Eavesdropping on whales; the acoustic detection of ultra high energy neutrinos in the Mediterranean Sea

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Eavesdropping on whales

The acoustic detection of ultra high energy neutrinos in the

Mediterranean Sea

Rosa Anna Pauline van den Ende

10734708

Amsterdam, 9

th

of July 2018

in partial fulfillment of the requirements for the degree of Bachelor of Science in B`eta-gamma

with a major in Physics at the Faculty of Science of the University of Amsterdam

conducted between April 4th and July 6th 2018

size: 15 ECTS

Under supervision of:

dhr. dr. E.J. Buis

dhr. dr. I.B. van Vulpen

Second examiner:

dhr. prof. dr. ir. P.J. de Jong

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Neutrinos, they are very small. And they have no charge and have no mass And do not interact at all. The earth is just a silly ball To them, through which they simply pass, Like dust maids down a drafty hall Or photons through a sheet of glass. They snub the most exquisite gas, Ignore the most substantial wall, Cold-shoulder steel and sounding brass, Insult the stallion in his stall, And, scorning barriers of class, Infiltrate you and me! Like tall And painless guillotines, they fall Down through our heads into the grass. At night, they enter at Nepal And pierce the lover and his lass From underneath the bed you call It wonderful; I call it crass.

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Abstract

Neutrinos with an energy above 1018_{eV allow us to probe particle physics at energies that hadron}

colliders cannot reach, can provide crucial information about sources at considerable distances and o↵ers insight in cosmic ray propagation beyond the GZK-limit. However, to detect neutrinos at these extreme energies, new methods are required, as the investigation of Cherenkov radiotion does not suffice for these highly energetic neutrinos due to their low flux. Therefore, KM3net is aiming to develop a new method in which the acoustic pulse that is the result of the hadronic shower that arises when a neutrino interacts with the nucleon of a water molecule is investigated. A preparation for the large set-up that will consist of more than 1000 hydrophones, is the deployment of two hydrophones in the Mediterranean close to Pylos, Greece at the end of January 2018. These hydrophones have been recording for a period of three weeks. In this thesis, these sound files are analyzed in order to eventually create a model on how to distinguish the neutrino signal from the background noise. The background noise has been characterized, an algorithm based on the amplitude is introduced and a cross-correlation is conducted. It is found that both of these methods are not sensitive enough to detect the neutrino signal and further investigation as well as the deployment of more hydrophones are required.

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Populair-wetenschappelijke

samenvatting

Neutrino's zijn elementaire deeltjes met een spin van 1/2, geen elektrische lading en een erg lage massa. Afhankelijk van hun bron hebben neutrino' een energie tussen 10 6_{en 10}19_{eV. Omdat de}

neutrinos alleen interacteren via de zwakke kernkracht, zijn ze in staat informatie te verscha↵en over bronnen waarvan andere deeltjes ons niet kunnen bereiken. Echter maakt dit ook dat de neutrino's ingewikkeld zijn om te detecteren.

De meest gebruikelijke methode om neutrino's te detecteren, is via Cherenkov-straling. Dit is een blauw-achtig licht dat wordt uitgezonden op het moment dat een neutrino een interactie aangaat met een nucleon, bijvoorbeeld van een watermolecuul, en er een muon ontstaat. KM3NeT, een internationale samenwerking met een neutrinotelescoop van ongeveer een kubieke kilometer, houdt zich bezig met het waarnemen van deze straling.

Echter, neutrinos met een energie hoger dan 1018_{hebben een zodanig lage flux, dat het volume}

dat nodig is om zo'n neutrino te detecteren nog veel groter moet zijn dan een kubieke kilometer. Aangezien geluidsgolven in water veel verder kunnen voortbewegen dan bijvoorbeeld de Cherenkov-straling, kan hiermee veel groter volume bereikt worden. Dit is de reden waarom KM3NeT bezig is met het ontwikkelen van een experiment om neutrino's aan de hand van een akoestisch signaal te detecteren. Namelijk, als een neutrino een interactie aangaat met een nucleon, ontstaan er deeltjes waarbij er een energie-overdracht plaatsvindt. Deze energie-overdracht zorgt voor een kleine temperatuurstijging van het water, waardoor het water gaat uitzetten. Deze expansie verspreidt zich verder en dit is precies een geluidsgolf.

