom National Oceanography Centre,British Antarctic Survey, and UNAVCO collabo-rated in February 2013 to construct the King EdwardPoint Geodetic Observatory on South Georgia, in theSouth Atlantic Ocean [26]. The remote location ofthe South Georgia Island within the South Atlanticas well as the proximity to the Scotia tectonic plateamplifies the importance of this region for numerousglobal monitoring networks. The seismic, geomag-netic and oceanic domains in particular continue tobenefit from the presence of monitoring networks inthe South Atlantic. The King Edward Point Geode-tic Observatory comprises of two autonomous GNSSstations (character ID: KEPA and KRSA) that em-ploys a Trimble NetR9 GNSS receiver and Trimblechoke ring GNSS antenna.

The ionospheric TEC perturbations were capturedby a GNSS receiver at KEPA for GPS satellites G20,G25, and G31, as well as for GLONASS satellite

R20, see Figure 12.It is generally assumed that the background iono-

spheric parameters such as the absolute VTEC inthe registration zone (in this case the GNSS receiversite) are one of the main factors that may influencethe behavior of the TEC perturbation [4]. The per-turbation is transferred using the neutral waves viacharged particles. Therefore for a successful com-parison of TEC residuals from different earthquakesshould also consider the geometry of the satellite-receiver pair.

From all four plots, the R20 satellite was the clos-est satellite-receiver pair that captured the most pro-found ionospheric disturbance with a recorded TECresponse occurring at ∼11 min after the earthquakewith a largest amplitude of ∼1.3 TECU registered.A significant variation of TEC values was observedwith a period of ∼9 min. The amplitude of thisvariation is ∼1.2 TECU with a background of ab-solute TEC being ∼46–48 TECU. Consequently theobserved variation has a range of ∼2.6% of the back-ground TEC. GPS satellite G20 recorded a largestamplitude of ∼0.6 TECU at ∼19 min after the earth-quake whereas G25 registered an even smaller ampli-tude of ∼0.3 TECU at ∼20 min later. For G20 thiscorresponds to an amplitude variation of ∼0.6 TECUwith a background of absolute TEC being 37 TECU,leading to 1.6% of the background TEC. For G31 dueto the wave-like nature of the residual curve beforeand after the earthquake, no disturbance is observedalthough there does appear to be a more apparentperturbation at ∼60 min; however since the ampli-tude in the residual plot does not appear more sig-nificant than the background TECU variation thisperturbation is consequently deemed negligible.

19

(a) (b)

(c) (d)

Figure 12: VTEC and residual plots at KEPA on 17 November 2013. The blue curve in the upper portion ofthe plot is the observed VTEC value and the red-dashed curve is the polynomial fitting applied to the curve.The vertical grey-dashed line signifies the earthquake epoch. The lower portion of the plot demonstratesthe residuals, which have been calculated from the observed VTEC minus the polynomial fit. The plots arefrom the perspective of the GNSS receiver at KEPA, for one GLONASS satellite (a) R20 and three GPSsatellites (b) G20; (c) G25; (d) G31.

20

Figure 13: Geometry of the satellites’ projectedground track whereby the IPP is set to 300 km alti-tude. The orange lines correspond to tectonic plateboundaries.

3.3 South Georgia Earthquake

In the South Georgia Island region located in theNorth Scotia Ridge Transform (NSRT) plate bound-ary between the South American and Scotia plates[29] on 19 August 2016, a magnitude of 7.4 MW

earthquake struck at 7:32:22 UT. This subsectionanalyses the data retrieved from KEPA and KRSA.As well as computing the GPS and GLONASS TECvalues, four Galileo satellites (E08, E14, E26, E28)are also analysed. Taking a look at the Galileo satel-lites first, Figure 14 demonstrates the TEC pertur-bations as computed for the Galileo L1 and L5 car-rier frequencies. It should be noted that these com-puted values do not take into consideration the DCBvalues and are therefore not included in the finalVTEC values. The L1 and L5 carrier frequenciesare outlined here first because of the phase differ-ence between L1 (frequency band E1, 1575.42 MHz)and L5 (frequency band E5a, 1176.45 MHz). Fromall five Galileo frequency bands (E1, E5a, E5b, E5,E6) these two combinations in particular create thelargest phase difference, and when considering thedispersive nature of the ionosphere, this phase dif-ference facilitates an optimised condition for analy-sis for TEC perturbation. Nevertheless later on in

this report several other signal combinations are pre-sented and discussed to augment the case for wideseparation of signal carriers for TEC observation, asopposed to a narrow separation of signal carriers.

