Modelação Numérica 2017 - ULisboa · Susana I. S. Custodio,1 Joao F. B. D. Fonseca,1 Nicolas F. d’Oreye,2 Bruno V. E. Faria,3 and Zuleyka Bandomo 4 Received 27 January 2003;

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Figura3.RegistosísmicoobtidonaestaçãodoIDLlocalizadaemMarmelete,Algarve(MORF).Oregistomostraavelocidadedosolonadirecçãoeste-oeste.Vêm-sedistintamenteosismoprincipaldemagnitude6.3eduasdasréplicascommagnitudespróximasde5.EstesismofezdispararosistemadealertadetsunamisdoMediterrâneo,tendoduasagênciademonitorização(CENALT,FrançaeINGV,Itália)dadoaviso2eoutra(NOA,Grécia)oaviso3,numaescalade1a3,paraascostasmaispróximas.Observaçõesdirectasposterioresmostraramqueapenasseobservouumaondade5cmnosmarégrafosjuntoàcostaemMálagaeoavisoacabouporsercanceladoporambasasagências.Nota:AlgumasfigurasforamfeitascomdadosobtidosapartirdoportalwebdoEuropean-MediterraneanSeismologicalCentre(EMSC,http://www.emsc-csem.org).Maisinformaçõessobreosismo:http://www.emsc-csem.org/Earthquake/241/M6-3-STRAIT-OF-GIBRALTAR-on-January-25th-2016-at-04-22-UTCNaimprensa:https://www.publico.pt/mundo/noticia/terramoto-de-intensidade-63-atinge-mar-entre-a-andaluzia-e-norte-de-africa-1721311

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1.  RepresentaçãonuméricadesistemasXsicosespaço-temporais.AnálisedeFourierecaracterizaçãodesériesdedados(teoremadaamostragem,propriedadesdatransformadadeFourier).Filtrosdigitais.



Tidal modulation of seismic noise and volcanic tremor

Susana I. S. Custodio,1 Joao F. B. D. Fonseca,1 Nicolas F. d’Oreye,2 Bruno V. E. Faria,3

and Zuleyka Bandomo4

Received 27 January 2003; revised 31 March 2003; accepted 20 May 2003; published 13 August 2003.

[1] We present seismic data from Fogo Volcano (CapeVerde Republic) that document a tidal control on theamplitude of seismic noise and volcanic tremor. The effectis detectable in the raw data by simple eye inspection. Weidentified the main periodicity in the noise modulation,which coincides with the tidal component M2. The signalduration of 40 days, together with a sampling rate of 1440samples per day (seismic r.m.s. time series) allowed theresolution of M2 from the neighbor solar frequencies thatare often related to environmental effects. Spectral analysisshows that the modulation affects selectively the frequencyrange 2.0 Hz–3.0 Hz, which we interpret as volcanictremor. White noise from 1.5 Hz to 7 Hz is also modulated.Comparison with meteorological data reinforces theconclusion that the effect is not due to environmentalparameters. INDEX TERMS: 1249 Geodesy and Gravity:Tides—Earth; 7280 Seismology: Volcano seismology (8419);8419 Volcanology: Eruption monitoring (7280); 8424Volcanology: Hydrothermal systems (8135). Citation: Custodio,S. I. S., J. F. B. D. Fonseca, N. F. d’Oreye, B. V. E. Faria, and Z.Bandomo, Tidal modulation of seismic noise and volcanic tremor,Geophys. Res. Lett., 30(15), 1816, doi:10.1029/2003GL016991,2003.

1. Introduction

[2] In this paper, we present evidence of tidal modula-tion of seismic noise and volcanic tremor, derived fromdata recorded at Fogo Volcano (lat. 14.9N; long. 24.3W;Cape Verde Republic). Fogo is an active stratovolcano[Day et al., 1999] whose last eruption occurred in 1995[Heleno et al., 1999]. Since 1999 a network of seismo-graphic stations, both short-period and broadband, havebeen in operation in Fogo and in neighbor Brava Island aspart of a monitoring program [Fonseca et al., 2003], andan automatic meteorological station is operated since 2001in the volcano’s caldera. We used 3-component records ofseismic noise from five stations (see Table 1 for instru-ment characteristics), digitized at 50 samples per second,acquired over a period of 47 days in the summer of 2001.The data display a semi-diurnal amplitude modulation thatis often strong enough to be detected by simple eyeinspection of a sufficiently long record of the raw signal,as depicted in Figure 1. This effect is strongest on the EWcomponents of seismic records, which is usually the case

for tidal tilt data [Melchior, 1983], and this raised ourinterest in investigating a possible link with the tides.