Ter voorbereiding op het grote experiment in de Middellandse Zee van meer dan 1000 hydro-foons, waterdichte microhydro-foons, zijn er twee hydrofoons geplaatst bij de kust van Griekenland. Deze hydrofoons hebben drie weken lang de geluiden van de zee opgenomen. In deze thesis zijn deze geluidsbestanden geanalyseerd als startpunt voor een model om het neutrinosignaal te kunnen onderscheiden van de achtergrondgeluiden. Informatie is vergaard over het verwachte neutrin-osignaal en de andere geluidsbronnen- bijvoorbeeld de klik van een potvis of de wind op het wateroppervlak- om op basis daarvan twee algoritmes te testen. Het eerste algoritme gaat uit van de amplitude. Hiervoor is eerst de hoogte van het achtergrondgeluid bepaald, waarna een trigger werd beschouwd als een signaal dat deze hoogte overschrijdt. De tweede manier focust op de vorm van de signalen. Het theoretische signaal is als het ware over de data heen geschoven en als deze template op een stuk van de data paste, was er een zogenaamde match. Het is gebleken dat deze beide methoden leiden tot te veel triggers of matches. Verder onderzoek is dus nodig, waarbij de installatie van meerdere hydrophones cruciale informatie zou kunnen verscha↵en.

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List of Figures

2.1 The flux for various neutrino energies [14]. The energy of the neutrino depends on its source. The higher the energy of the neutrino, the lower the flux. . . 3

2.2 The expected neutrino amplitude and relative power spectrum for a 1011_GeV

had-ronic shower at a distance of 1 km [3], as first developed by Askaryan et al. [2]. . . 5

3.1 The vessel routes around Pylos, Greece. The location of the deployment of the hydrophones is marked with a star. Source: marinetraffic.com, retrieved June 2018 6

3.2 Ambient noise spectra [22], adapted by [13]. For frequencies between 10 Hz and 1 kHz, shipping plays a dominant role. In the domain between 1 and 40 kHz, the sea state noise is preeminent, indicated by the blue curves. . . 7

3.3 Spectrogram with on the y-axis the frequency and on the x-axis the time. The colours indicate the strength of the frequency: the more red, the higher the strength. Clicks from a marine mammal are clearly visible as the vertical stripes. . . 8

4.1 The used hydrophone. The hydrophone is based on a piezoelectric transducer that generates a voltage when a change in pressure is detected by the small object on top. 9

4.2 E↵ect of the 5th order Butterworth filter on the PSD. The filter results in a relatively flat passband and has decreased the strength of the frequencies that are not of interest for the neutrino detection. . . 11

4.3 On the left, the ADC distribution for the filtered signal between 1-40 kHz is shown. It appears to be a Gaussian distribution with a width . The value of this width is higher for higher frequencies, as shown in the right part of this figure. . . 12

4.4 The filtered signal for 500 ms and 3 ms. The signal oscillates around zero with fluctuating peaks.. . . 12

4.5 The noise level, defined as 5 , and the number of triggers per two minutes for a period of 2,5 days, from 02-02-2018 to 05-02-2018. . . 13

4.6 The total number of triggers and the number of triggered peaks as well as the ratio between those, for 02-02-2018.. . . 14

4.7 Scatter plot of the number of triggers and the noise level for the data as shown in figure 4.5. Two trends are visible, one that follows the y-axis and one that follows the x-axis. This can be explained by the nature of the sounds. . . 15

4.8 The number of triggers for noise levels of 5 to 9 sigma, for a period of approximately 10 hours at January 29th, 2018 . . . 15

4.9 The ADC distribution as in figure 4.3a, but now on a logarithmic scale. It can be seen that the ADCs deviate from the Gaussian distribution at the tails. . . 16

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LIST OF FIGURES

4.10 Signals that resulted in triggers. The red dotted line is the noise level 5 . It can be seen that the triggers vary in shape.. . . 17

4.11 The template neutrino signal as obtained by R. Lahmann and its time-reversed signal. The value of the y-axis is arbitrary and can be normalized. . . 17

4.12 Top: the time series for a period of 120 seconds, oscillating around zero and with some peaks. Bottom: the result of the cross-correlation. The better the template signal fits in the data, the higher the value of the cross-correlation. . . 18

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Chapter 1

Introduction

Ultra-high-energy (UHE) neutrinos could open a new door to our universe. Being neutral, very stable and only weakly interacting, they enable us to probe particle physics at extreme energies that hadron colliders cannot reach, E > 1018 _{eV. Furthermore, they can supply essential information}

about sources at considerable distances, even larger than 50 Mpc, and cosmic ray propagation beyond the Greisen-Zatsepin-Kuzmin limit.

However, currently relatively little is known about the neutrino in general and the UHE neut-rino in particular. Many researchers are investigating the fundamental neutneut-rino properties, such as the mass hierarchy or energy spectrum. Most of this research is conducted by the investiga-tion of Cherenkov radiainvestiga-tion that is induced by a particle shower after a neutrino interacinvestiga-tion in e.g. water. A great example of research that focuses on the latter, is KM3NeT: an international collaboration that has a neutrino research infrastructure with a detector volume of about a cubic kilometre, focusing on finding either neutrinos from distant astrophysical sources or neutrinos that are generated in the earth’s atmosphere [1].