On Galileo satellite E08 and applying a five-orderpolynomial fitting, it can be seen that the residualplot after the earthquake event shows little or nostriking perturbation. Interestingly though is thedisturbance seen∼40-45 min prior to the earthquake.The debate of preseismic TEC changes has injectedexcitement into this research area ( [12] [20] [13])and remains a contested topic, however this partic-ular avenue of discussion is beyond the scope of thisreport. The observations for E14 show almost no no-ticeable TEC perturbation and so are deemed as neg-ligible. For plot E24, the reader should be aware thatthe vertical grey-dashed lined representing the earth-quake epoch is located almost on the y-axis itself.This is because for this particular data set, the firsttracked epochs coincide with the minutes just beforethe actual earthquake itself. At ∼4 min following theearthquake a very slight magnitude of ∼0.3 TECUcan be seen, which compared to a background abso-lute TEC of ∼29 TECU gives 1.0% observed varia-tion. Lastly, for satellite E26 a slight TEC pertur-bation is seen at ∼15 min following the earthquake.A magnitude of ∼0.3 TECU can be seen, and com-pared to a background absolute TEC of ∼20 TECUgives 1.5% observed variation.

21

(a) (b)

(c) (d)

Figure 14: VTEC and residual plots at KRSA on 19 August 2016. The plots are from the perspective ofthe GNSS receiver at KRSA, for four Galileo satellites (a) E08; (b) E14; (c) E24; (d) E26. The y-axes andx-axes in all plots do not conform with one another but are adjusted to fit the data. The y-axes for theresidual section of each plot is consistent with one another.

22

Figure 15: Geometry of the Galileo (E08, E14, E24and E26) satellites’ projected ground track wherebythe IPP is set to 300 km altitude. The orrange linescorrespond to tectonic plate boundaries.

For Galileo satellite E08, Figure 16 demonstrates acomparison of two further signal combinations usedfor analysing TEC perturbations. The left plot inFigure 16 is for the frequency band combination E5a-E5b, and the plot on the right for frequency bandcombination E5b-E5. The phase difference betweenE5a-E5b equates to 30.7 MHz, whereas the phase dif-ference between E5b-E5 is 15.3 MHz. Therefore inorder to facilitate an analysis of TEC perturbation,when comparing these two signal combinations, theE5a-E5b signal combination is favored over the E5b-E5 combination due to a greater phase difference.This is further augmented by Figure 16 wherebythe background absolute TEC range for the E5a-E5b signal combination is ∼5.1 TECU compared to∼3.4 TECU for the E5b-E5 combination. This im-plies that any perturbation in the TEC value seenin the residuals is more profound for the E5a-E5b

combination (wider phase difference) as opposed towhen the TECU is lower. This can be seen – albeitslightly – from the residual plots in the lower sec-tion of each plot. For satellite E08 in Figure 14 thephase difference for the E1-E5 signal combination is399.9 MHz and consequently the residuals display amore significant TEC disturbance.

23

(a) (b)

Figure 16: VTEC and residual plots at KRSA on 19 August 2016. Both plots are from the perspective ofthe GNSS receiver at KRSA, for the same Galileo E08 satellite, however for the signal combinations (a)L5-L7 (frequency band E5a-E5b); (b) L7-L8 (frequency band E5b-E5).

Figure 17: VTEC and residual plots for KRSA on19th August 2016 for GLONASS R03.

24

Further TEC perturbations can be seen forGLONASS R03 at ∼12 min (see Figure 17) follow-ing the earthquake. Note the zigzag-like effect onthe observations for up to ∼14 min after the ini-tial disturbance, comprising what appears to be fivevery small waves, each with ∼3 min in wavelength.However these disturbances are so slight that theresulting residuals appear almost uninterrupted, de-spite the TEC perturbations being more apparent inthe absolute TEC observations (VTEC). This indi-cates that even when the amplitude of the residualsis minimal with the resulting plot indicating a neg-ligible effect, sometimes the nature of the absoluteTEC observations may indicate a TEC perturbationcharacteristic of a seismic active signature.

Like that of GLONASS R03, the GPS G10satellite observations shows TEC perturbations at∼10 min after the earthquake for both KEPA andKRSA (see Figure 18), however like that of R03 (Fig-ure 17) the disturbance on the ionosphere is more ap-parent on the absolute TEC observations as opposedto the residual plots. The plots shown in Figure 18are shown on the same scale. The elevation angles forboth pairwise combinations (KEPA-G10 and KRSA-G10) are identical because of the close proximity ofthe two stations with one another. Therefore whenconsidering the possible culprits for the difference inmaximim VTEC (∼3 TECU) between the two plotsin Figure 18, the satellite-receiver geometry can beexcluded. A more likely culprit for this discrepancycould be the receiver DCBs, which for this reporthas not been individually assessed for each station.

Since this observation in TEC perturbation is seenat two independent GNSS receiver sites for the samesatellite, this augments the notion that the earth-quake in the South Georgia Island Region on 19August 2016 was detected in the ionosphere via theTEC perturbations, albeit not very strikingly.

