Anàlisi temps-freqüència de l’estat de polarització del senyal magnetotel·lúric
Polarisation analysis of the magnetotelluric signal in the time-frequency domain
Magdalena Escalas Oliver
Aquesta tesi doctoral està subjecta a la llicència Reconeixement- NoComercial – SenseObraDerivada 3.0. Espanya de Creative Commons.
Esta tesis doctoral está sujeta a la licencia Reconocimiento - NoComercial – SinObraDerivada 3.0. España de Creative Commons.
This doctoral thesis is licensed under the Creative Commons Attribution-NonCommercial- NoDerivs 3.0. Spain License.
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Conclusions i perspectives de futur
Conclusions
En aquesta tesi s’ha analitzat l’estat de polarització del senyal MT en el domini (t-f). S’ha creat una nova eina que permet calcular els atributs de polarització dels camps E i B a partir de la TW de les sèries temporals MT, i s’ha aplicat a la detecció i caracterització de fonts de soroll cultural i senyals geomagnètics polaritzats. D’aquesta manera l’objectiu principal de la tesi i els objectius concrets plantejats inicialment han estat completament assolits.
A cada capítol d’aquesta memòria s’han exposat detalladament les conclusions dels resultats obtinguts, a continuació s’analitzen de manera més general.
La contribució metodològica de la tesi ha estat el disseny d’un mètode que proporciona els atributs de polarització del senyal MT en el domini (t-f). Aquests són l’el·lipticitat, l’angle de polarització i el desfasament entre els components ortogonals de cada un dels camps, així com la diferència d’el·lipticitat entre ambdós camps i la desviació de l’angle que formen entre ells respecte a l’ortogonalitat. La base teòrica del mètode és la proposada per Diallo et al.
(2006) per a l’anàlisi de senyals sísmics. S’hi han fet nombroses modificacions, tant respecte al càlcul de la TW com al dels atributs. La modificació més rellevant és la que fa referència a la regió significativa del domini (t-f) on es calculen els atributs. S’ha dissenyat un nou procediment per obtenir-la, basat en el càlcul de la TWI, per a la qual també s’ha proposat una expressió empírica. Finalment s’ha dissenyat una estratègia de filtratge del senyal segons el valor dels seus atributs de polarització en el domini (t-f) tenint en compte la regió significativa i el càlcul de la TWI.
El mètode dissenyat s’ha implementat en el codi MTWAVELETS, en llenguatge Matlab.
Mitjaçant l’anàlisi de nombrosos senyals sintètics s’ha comprovat el seu correcte funcionament.
Per aplicar el nou mètode a l’anàlisi de senyals MT reals, en primer lloc s’ha dissenyat i dut a terme l’experiment “Hontomín-font” a Hontomín (Espanya). Ha consistit en la
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contaminació de sèries temporals MT amb el senyal generat per dos dipols elèctrics horitzontals alimentats per una font de corrent. L’anàlisi de les dades experimentals amb el codi MTWAVELETS ha permès diferenciar el senyal MT del senyal artificial generat amb la font, a partir de l’anàlisi del seu estat de polarització en el domini (t-f). En general el senyal MT no té un estat de polarització determinat, en canvi el senyal artificial es pot caracteritzar pels seus atributs de polarització. La realització de l’experiment i l’anàlisi de les dades obtingudes han resultat ser molt satisfactoris ja que han posat de manifest la utilitat del mètode desenvolupat en aqueta tesi per detectar una font de soroll EM.
S’ha modelitzat l’experiment amb el codi DIPOLE1D (Key, 2009), per conèixer el comportament teòric de l’amplitud dels camps E i B i els seus atributs de polarització en funció del medi, la freqüència i la posició respecte la font. D’aquesta manera s’han pogut interpretar els resultats de l’experiment obtinguts amb el codi MTWAVELETS. La modelització s’ha dut a terme considerant medis homogenis i el medi estratificat 1D- Hontomín (Ogaya et al., 2013). La comparació dels resultats experimentals i els modelitzats ha permès identificar el tipus de font utilitzada i la seva posició relativa respecte els punts de mesura. D’altra banda, ha posat de manifest la presència d’inhomogeneïtats en el medi, fet que era d’esperar tenint en compte el model 3D d’Hontomín (Ogaya et al., 2014).