Notwithstanding, these techniques do not suffice for detecting neutrinos with an energy higher than 1018 _{eV [}₁₅_{]. Luckily, a promising method is being developed to detect the UHE neutrino}

signal: acoustically. With this method, the sound disk that arises when a neutrino interacts with a nucleon of for example a water molecule is investigated[15].

As sound waves have a very long attenuation distance in water, scientists from KM3NeT aim to develop an experimental set-up in the Mediterranean Sea of over 100 strings and more than 1000 hydrophones at a volume of more than 100 km3. A preparation for this is the deployment of two deep-sea recorders in January 2018 close to Pylos, Greece. These hydrophones have been continuously recording for a period of three weeks.

In this thesis, data from these hydrophones is analysed to obtain more insight in the sounds of the deep sea, to eventually create a model on how to distinguish the neutrino signal from the background noise. To do this, chapter 2 focuses on the neutrino and the thermo-acoustic properties. In chapter 3, the ambient and transient noise of Mediterranean Sea is discussed. Chapter 4 aims attention at the signal processing: the general noise level is determined, a trigger algorithm is applied and a matched filter is implemented to conduct a cross-correlation.

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Chapter 2

Theoretical background

This chapter focuses on the neutrino and its characteristics that are relevant for the acoustic detection. First, in section 2.1, the basic properties of the neutrino are discussed. Section 2.2

points out the interest in neutrinos with an energy above 1018_{eV by explaining the GZK-paradox}

and how these UHE neutrinos can serve as a solution to this paradox. Lastly, section 2.3 aims attention at the thermo-acoustic model and the acoustic signal that is expected as a result of the neutrino-nucleon interaction in sea water.

2.1 Neutrino properties

Being electrically neutral fermions with a mass below 1eV /c2_{, neutrinos only interact via the}

weak force and can hence traverse matter almost unimpededly. Neutrinos cannot be observed directly: they are only detected through their weak interactions [17]. The neutrino occurs in three flavours, ⌫e, ⌫µ and ⌫⌧ which can only be distinguished by the flavour of the charged lepton that

is produced in a charged-current weak interaction. The electron neutrino for instance, is defined as the neutrino state produced in a charged-current weak interaction with an electron [17]. The neutrino is in quantum superposition of all three flavours: it oscillates between the mass states. As can be seen in figure2.1, neutrino energies range fromµeV to EeV, depending on the source: cosmological neutrinos for example have a relatively high flux (_{⇠ 10}20_cm 2_s 1_sr 1_{M eV} 1_{) and}

a low energy (_{⇠ 10} 4_{eV ).}

For each of these energy ranges, di↵erent detection methods are required. To obtain more information about for instance neutrinos in the energy range of amongst others the solar neutri-nos and neutrineutri-nos from supernova bursts, underground experiments are conducted, such as the Sudbury Neutrino Observatory (SNO) in Canada [11] or the Super-Kamiokande in Japan [7]. To detect atmospheric neutrinos or neutrinos from AGNs (active galactic nuclei), Cherenkov radiation is investigated. KM3NeT is one of the main collaborations that focuses on this kind of detection. However, as can be seen in figure 2.1, the flux of the neutrinos with an energy above 1018 _{eV is}

profoundly low. Therefore, the current techniques do not suffice to detect these ultra high energy neutrinos: a larger detection volume is required. As sound waves have a long attenuation length in water, namely approximately 10 km at a frequency of 5 kHz, acoustic detection may be a good candidate for the detection of these UHE neutrinos.

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CHAPTER 2. THEORETICAL BACKGROUND

Figure 2.1: The flux for various neutrino energies [14]. The energy of the neutrino depends on its source. The higher the energy of the neutrino, the lower the flux.

2.2 The GZK-limit

In 1966, Greisen, Zatsepin and Kuzmin computed an upper-limit for the spectrum of cosmic rays [12]. If the energy of these cosmic rays would exceed the threshold energy of 5· 1019 _{eV, the}

protons would interact with the photons of the cosmic microwave background (CMB). Along this interaction, pions are produced via the delta resonance: a delta baryon decays into a nucleon and a charged or uncharged pion:

CM B+ p! +! p + ⇡0 (2.1)

CM B+ p! +! n + ⇡+ (2.2)

Consequently, as a result of the weak interaction, the pion and neutron can decay into a lepton and the corresponding neutrino. The pion production process can occur as long as the energy of the cosmic ray is higher than the pion production threshold, while each newly produced pion takes about 20 % of the cosmic rays original energy [12]. Because of this, Greisen, Zatsepin and Kuzmin stated that cosmic rays with an energy higher than the cuto↵, or from a distance larger than 50 Mpc, cannot be observed on earth [12].