3.4 Kaikoura Earthquake

The recent Kaikoura earthquake that struck 13November 2016 at 11:02 UT was a magnitude of 7.8MW. The epicenter was approximately 15 km north-east of Culverden and 60 km south-west of Kaikoura.

Several sites were used to analyse the effects of

(a)

(b)

Figure 18: VTEC and residual plots at KEPA andKRSA on 19 August 2016. The plots are for one GPSsatellite (a) G10 as seen from KEPA; (b) G10 as seenfrom KRSA. Both the y and x axes are identicallyscaled.

25

the ionospheric disturbances caused as a result ofthis earthquake and shall be discussed within thissubsection. The Galileo satellites were recorded at30 second samples at several sites in the New Zealandregion.

The absolute VTEC values as seen in Figure 20have been calculated without compensating for theGalileo DCBs. In any case it is the residuals thatare of greater importance for this analysis and so fornow the DCBs can be neglected.

At HOIK a TEC perturbation can be seen forboth E08 and E22. The more profound of thetwo satellites, E22, shows a variation of ∼1.8% at∼20 minutes after the earthquake.

For KAIK it is E08 that shows a significant TECdisturbance at ∼20 minutes after the earthquake,with a residual of ∼0.6 TECU. However for this par-ticular plot (plot (c)), the residuals were already in-dicating an unstable behavior beginning even be-fore the earthquake event.Consequently it is E22(plot (d)) that provides a clearer impression of TECperturbation. The residuals of E22 are very sta-ble throughout the two hours with the exceptionof ∼20 minutes after the earthquake where a slightTEC disturbance of ∼0.3 TECU can be seen. ForWEST (plot (e)) no significant TEc disturbance canbe seen.

Lastly LKTA (plot (f)) shows a lot of similaritywith that of plot (d), whereby a TEC disturbance forE22 can be seen ∼20 minutes after the earthquake.This plot shows a marginally more significant TECdisturbance than that of plot (d).

26

Figure 19: Location of the sites under analysis andthe epicenter of the earthquake, as given by thebeachball (focal mechanism). The orange line repre-sents the tectonic plate boundary between the Aus-tralian Plate (above plate) and the Pacific Plate (be-low plate). The blue lines denote the geometry of theGalileo (E08 and E22) satellites’ projected groundtrack whereby the IPP is set to 300 km altitude. Thered stars along these blue lines is the projected lo-cation of the satellite at the moment the earthquakeoccurs.

27

4 Discussions

Observational evidence of the ionospheric signaturesfollowing a major (> 7.0 M) earthquake have beenpresented. This has been demonstrated firstly nearto the epicenter of the Tohok-Oki event of March11th 2011. The observed TEC perturbations as seenin the residual plots are consistent with the TEC per-turbation plots by Galven et al (see in [11]). Thisaugments the demonstration of employing GNSS re-ceiver to monitor ionospheric disturbances.

The proximity of the MIZU site and magnitudeof the Tohoku event has provided a remarkable –albeit a poignant – opportunity to analyse the ocean-ionospheric coupling aftermath of a deep submarineseismic event. The Tohoku event has also enabledthe observation of the origin and nature of the TIDsgenerated by both a major earthquake and tsunamiin close proximity to the epicenter [11].

Throughout this report, projected ground trackplots (for example, like those in Figures 11, 13, 15,and 19) have been given. The projected ground trackplot like that shown in [4] has been replicated byFigure 13 in this report. A slight discrepancy withG25 has been observed, which may be attributed toa difference in the IPP height used. For this reportan IPP height of 300 km has been employed whereasfor [4] an IPP height of 350 km was used.

In the meantime differentiating between tsunami-driven signatures from other TEC perturbations in-duced by other sources remains an unresolved chal-lenge for a real-time detection system.

After the Tohoku earthquake the first TEC pertur-bations were observed ∼12 min after the earthquake.This is congruent with the velocity of the acous-tic and Rayleigh waves generated by an earthquakewhich typically take ∼10 min to reach the ionospherefrom the surface of the ocean.

Comparisons made between TEC observations in-duced by acoustic waves from different tsunami orearthquake events are to be made with caution. Thecharacteristics of an earthquake and tsunami varydepending on the magnitude of the earthquake, dis-tance between the epicenter and measurement point(GNSS receiver), the type of earthquake (strike–slip,thrust, dip), wave period, and so on.

Between the results demonstrated in this report,and that of the Astayfeva und Galven papers, thewavelength, amplitude and period of fluctuationsfor the observed absolute VTEC and TEC residu-als are indeed similar. This implies that the mod-els and calculations applied in this report provide amore than sufficient procedure in identifying an iono-spheric signature from strong seismic activity. Fur-ther, the Python software developed is more than ca-pable of providing this functionality, by drawing onits mathematical packages, such as numpy, pandas,scipy, and matplotlib, as well as employing the carto-graphic toolkit provided from the basemap package,and finally by utilizing the focal mechanism genera-tion library, obspy.