El mètode desenvolupat s’ha aplicat també a l’anàlisi de senyals MT contaminats per fonts de soroll cultural. A diferència de les respostes MT, l’anàlisi de l’energia i els atributs de polarització en el domini (t-f) sí ha permès identificar en cada cas la font de soroll i la seva posició relativa. Així s’ha caracteritzat el senyal creat per línies elèctriques, la circulació de trens per vies fèrries electrificades amb CC, aerogeneradors i entorns industrials, a partir de dades mesurades a Hontomín i a Lamezia Terme (Itàlia). Gràcies a aquest estudi es coneix el patró que creen aquestes fonts de soroll, i per tant es podran identificar fàcilment en futures anàlisis de sèries MT contaminades. A més, la identificació concreta dels intervals de temps i les freqüències afectades pel soroll és molt útil de cara a filtrar el senyal MT en el domini (t-f) i seleccionar només els segments de major qualitat per obtenir les respostes MT.
Així mateix, amb el codi MTWAVELETS s’han detectat i caracteritzat senyals geomagnètics que presenten un estat de polarització determinat. Per una banda, l’anàlisi de les sèries temporals mesurades a Tramutola (Itàlia) ha permès identificar nombrosos esdeveniments com a pulsacions Pc3, i suggerir aquests senyals com una de les causes de les variacions de les respostes MT detectades en aquest site per Romano et al. (2014). Per l’altra banda, s’han detectat les SR a partir de les sèries temporals mesurades a Huidobro (Espanya), i s’ha caracteritzat el comportament de la seva energia i els seus atributs de polarització en el domini (t-f).
Els resultats obtinguts en aquesta tesi suposen una important contribució, ja que el mètode desenvolupat i la seva implementació en el codi MTWAVELETS permeten analitzar el senyal MT des d’una nova perspectiva. La seva aplicació per detectar fonts de soroll i senyals geomagnètics polaritzats ha mostrat el potencial de la metodologia desenvolupada.
En concret, pel que respecta al soroll cultural el mètode proposat suposa una nova eina per detectar-lo a partir de les sèries temporals MT, així com per determinar la posició relativa de
189 la seva font respecte el punt de mesura. Actualment, gràcies al desenvolupament de codis d’inversió 3D, en els estudis MT es mesuren dades en un gran nombre de sites. El més habitual és intentar minimitzar el soroll cultural que les pot afectar en l’etapa de processat per obtenir les respostes MT, i en pocs casos s’analitzen prèviament i amb detall les sèries temporals mesurades (Chave i Jones, 2012). Per aquest motiu, la nova eina desenvolupada es considera útil per a detectar soroll cultural a partir de les sèries temporals, prèviament a realitzar el seu processat. D’aquesta manera, durant una campanya d’adquisició de dades MT ja es poden identificar les fonts culturals que les afecten, i si és possible modificar la posició dels sites. Una altra possibilitat que ofereix el mètode és poder seleccionar, en funció del temps i la freqüència, els segments més idonis (menys afectats pel soroll) per a realitzar-ne el seu processat.
Pel que fa als senyals geomagnètics analitzats, tant les pulsacions Pc3 com les SR se solen analitzar habitualment a partir dels registres del camp B en observatoris geomagnètics.
L’anàlisi de les sèries temporals MT en el domini (t-f) ha posat de manifest que tant el camp B com el camp E proporcionen informació útil sobre aquests senyals. Tenint en compte que tant l’energia com l’estat de polarització d’aquests senyals en el domini (t-f) són característics de cada un d’ells, el nou mètode proposat és molt útil per detectar-los i analitzar la seva evolució en el temps i la freqüència. L’estudi tant de les pulsacions Pc3 com de les SR té nombroses aplicacions, com per exemple determinar l’estat de la magnetosfera i la ionosfera.
El fet d’analitzar aquests senyals a partir de sèries temporals MT en comptes de fer-ho a partir del camp B mesurat en un observatori geomagnètic implica que també es pot conèixer la resposta geoelèctrica del medi on es detecten. És un aspecte a tenir en compte si es comparen en registres mesurats en localitzacions diferents. Pel que fa a les pulsacions Pc3, detectar la seva presència és especialment convenient en l’aplicació del mètode MT ja que s’ha mostrat com les respostes MT es poden veure modificades per aquests senyals. Caldrà determinar en cada cas fins a quin punt les variacions de les respostes són acceptables.