However, air showers initiated by protons with an energy above the GKZ-limit have been observed [23]. Many scientist are puzzled by this paradox, and one promising solution involves neutrinos: the Z-burst model in which a UHE neutrino and a relic anti-neutrino annihilate into a virtual Z-boson [16]:

⌫ + ¯⌫C⌫B ! Z0 (2.3)

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energy of the Z-boson:

E⌫res= m2 Z 2m⌫ ⇡ 4 · 10 21eV m⌫ (2.4)

This resonant neutrino annihilation results in a hadronic Z-burst approximately 70% of the time, which contains on average 30 photons and 2.7 nucleons that have an energy above the GZK-cuto↵ [21]. Because neutrinos can freely propagate through the universe, the processes as given in (2.3) may occur close to Earth, where they result in the observed super-GZK air showers [21]. Hence, the detection of UHE neutrinos is not only relevant as it allows physicists to probe particle physics at high energy scales and to investigate the cosmic neutrino background, it also enables the observation of sources at great distances, thereby o↵ering an explanation for the GZK-air showers.

2.3 The acoustic neutrino signal in sea water

Each neutrino flavour is able to interact with an electron, proton or neutron of a water molecule via the exchange of one of the weak vector bosons; namely the Z0_{-boson for non-charged current}

(NC) reactions or the W± _{for charged current (CC) reactions. When a nucleus within the water}

molecule breaks up, a hadronic shower will arise. This hadronic shower of secondary particles will result in an energy deposition ✏ that leads to a slight increase of the temperature [15]. According to the thermo-acoustic model, this will lead to the formation of a pressure pulse that can be described by r2_p 1 c2 @2_p @t2 = ↵ Cp @2_✏ @t2 (2.5)

with c, ↵ and Cprespectively the speed of sound, heat capacity and expansion coefficient. Hence,

the properties of the sea water play a role in the height of the signal. The three-dimensional pressure pulse propagates within a flat disk, and is therefore often referred to as a pancake-pulse [15]. As can be seen in figure2.2, this pressure pulse can be described with a bipolar signal with a peak at approximately 1 mPa for a 1018 _{eV hadronic shower at a radial distance of 1 km. The}

signal is assymetrical, which is in the far field due to the complex attenuation of the signal in the water, that leads to a non-linear frequency dependence of the phase shift. In the near field, the signal approximates a monopolar signal as a result of the interference of the emission from di↵erent parts of the shower [15]. The frequencies in which the signal occurs lie between 1 en 50 kHz, with a peak at approximately 10 kHz, as can be seen in figure2.2.

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Figure 2.2: The expected neutrino amplitude and relative power spectrum for a 1011_{GeV hadronic}

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Chapter 3

Noise

The hydrophones in the Mediterranean Sea record not only the neutrino pulse, but also the general background noise and pressure pulses coming from other sources. Therefore, it is of importance to gain insight in both the ambient and transient noise of the Mediterranean Sea, which is done in respectively section3.1and section3.2.

3.1 Ambient noise

The ambient noise can be seen as the omnipresent background noise that excludes momentary, occasional sounds as well as all forms of self-noise, for instance the noise of current flow around the hydrophones [19]. At frequencies below 100 Hz, the seismic activity of the earth and the turbulence, which is the random and chaotic flow of the sea water, play an important role.

At frequencies below 1 kHz, shipping has a crucial influence on the noise level. For example, the cavitation that takes place at the propeller blade tips leads to the formation of bubbles, resulting in a change in pressure. As sound is able to propagate far at these low frequencies, depending on the water temperature and pressure, the background noise below 1 kHz is dominated by the sounds generated by ships [8]. This is supported by figure 3.1 in which the location of the two hydrophones is indicated with a star: this turns out to be close to crowded vessel routes.

Figure 3.1: The vessel routes around Pylos, Greece. The location of the deployment of the hydrophones is marked with a star. Source: marinetraffic.com, retrieved June 2018

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CHAPTER 3. NOISE

Figure 3.2: Ambient noise spectra [22], adapted by [13]. For frequencies between 10 Hz and 1 kHz, shipping plays a dominant role. In the domain between 1 and 40 kHz, the sea state noise is preeminent, indicated by the blue curves.

However, in the frequency domain that is of main interest for the neutrino, namely between 1 and 40 kHz, the most dominant factor is the sea state noise: the noise due to the weather conditions, mostly the wind, at the surface, for example rain or bursting micro bubbles created by the wind, resulting in a pressure pulse that is measured by the hydrophone [8]. In 1948, Knudsen developed a model that predicts the contribution of the sea surface agitation to the noise level:

N Lsurf ace= 8 < : N L1K, if f < 1000Hz N L1K 17 log(₁₀₀₀f ) if f > 1000Hz (3.1)

where N L1K depends on the sea state as described by the Beaufort scale. The value of N L1K

ranges from 44.5 for sea state 0 (calm sea like a mirror) to 70 for sea state 6 (large waves with white foam crests) [19].