5 Conclusions

Numerous challenges remain in the endeavors for along-term, robust, and reliable tsunami warning sys-tems that can be assisted with TEC observations.Despite TEC observations comprising varying am-plitudes and periods, empirical data from severalreceiver-satellite pairs is required if a TID is to beproved that it is associated with seismic activity anda tsunami. Such empirical data may indicate the di-rection, velocity, and magnitude of the TID. Whenanalysing empirical data retrieved from the epicen-ter of the earthquake, consideration must be taken todifferentiate the generated TEC perturbations gen-erated by the earthquake which is not dependent onthe existence of a tsunami.

As a potential research area and implementa-tion, an automated monitoring system that numbercrunches RINEX data, produces TEC residual data,and enables easily accessible summarised plots to beverified, is recommended. In doing so this may facili-tate the process of flagging potential impending nat-ural disasters such as tsunamis and earthquakes. De-spite open questions still remaining to be resolved inthe studies of atmosphere-ionosphere coupling, thisresearch should contribute towards evaluating sucha TEC automated monitoring system and the logis-tical challenges faced with establishing such a sys-tem. In particular this could also employ existing

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(a) (b)

(c) (d)

(e) (f)

Figure 20: VTEC and residual plots for two Galileo satellites, E08 and E22, on 13 November 2016. The plotsare from the perspective of the GNSS receiver at four sites (a) E08 and (b) E22 at HOIK; (c) E08 and (d)E22 at KAIK; (e) E08 at WEST; (f) E22 at LKTA. The y-axes and x-axes in all plots do not conform withone another but are adjusted to fit the data. The y-axes for the residual section of each plot is consistentwith one another.

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real-time GNSS receiver networks. Current tsunamiwarning systems are dependent on numerical mod-eling and a mesh of oceanic buoys [10]. In futuresuch tsunami warning systems could benefit and beaugmented with the employment of an automatedmonitoring systems.

A RINEX parser able to read both RINEX V2 andRINEX V3 written in the Python programming lan-guage has been demonstrated to sufficiently verifyionospheric perturbations in terms of TEC fluctua-tions after strong seismic activity. Though the aimof this report was not to prove the capability usingPython, but to demonstrate Python’s ability to plotthe results using the Basemap Library where tradi-tionally the Generic Mapping Tool (GMT) packagewould be employed. In addition, the obspy Libraryhas demonstrated its capability to also generate focalmechanisms, all within one Python program.

Absolute VTEC plots, residuals plots, projectedground tracks maps with an applied IPP, have allbeen cross-checked and their congruence confirmedwith past papers, thus further augmenting the qual-ity and exactness of the Python program.

The results presented in this paper are significanttoo because we have been able to verify ionosphericperturbations after an earthquake event, by utilisingdata retrieved not only from GPS and GLONASSsatellites but also from the Galileo Satellites.

A future follow-up project could comprise of mak-ing this software more robust and enhanced perfor-mance via robustness and speed. This could entailfor example, augmenting the program in a analysiscenter that triggers the software to run following ma-jor earthquake events. The Python software devel-oped has been written in such a simplified way thatrequires the use of a standard desktop laptop. Sincespeed of data crunching, particularly processing bigdata, in today’s world is becoming increasingly moresought after, the execution of the program over amulti-core processor could also be investigated.

China’s BeiDou satellites were not considered forthis report and it is in this area where a very ob-vious expansion of the Python program could re-searched and developed. This could ultimately leadto a greater understanding of the ionospheric-seismiccoupling, since a greater global coverage means a

greater number of satellite-receiver pairs to analyse,thus increasing the chances of identifying the moreinteresting satellite-receiver pairs following an earth-quake event.

Finally, pre-seismic cursors have been investigatedin the past and strongly advocated in particular byKosuke Heki. The topic of pre-seismic ionosphericdisturbances remains somewhat controversial. A po-tential future study area could be the utilization ofthe Python program - along with algorithmic amend-ments - to verify the existence of this phenomenon.

6 Acknowledgments

Date files from the New Zealand sites were re-trieved from the GeoHazard Monitoring Depart-ment, GeoNet, New Zealand. The data used fromthe KEPA and KRSA sites were retrieved from theGeophysics Laboratory, University of Luxembourg,Luxembourg. I would like to thank Addisu Huneg-naw and Norman Teferle from the University of Lux-embourg for their helpful reviews of the manuscript.I would also like to thank Lion Krischer for his ad-vice on the obspy Python library. This work wascompleted under a self-funded assignment courtesyof Holding Engineering Consultancy.

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