Actualment s’aplica molt sovint el mètode MT pel monitoratge de reservoris, per exemple en l’emmagatzematge de CO2, i el seguiment de fenòmens naturals com el vulcanisme. Per aquest motiu és molt important discriminar si les variacions observades en les respostes MT són degudes a canvis en el subsòl o bé son causades per la inestabilitat de les fonts del senyal MT. L’aplicació del mètode proposat en aquesta tesi pot ajudar a diferenciar aquestes situacions.
Perspectives de futur
En un futur seria convenient dur a terme les següents ampliacions del mètode desenvolupat per l’anàlisi del senyal MT en el domini (t-f) i el codi MTWAVELETS en què s’ha implementat:
• Analitzar l’efecte d’utilitzar noves wavelets mare en la TW. És ben conegut que la wavelet de Morlet és idònia per a l’anàlisi del senyal MT, però per a l’anàlisi del soroll cultural seria interessant investigar l’efecte que causa l’ús de wavelets mare diferents.
Podrien proporcionar una major resolució segons el tipus de soroll.
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• Detectar automàticament regions del domini (t-f) amb un estat de polarització determinat, per identificar de manera automàtica en una sèrie temporal MT la possible presència de soroll cultural o senyals geomagnètics polaritzats.
• En el cas del soroll cultural, un cop determinada la regió (t-f) afectada, filtrar-la per obtenir un senyal MT lliure de soroll, i en conseqüència, millorar la qualitat de les respostes MT
• Analitzar estadísticament els resultats obtinguts amb el codi MTWAVELETS en l’anàlisi de diversos segments d’una sèrie temporal de llarga durada, per poder extreure conclusions de l’estudi de sèries temporals MT en experiments de monitoratge.
Respecte els conjunts de dades analitzats, els dos següents ofereixen diverses possibilitats per ampliar-ne el seu estudi:
• Lamezia Terme, en l’anàlisi del soroll cultural creat per una via fèrria electrificada amb CC: ja que es disposa de dades mesurades a diferents sites al llarg d’un perfil que uneix els sites S4 i N6, amb freqüències de mostreig = 6.25 i
= 500 , es proposa dur a terme l’anàlisi complet de totes aquestes dades per conèixer el comportament de l’energia i els atributs de polarització dels camps en el domini (t-f) en funció de la posició dels sites respecte de les vies fèrries. D’aquesta manera es podria analitzar com la variació dels atributs al llarg d’un perfil pot proporcionar informació sobre la font de soroll. En concret, permetria determinar el patró que causa la circulació de trens per una via fèrria electrificada a diferents distàncies d’aquesta.
• Tramutola, en l’estudi de les pulsacions geomagnètiques Pc3: a partir dels registres complets del monitoratge de què es disposa, es podria identificar automàticament la presència de les pulsacions Pc3 amb dues finalitats:
analitzar amb detall l’efecte de les pulsacions Pc3 sobre les respostes MT per determinar fins a quin punt, en cada cas particular, aquests senyals constitueixen una font útil pel mètode MT o bé cal tractar-les com a soroll;
analitzar l’energia i els atributs de polarització dels seus camps E i B en el domini (t-f) segons l’hora del dia i l’estació de l’any, per conèixer millor les propietats de les regions de la magnetosfera on es generen aquestes pulsacions i per les quals es propaguen.
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Conclusions
In this thesis, the polarisation state of the magnetotelluric (MT) signal is analysed in the time- frequency (t-f) domain. A new tool has been developed to compute the polarisation attributes of the electric (E) and magnetic (B) fields from the wavelet transform (WT) of the MT time-series. It has been applied to the detection and characterisation of cultural noise sources and geomagnetic polarised signals. In this way, both the aim of this thesis and its specific objectives were achieved.
The specific conclusions inferred from the results obtained are presented in each chapter of this dissertation. Below, they are analysed in more general terms.