This is all summarized in figure3.2. In this figure can also be seen that the noise level generally decreases for higher frequencies. Furthermore, the noise level is also reduced at great depths, as most of the noise sources are at the surface [13].

3.2 Transient noise

However, not only is there an ambient background noise, but there are also some transient sounds, distinguishable from the ambient noise by their short character. Most of the transient sounds come from biological sources, such as the snapping of shrimps that happens in the frequency domain between 1 and 10 kHz. Whales and dolphins also make use of sound waves for communication and echolocation. For example, the sperm whale sends out clicks in the frequency domain between 1 and 20 kHz to navigate or locate food. Besides sperm whales, the Mediterranean Sea close to Pylos is also home to among other the common bottlenose dolphin, Cuviers beaked whale and the

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CHAPTER 3. NOISE

Figure 3.3: Spectrogram with on the y-axis the frequency and on the x-axis the time. The colours indicate the strength of the frequency: the more red, the higher the strength. Clicks from a marine mammal are clearly visible as the vertical stripes.

fin whale [9]. In figure3.3, a spectrogram of approximately 8 seconds of data is shown, in which the clicks of a marine mammal, with a frequency between 25 and 45 kHz are clearly visible as the vertical stripes. These clicks occur regularly and their frequency domain partly overlaps with the frequency domain of the expected neutrino signal. Accordingly, the existence of these clicks should be kept in mind during the further analysis.

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Chapter 4

Signal processing

Let's have a look at the signal that the two hydrophones, pictured in figure4.1 recorded. More than three weeks of continuously recording of one hydrophone, from 29/01/2018 until 21/02/2018, resulted in 276 WAV-files of each almost two hours and each containing 2 GB of data. The sampling frequency of this data is 144 kHz, generating approximately 109 _{samples per file. This sampling}

frequency leads to a Nyquist frequency of 72 kHz. To prevent aliasing, an artifact in which the Fourier transform of a signal xn contains signals that were not present in the original continuous

signal x(t), one must not take samples with a frequency lower than the Nyquist frequency [20].

Figure 4.1: The used hydrophone. The hydrophone is based on a piezoelectric transducer that generates a voltage when a change in pressure is detected by the small object on top.

In this chapter, first the noise will be characterized in section 4.1. After that, light is shed at the signals and the algorithm based on the amplitude is introduced to define and detect triggers in section4.3. Lastly, in section4.4.2, the shapes of these triggers are compared to the expected neutrino signal after which a cross-correlation is conducted by applying a matched filter.

4.1 Characterizing noise

4.1.1 Butterworth filter

As can be seen in figure2.2, the neutrino signal lies in the frequency range between 1 and 40 kHz. Therefore, the unneeded frequencies are filtered out by using the Butterworth filter. This filter is chosen because it o↵ers the best compromise between attenuation and phase response [24]. The

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CHAPTER 4. SIGNAL PROCESSING

main characteristic of this filter is that it not only rejects the unwanted frequencies, but also has uniform sensitivity for the frequencies of interest [4].

To o↵er more insight in the algorithm behind the Butterworth filter, we have a closer look at a normalised low-pass filter, that has the following amplitude response [6]:

|H(i!)| = p 1

1 + !2n (4.1)

with ! the angular frequency and n the order of the filter, which is equal to the number of poles. It becomes clear that if n _{! 1, the gain is 1 for frequencies lower than the cut-o↵ frequency,} !_{ 1, and 0 for frequencies above the cut-o↵ frequency, ! > 1.}

In order to get rid of the complex values, s = i! is substituted in the amplitude response equation. This gives

H(s)H( s) = _{1 + (s/i)}1 2n (4.2)

This results in poles at s2n₌ ₁_{⇤ (i)}2n _[₆_{]. Using e}i⇡(2k 1)₌ _{1 and e}i⇡/2_{= i, obtaining}

sk = e i⇡

2n(2k 1+n), (4.3)

where k is an integer that goes from 1,2,3,...,2n. Hence, the poles of this normalized filter lie on the unity circle [6]. In the left-hand plane, _{H(s), this can be written as a polynomial, which is} useful as it now can be expressed with real coefficients:

H = _(s _s 1

1)(s s2)...(s sn) (4.4)

The filter should result in a maximally flat frequency response in the passband and goes to-wards zero in the stopband. The higher the order of the filter, the steeper this roll-o↵ [6].