2. Data Processing and Analysis

[3] As a first step, we analyzed samples of the seismicdata corresponding to high noise amplitude and low noiseamplitude separately. Details of the analysis are given inthe legend of Figure 2, and the main results are: noiselevel in the range 1.5 Hz–7 Hz was amplified by 50% to75% from low noise time-windows to high noise time-windows; in some stations, the amplification affectedselectively certain frequencies; the central frequenciesof these peaks are station-dependent, but stay in therange 2 Hz–3 Hz; these effects were clearest in the EWcomponents.[4] Next, the seismic traces were band-pass filtered

from 1.5Hz to 7Hz with a 4-pole Butherworth filter,and the r.m.s. was computed on a moving window of2 minutes and at time steps of 1 minute. In this way, anew time series was derived for each seismic trace, with asampling rate of fs = 1440 samples per day and a length of40 days (total duration of 47 days but with interruptionsadding up to 7 days, with slight variations for sometraces). Gaps due to operational problems in the acquisi-tion were removed by linear interpolation, in order tominimize their impact on the spectral analysis. The rela-tive importance of the modulation for the different stationsand components is quantified by the histograms in

Figure 1. A) Five day long sample of seismic noise atstation FMLN, EW component, showing the semi-diurnalmodulation of amplitude. The power spectral densitiesgiven in this paper were derived from 40 day long timeseries. B) Band-pass filtering the same noise samplebetween 1.85 Hz and 2.25 Hz enhances the modulation.

GEOPHYSICAL RESEARCH LETTERS, VOL. 30, NO. 15, 1816, doi:10.1029/2003GL016991, 2003

1ICIST, Instituto Superior Tecnico, Lisbon, Portugal.2ECGS-MNH, Luxembourg.3INMG, Mindelo, Republic of Cape Verde.4LECV, Praia, Republic of Cape Verde.

Copyright 2003 by the American Geophysical Union.0094-8276/03/2003GL016991$05.00

SDE 10 -- 1

Custódioetal,2003



modeling of ocean loading [Sherneck, 1991; Francis andMelchior, 1996].

5. Discussion

[9] The formal spectral resolution of 0.022 c.p.d., inconjunction with the high signal to noise ratio of the seismicr.m.s. series, allowed us to identify the tidal component M2

and resolve it from the solar frequency of 2.0 c.p.d. Wetested the effect of the data gaps on the spectra andconcluded that it amounted to the introduction of low levelnoise and broadening of the tidal peaks, without significantloss of information (this reflects the fact that the gaps hadrandomly distributed onsets and variable durations). Thegood agreement in the frequency domain between theseismic r.m.s. series on one side, and synthetic tidal gravitypotential and ocean-tide data on the other side (Figure 6),points to a tidal control on the seismic noise in Fogo. Atleast in some of the stations - FMLN, FMVE and maybeFPPC–frequencies in the range 2 Hz–3 Hz are selectivelyamplified, and we interpret this part of the signal asamplitude-modulated volcanic tremor.[10] Neuberg [2000] advises against using continuous

noise and volcanic tremor data to identify tidal periodicities,on the grounds that these types of data are prone toenvironmental contamination. However, this obstacle wascircumvented through the recording of air pressure and airtemperature data close to the stations, which upon frequencyanalysis did not show the same tidal frequencies that wereidentified in the seismic data. The danger of periodic culturalnoise in our data is minimum since Fogo Island is veryunderdeveloped. Further investigation of the processes in-volved in the reported amplitude modulation may provide auseful new tool for volcanic monitoring, but it requires acareful modeling of the ocean loading and other tidal effects.

[11] Acknowledgments. This research is part of Project ALERT,funded by FCT (Lisbon), under contract POCTI/32730/99. Seismic moni-

toring of Fogo Volcano has been supported by ICP (Lisbon), FCT (Lisbon),the Gulbenkian Foundation (Lisbon), ECGS (Luxembourg) and LECV(Praia, Cape Verde). One of the authors (SISC) acknowledges a researchaward by the Gulbenkian Foundation.

ReferencesChouet, B., Resonance of a fluid-driven crack: Radiation properties andimplications for the source of long-period events and harmonic tremor,J. Geophys. Res., 93, 4375–4400, 1988.

Day, S. J., S. I. N. Heleno da Silva, and J. F. B. D. Fonseca, A past giantlateral collapse and present-day flank instability of Fogo, Cape VerdeIslands, J. Volc. Geotherm. Res., 94, 191–218, 1999.

Emter, D., Tidal triggering of earthquakes and volcanic events, Lecturenotes in Earth Sciences, vol. 66, edited by H. Wilhem, W. Zurn, andH.-G. Wenzel, pp. 293–309, Springer-Verlag, Berlin, 1997.

Fonseca, J. F. B. D., B. V. E. Faria, J. N. P. Lima, S. I. N. Heleno,C. Lazaro, N. F. d’Oreye, A. M. G. Ferreira, I. J. M. Barros, P. Santos,Z. Bandomo, S. J. Day, J. P. Osorio, M. Baio, and J. L. G. Matos,Multiparameter Monitoring of Fogo Island, Cape Verde, for VolcanicRisk Mitigation, J. Volc. Geotherm. Res., in press, 2003.