The methodological contribution of this thesis is the design of a method to obtain the polarisation attributes of the MT signal in the (t-f) domain. These attributes are the ellipticity, the polarisation angle, the phase difference between the orthogonal components of each field, the ellipticity difference between both fields and the deviation of the angle between them from the orthogonality. The theoretical background of the method is the same as the one proposed by Diallo et al. (2006) for the analysis of seismic signals. It has been modified in numerous aspects with regard to the calculation of the WT and the attributes. The most relevant modification concerns the significant region of the (t-f) domain where the attributes are computed. A procedure has been designed to obtain that region, based on the calculation of the inverse wavelet transform (IWT). In addition, an empirical expression has been proposed for the IWT. Finally, a filtering strategy is proposed according to the values of the polarisation attributes in the (t-f) domain, taking into account the significant region and the computation of the IWT.
The resulting method has been implemented in a Matlab code named MTWAVELETS. It has been successfully tested through the analysis of many synthetic signals.
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In order to apply the new method to the analysis of real MT signals, an experiment named
“Hontomín-font” has been designed and performed in Hontomín (Spain). It involved contamination of MT time-series with the signal transmitted from two horizontal electric dipoles powered by a current source. The analysis of the experimental data with the MTWAVELETS code has allowed differentiation of the artificial signal from the natural MT signal through the analysis of their polarisation state in the (t-f) domain. The MT signal does not generally have a specific polarisation state. In contrast, the artificial signal can be characterised in terms of its polarisation attributes. The performance of the experiment and the analysis of the experimental data have proven the utility of this new method in detecting sources of electromagnetic noise.
In addition, the experiment has been modeled with the DIPOLE1D code (Key, 2009). The results show the theoretical response of the amplitude and polarisation attributes of the E and B field as a function of the earth model, the frequency and the location with respect to the source. In this way, the experimental results obtained with the MTWAVELETS code are interpreted. The modeling was done using homogenous earth models and the stratified model 1D-Hontomín (Ogaya et al., 2013). The comparison of the experimental and modeled results allowed identifying the source used in the experiment and its location with respect to the sites. Furthermore, it suggests the presence of inhomogeneities in the earth models, which were already expected taking into account the 3D model of Hontomín (Ogaya et al., 2014).
The method developed was applied to the analysis of MT signals contaminated by sources of cultural noise. In contrast to the MT responses, the analysis of the energy and polarisation attributes in the (t-f) domain allowed identifying, in each case, the noise source and its location relative to the source. In this way, the signal created by power lines, electric railways with direct current (DC), wind turbines and industrial areas was characterised in data acquired at Hontomín and Lamezia Terme (Italy). This study has provided the pattern of these noise sources. Thus, in the future they will be identified more easily from the analysis of MT contaminated time-series. Furthermore, the accurate identification of time intervals and frequencies affected by noise is helpful to filter the MT signal in the (t-f) domain and select the highest quality segments to obtain the highest quality MT responses.
Moreover, geomagnetic signals with a particular polarisation state were detected and characterised with the MTWAVELETS code. On the one hand, the analysis of time-series acquired at Tramutola (Italy) has helped to identify numerous events as Pc3 pulsations. It has also suggested that these signals are one of the causes of the oscillation of the MT responses detected at this site by Romano et al. (2014). On the other hand, the Schumann resonances were detected in time-series acquired at Huidobro (Spain). The behavior of its energy and its polarisation attributes have been characterised in the (t-f) domain.
This thesis is an important contribution to the current knowledge in electromagnetic geophysical techniques since the method developed and the MTWAVELETS code are an innovative tool to analyse the MT signal. Its application to the detection of cultural noise sources and geomagnetic signals demonstrates the viability of the method.
193 In particular, the proposed method has proven to be a new tool to detect cultural noise from MT time-series, and to identify its source and location. At present, in MT studies data are commonly acquired at a huge number of sites due to the development of 3D inversion codes. Cultural noise tends to be usually minimized during the processing stage to obtain the MT responses, and only in a small number of cases the MT time-series are analysed previously in detail (Chave and Jones, 2012). For that reason, the new method will help to identify sources of cultural noise from the time-series before the processing stage. In this way, the noise sources can be identified during a field campaign, and if it is possible, the location of the sites can be modified. Another advantage of the proposed method is that it allows doing the (t-f) selection of the best (less affected by noise) segments to process.