4.1.2 Power Spectral Density

In figure 4.2, the power spectral density (PSD) is plotted for various frequencies, for both the filtered and the unfiltered signal. The PSD is a measure for the relative strength of the frequencies, and is here obtained by using Welchs method. With this method, the signal is split up into segments, where two neighbouring segments have an overlap with each other. To avoid spectral leakage, the Hanning Window is used, a cosine function that causes the window to have no sharp edges: more influence is assigned to the signal at the center of the window. The loss of information that thereafter arises at the edges is diminished because of the overlap between the segments [20]. Subsequently, the Fast Fourier Transform (FFT) is applied in order to get the signal as a function of frequency instead of time. The FFT algorithm uses a Discrete Fourier Transform (DFT), but scales with N log(N ) instead of N2_{, to quicken the process [}₂₀_{]. In the conventional}

definition of a DFT, a list of numbers x[n] with n = 0, 1, ...N 1 is transformed in to X[k] with k = 0, 1, ..., N 1 : X[k] = 1 X n=0 x[n]e i2⇡kNn (4.5)

where X[k] can be converted into X[!] by substituting k = !T 2⇡ [20].

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Figure 4.2: E↵ect of the 5th order Butterworth filter on the PSD. The filter results in a relatively flat passband and has decreased the strength of the frequencies that are not of interest for the neutrino detection.

It can be seen in figure4.2that the passband is relatively flat, and at high frequencies there is a steep roll-of. In the unfiltered signal, the low frequencies (below 1 kHz), are dominant. In the filtered signal, the PSD of these frequencies has decreased from about 104_{to 10} 2_ADC/p_{Hz, but}

it is important to note that these frequencies are still present to some extent in the filtered signal.

4.1.3 Gaussian Noise Distribution

The amplitudes of the signal with a fifth order Butterworth filter of 1 to 40 kHz seem to result in a Gaussian normal distribution, as can be seen in figure4.3. Because of the Butterworth filter, the DC-o↵set has been removed, leading to a mean of 0. The width of the Gaussian distribution, , depends on the frequency. For low frequencies, the standard deviation is larger: in the right part of figure4.3the relation between and the frequency is shown. This is in compliance with the results of section 3.1 in which was stated that the general noise level decreases for higher frequencies.

From this it can be concluded that the ambient background noise is by approximation white Gaussian noise: it has a probability distribution with zero mean and finite variance, and two events are statistically independent, meaning that the existence of one event has no influence on the existence of another event [10]. This statement is supported by figure4.2: in the filtered signal, the pass band is relatively flat, which means that it has equal sensitivity for each frequency, as opposed to the unfiltered signal that is pink noise: the PSD inversely proportional to the frequency. The ambient noise being white Gaussian noise is the starting point for the trigger algorithm that is described in section4.3.

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Figure 4.3: On the left, the ADC distribution for the filtered signal between 1-40 kHz is shown. It appears to be a Gaussian distribution with a width . The value of this width is higher for higher frequencies, as shown in the right part of this figure.

4.2 The filtered signal

Having applied the Butterworth filter and knowing that the noise is white Gaussian noise, we now have a closer look at the filtered signal. In figure 4.4a is the analog to digital conversion (ADC), which means the strength of the signal and can hence be considered as the amplitude of the signal, plotted for 500 ms. Generally, the data oscillates around zero while the peaks fluctuate. Furthermore, there is a constant noise-level: the background noise. In figure4.4b the same signal is plotted for only 3 ms.

Some signals in figure 4.4 attract one's attention. For example, after approximately 275 ms, there is a peak visible in the ADC. In the next section, an algorithm is introduced to detect these signals.

Figure 4.4: The filtered signal for 500 ms and 3 ms. The signal oscillates around zero with fluctuating peaks.

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4.3 Trigger algorithm on amplitude: 5

Noting some remarkable signals, the next step is to define a way to find those signals. Considering the findings of section 4.1.3, namely that the background noise shows a Gaussian distribution with width , in this section a trigger is defined as a signal that has an amplitude that is larger than 5 . Thus, 5 is a measure for the background noise that is redetermined every two minutes.

4.3.1 Expectations

For a perfect Gaussian distribution, a signal with an amplitude above 5 should should occur once every 1 744 278 samples. With the sampling frequency of 144 000 Hz, this equals approximately once every 12 seconds or 10 triggers per two minutes. However, as there are 144 000 samples per second, one trigger is not a full oscillation. Instead, one oscillation can produce tens of triggers, leading to a higher expected number of triggers per two minutes than the value of 10 of a perfect Gaussian. If there are more triggers, then the total signal shows an imperfect Gaussian distribution. This can have two reasons: firstly, the background noise is not as Gaussian in the tails as expected, or secondly: there is a relatively long-lasting signal with a large amplitude.

4.3.2 Results

The noise level, defined as 5 , as well as the number of triggers per two minutes are shown in figure4.5 for a period of 2,5 days.

Figure 4.5: The noise level, defined as 5 , and the number of triggers per two minutes for a period of 2,5 days, from 02-02-2018 to 05-02-2018.

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Figure 4.6: The total number of triggers and the number of triggered peaks as well as the ratio between those, for 02-02-2018.

As can be seen, the noise level deviates around 50 (unit dependent on calibration) with quite some outliers, some even with a value over 500. The number of triggers is determined by checking if each sample has an amplitude larger than the noise level of 5 . To quantify the e↵ect of one oscillation leading to more triggers, figure 4.6 shows both the total number of triggers and the number of triggered peaks, as well as the ratio between those. Around 16:00h, there is a large increase in the total number of triggers, whereas the number of triggered peaks remains relatively constant. This means that the signal that resulted in the triggers was a long-lasting signal with a large amplitude. The increase in the number of triggers around 19:00h however, leads to a large increase in the number of triggered peaks as well. Hence, the sound underlying these triggers consists of multiple short oscillations.

4.3.3 The relation between the noise level and the number of triggers

Sometimes a higher noise level leads to more triggers, but sometimes it does not. For example, in figure4.5the peak in the noise level with a value just below 200, at approximately 02-02-2018, 20:00h, leads to a very large peak in the number of triggers: over 40 000. On the other hand, roughly five hours later, there is an enormous peak in the noise level that results only in a small peak in the number of triggers. This is also visible in figure4.7in which the number of triggers is plotted over the noise level: there are two trends noticeable: one that follows the y-axis and one that follows the x-axis. This can be explained by the nature of sounds. Some ships, for example, generate a loud yet constant sound. This results in an increase of the noise level, but due to the sound being constant and not having many outliers, it does not result in many triggers. On the other hand, there are some sounds that have the opposite behaviour: not loud but irregular, resulting in an increase of the number of triggers while the noise level remains relatively low.

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Figure 4.7: Scatter plot of the number of triggers and the noise level for the data as shown in figure4.5. Two trends are visible, one that follows the y-axis and one that follows the x-axis. This can be explained by the nature of the sounds.

4.3.4 Discrepancy

Even though an increase of the number of triggers can be explained by the nature of some sounds, the discrepancy between the expected number of triggers based on the Gaussian statistics, namely 10 per 2 minutes, and the found number of triggers, generally around 50 with regular peaks at 5000 and sometimes even as high as 40 000, is too high. This is supported by figure4.8, in which the number of triggers per two minutes is shown for a noise level that is defined as not only 5 , but also 6 to 9 . If a distribution is perfectly Gaussian, a value above 7 should, with a sampling frequency of 144 kHz, occur only once every 31 days. A value above 8 or 9 should arise even less frequently. However, as can be seen in figure4.8, these values occur repeatedly.

Figure 4.8: The number of triggers for noise levels of 5 to 9 sigma, for a period of approximately 10 hours at January 29th, 2018

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Figure 4.9: The ADC distribution as in figure4.3a, but now on a logarithmic scale. It can be seen that the ADCs deviate from the Gaussian distribution at the tails.

This means that the background noise does not show perfectly Gaussian behaviour: the tails of the distribution deviate from the Gaussian distribution. Figure4.9, in which the ADC-distribution is shown on a logarithmic scale, confirms this: the distribution is Gaussian for the values close to zero, but deviates in the tails. From this, it can be concluded that in order to detect the neutrino signal, a trigger algorithm based on solely the amplitude is too naive as it results in too much data points that require further investigation.

4.4 Trigger algorithm on shape: matched filter

4.4.1 The shape of the triggered signals

In section4.3, it was found that the trigger algorithm based on the amplitude results in too many triggers. Therefore, this section focuses on the shape of the triggered signals. In figure 4.10, six signals are shown that resulted in an amplitude trigger. It can be seen that these signals vary regarding their shape. Recall that the theoretical neutrino signal as first introduced by Askaryan [2] looks bipolar as in figure 2.2. To see if this shape corresponds to some of the triggers, a cross-correlation is conducted in the following subsection.

4.4.2 Matched filter

A method to detect certain signals that is often used in medical sciences, for example to detect a heart beat in an ECG, but also in physics to find for instance a gravitational wave, is the use of a matched filter. With this method, a cross-correlation is executed in which a template signal that is similar in shape to the expected neutrino signal is shifted over the files to see if the template matches the real signal, resulting in a pulse [18]. This linear matched filter results in a maximal signal to noise ratio of the output signal. The correlation should be performed on a finite impulse response (FIR) filter, which is by definition a convolution operator [5]. The convolution of two

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Figure 4.10: Signals that resulted in triggers. The red dotted line is the noise level 5 . It can be seen that the triggers vary in shape.

functions u(x) and v(x) is defined as [10]

u(x)⇤ v(x) = Z 1

1

u(t)v(t ⌧ )d⌧. (4.6)

Note that this is exactly the time-reversal of the cross-correlation, which is [10]

u(x) ? v(x) = Z 1

1

u(t)v(t + ⌧ )d⌧ (4.7)

Therefore, to obtain the FIR coefficients, the template neutrino signal developed by R. Lahmann, is time-reversed, as can be seen in figure 4.11. The y-value of this template signal is in arbitrary units and can be normalized.