Regarding the analysed geomagnetic signals, Pc3 pulsations and Schumann resonances are usually analysed from the B field recordings at geomagnetic observatories. The analysis of MT time-series in the (t-f) domain has shown that both fields, E and B, provide useful information of these signals. Since the energy and the polarisation state characterise these signals in the (t-f) domain, the proposed method is useful to detect them and analyse their evolution in time and frequency. The examination of Pc3 pulsations and Schumann resonances has many applications, as they reflect the ionosphere and magnetosphere state.
Contrary to the analysis of these signals from the B field recorded at geomagnetic observatories, their analysis from MT time-series also provides the geoelectric response of the earth where they are detected. This is an important aspect to consider in the comparison of data from different locations. With regard to Pc3 pulsations, their detection is particularly convenient for the MT method since it has been demonstrated that MT responses can be affected by these signals. The oscillation of MT responses must be evaluated in each case to determine its acceptability. At present, the MT method is applied to reservoir monitoring, for example in CO2 storage, and to the monitoring of natural phenomena, such as volcanism.
For this reason it is very important to determine if the oscillations of the MT responses are due to soil variations or due to the instability of MT sources. The method proposed in this thesis can help to differentiate between both situations.
Future work
Finally, some perspectives of future work are presented. Regarding the method developed for the analysis of the MT signal in the (t-f) domain and the MTWAVELETS code, the following tasks are proposed:
• Check the effect of using different mother wavelets for the WT. It is well known that the Morlet wavelet is appropriate for the analysis of the MT signal. However, it would be interesting to study up to what extent the use of a different mother wavelet modifies the results. It could provide a better resolution depending on the characteristics of the noisy signal.
• Automatically detect (t-f) regions with a fixed polarisation state. It would help to automatically identify the presence of cultural noise or geomagnetic polarised signals from MT time-series.
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• Regarding cultural noise, once the (t-f) affected region is detected, its filtering would be fundamental to obtain MT signals free of noise, and thus, improve the quality of the MT responses.
• Statistically analyse the results obtained with the MTWAVELETS code when it is applied to the analysis of several segments of long-term time-series. It would be useful in order to analyse MT time-series from monitoring experiments.
Regarding the analysed data sets, the two following sets offer several possibilities to continue their study:
• Lamezia terme, for the analysis of cultural noise created by DC electric railways: MT data acquired along a profile connecting sites S4 and N6 are available, with sampling frequencies = 6.25 and = 500 . A complete analysis of these data is proposed, in order to know the energy and polarisation attributes of the fields in the (t-f) domain, as a function of the location of the sites with respect to the railways. It would show how the polarisation attributes can provide information about the noise source when they are analysed from a profile. In particular, it would provide the pattern created by DC electric railways at different distances.
• Tramutola, for the study of geomagnetic Pc3 pulsations: the presence of Pc3 pulsations could be automatically detected from the complete monitored data set, with two purposes:
carefully analyse the effect of Pc3 pulsations on MT responses to determine, in each case, up to what extent they constitute a useful source for the MT method, or if they should be treated as noise.
analyse the energy and polarisation attributes of their E and B fields in the (t- f) domain as a function of daily and seasonal variations, to improve the knowledge of the state of the magnetosphere regions where these pulsations are generated and propagated.
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Annex
Annex A: Expressió per calcular la TW de manera computacional
A continuació s’indica com s’obté l’expressió (2.12) utilitzada en aquesta tesi per calcular de manera computacional la TW mitjançant algoritmes de TF. Més detalls sobre la TF es poden trobar a Brigham (1974) i Papoulis (1962), i sobre la TW a Addison (2002) i Kaiser (2002).
La TF del senyal es defineix de la següent manera:
i la TF inversa (TFI):
La TF en cas de translació és:
i en cas de canvi d’escala:
La Identitat de Parseval relaciona el producte intern de dues funcions en el domini temporal i en el domini de freqüències:
[ ] ≡ = +∞ −
−∞ , ( A.1. )
= = 12
+∞
−∞ . ( A.2. )
[ − ]= − , ( A.3. )
[ ] = 1| | " # , $ % ≠ 0. ( A.4. )
+, · )∗
-, = 1
2 +, · ).∗
-, , ( A.5. )