Figure 4.11: The template neutrino signal as obtained by R. Lahmann and its time-reversed signal. The value of the y-axis is arbitrary and can be normalized.

This time-reversed signal is shifted over the filtered time series. If there is a match, a peak in the impulse response is visible. In order to improve the signal to noise ratio, the impulse response

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has been squared. In figure 4.12, two minutes of time series as shown as well as the impulse response of the applied matched filter. It can be seen that the peaks of the cross-correlation are located at the same places as the value the places that generated triggers in section4.3.

Figure 4.12: Top: the time series for a period of 120 seconds, oscillating around zero and with some peaks. Bottom: the result of the cross-correlation. The better the template signal fits in the data, the higher the value of the cross-correlation.

The y-value of the resampled template signal obtained from Lahmann used in this cross-correlation is very large: at the peak it reaches 800, whereas the general noise level is a bit above 40. Therefore, the neutrino template signal has been rescaled to 1% of its original, leading to a peak of not 800 but 8. The signal would then have an amplitude that is below the noise level. Applying the matched filter with this template signal leads to the exact same shape as in figure

4.12, with the di↵erence that the y-axis of the impulse response is in the order of magnitude of 106 _{instead of 10}10_.

To conclude, the cross-correlation results in a match at the exact same samples as the trigger algorithm based on amplitude. Hence, also this method leads to a number of matches that is too high. However, this method shows a relative strength of the match and is therefore an improvement compared to the algorithm that is solely based on the amplitude.

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Chapter 5

Discussion and conclusion

In this report, two algorithms have been tested in order to distinguish the neutrino signal from the background noise. The first algorithm was based on the amplitude and considered a sample with an ADC value larger than 5 as a trigger. This algorithm resulted in a large discrepancy between the expected number of triggers and the found number of triggers. The main reason for this discrepancy is that the amplitude distribution of the background noise does not show perfect Gaussian behaviour in the tails. The second algorithm was based on the shape of the signal: a cross-correlation by means of a matched filter, resulted in matches at the same samples as the amplitude trigger, but now with a relative strength of the trigger. Hence, the total number of matches for the cross-correlation is still too high, yet more information is obtained because of the relative strength of each match.

To be able to distinguish the neutrino signal from the ambient and transient background noise, more information about this background noise is required. For example, meteorological data, such as the wind speed or the amount of rain that has fallen, could lead to valuable insights regarding the composition of the data. Also, knowing more about the marine mammals, how often they occur, the exact sound they make and with what frequency allows for a more accurate characterization of the noise. Furthermore, there are some aspects that require more attention in future research. Firstly, the template signal: the one used for the cross-correlation is the theoretical bipolar signal as introduced by Askaryan. However, to conduct a cross-correlation with a higher reliability, attention should be paid to the possible distortion of this bipolar signal that could be induced by the hydrophone. Secondly, the linear and frequency-dependent calibration should be taken into account to be able to compare the amplitude of the theoretical signal with the real data. Namely, the theoretical bipolar signal shows a peak at 0.1 Pa for a 1011 _{GeV shower at a distance of 1}

km. The corresponding ADC value of such a signal depends on the calibration of the hydrophone. Hence, looking into the calibration might lead to valuable information.

Another aspect that could lead to helpful information, is the use of arrays of hydrophones instead of only one hydrophone. Namely, moving sources, such as animals, could be detected and filtered out. Or, if a signal is detected at one hydrophone and not at the hydrophone next to it, it is not plausible that the signal comes from a neutrino-nucleon interaction as the attenuation length of this signal should be longer. Furthermore, arrays of hydrophones would be able to determine the position of the interaction or maybe even the angle at which the neutrino hit the nucleon of the water molecule.

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CHAPTER 5. DISCUSSION AND CONCLUSION

Thus, based on this report, it should eventually be possible to detect the acoustic neutrino signal. However, triggering on solely the amplitude results in too many triggers, as well as con-ducting a cross-correlation. Therefore, more investigation regarding the background noise in the Mediterranean Sea as well as the hydrophone characteristics, and hence the expected amplitude and shape for this specific hydrophone, is required. A great help for this would be the deployment of multiple arrays of hydrophones.

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Acknowledgements

I would like to thank Ernst-Jan Buis and Ivo van Vulpen for their guidance and useful insights as well as for laughing with me at the mysterious sounds of the sea. Paul de Jong, thank you for being my second examiner, and for letting me join the KM3NeT outing. I genuinely enjoyed the serious sessions as well as the zigzagging at a river during a thunder storm.

Furthermore, to the entire KM3NeT group: thank you for making me feel at home from the first day onward. I enjoyed every conversation, riddle, or table-football game with you. Beware that I will come and surprise you every now and then, walk into your office, smile, and say that it's time for a plank.

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Eavesdropping on whales; the acoustic detection of ultra high energy neutrinos in the Mediterranean Sea