Francis, O., and P. Melchior, Tidal loading in south western Europe: A testarea, Geophys. Res. Lett., 23, 2251–2254, 1996.

Heleno, S. I. N., S. J. Day, and J. F. B. D. Fonseca, Fogo Volcano, CapeVerde Islands: Seismicity-derived constraints on the mechanism of the1995 eruption, J. Volc. Geotherm. Res, 94, pp. 219–231, 1999.

McNutt, S. R., Volcanic tremor from around the world: 1992 update, ActaVulcanologica, 5, 197–200, 1994.

Melchior, P., The Tides of the Planet Earth, Pergamon Press, New York,1983.

Neuberg, J., External modulation of volcanic activity, Geophys. J. Int., 142,232–240, 2000.

Scherneck, H.-G., A parametrized solid Earth tide mode and ocean loadingeffects for global geodetic base-line measurements, Geophys. J. Int., 106,677–694, 1991.

Wenzel, H. G., The nanogal software: Earth tide data processingpackage ETERNA 3.30, Bull. Inf. Marees Terrestres, 124, 9425–9439, 1996.

!!!!!!!!!!!!!!!!!!!!!!!S. I. S. Custodio and J. F. B. D. Fonseca, ICIST, Instituto Superior

Tecnico, Lisbon, Portugal. ([email protected]; [email protected])N. F. d’Oreye, European Center for Geodynamics and Seismology,

Museum of Natural History, Luxembourg, Belgium. ([email protected])B. V. E. Faria, INMG, Mindelo, Republic of Cape Verde. (vigil.isecmar@

cvtelecom.cv)Z. Bandomo, Laboratorio de Engenharia de Cabo Verde, Praia, Republic

of Cape Verde. ([email protected])

Figure 5. Power spectral density of atmospheric pressureand air temperature at Fogo Volcano meteorological station,acquired simultaneously with the seismic data. Semi-diurnalpeaks have a solar frequency of 2.00 cycles per day, andtherefore cannot explain the modulation at 1.93 c.p.d.

Figure 6. Normalized power spectral density of synthetictide gravity potential (dashed), ocean-tide data from SalIsland (dotted) and seismic noise r.m.s. at station FMLN,EW component (solid).

SDE 10 - 4 CUSTODIO ET AL.: TIDAL MODULATION OF SEISMIC NOISE AND VOLCANIC TREMOR

modeling of ocean loading [Sherneck, 1991; Francis andMelchior, 1996].

5. Discussion

[9] The formal spectral resolution of 0.022 c.p.d., inconjunction with the high signal to noise ratio of the seismicr.m.s. series, allowed us to identify the tidal component M2

and resolve it from the solar frequency of 2.0 c.p.d. Wetested the effect of the data gaps on the spectra andconcluded that it amounted to the introduction of low levelnoise and broadening of the tidal peaks, without significantloss of information (this reflects the fact that the gaps hadrandomly distributed onsets and variable durations). Thegood agreement in the frequency domain between theseismic r.m.s. series on one side, and synthetic tidal gravitypotential and ocean-tide data on the other side (Figure 6),points to a tidal control on the seismic noise in Fogo. Atleast in some of the stations - FMLN, FMVE and maybeFPPC–frequencies in the range 2 Hz–3 Hz are selectivelyamplified, and we interpret this part of the signal asamplitude-modulated volcanic tremor.[10] Neuberg [2000] advises against using continuous

noise and volcanic tremor data to identify tidal periodicities,on the grounds that these types of data are prone toenvironmental contamination. However, this obstacle wascircumvented through the recording of air pressure and airtemperature data close to the stations, which upon frequencyanalysis did not show the same tidal frequencies that wereidentified in the seismic data. The danger of periodic culturalnoise in our data is minimum since Fogo Island is veryunderdeveloped. Further investigation of the processes in-volved in the reported amplitude modulation may provide auseful new tool for volcanic monitoring, but it requires acareful modeling of the ocean loading and other tidal effects.

[11] Acknowledgments. This research is part of Project ALERT,funded by FCT (Lisbon), under contract POCTI/32730/99. Seismic moni-

toring of Fogo Volcano has been supported by ICP (Lisbon), FCT (Lisbon),the Gulbenkian Foundation (Lisbon), ECGS (Luxembourg) and LECV(Praia, Cape Verde). One of the authors (SISC) acknowledges a researchaward by the Gulbenkian Foundation.

ReferencesChouet, B., Resonance of a fluid-driven crack: Radiation properties andimplications for the source of long-period events and harmonic tremor,J. Geophys. Res., 93, 4375–4400, 1988.

Day, S. J., S. I. N. Heleno da Silva, and J. F. B. D. Fonseca, A past giantlateral collapse and present-day flank instability of Fogo, Cape VerdeIslands, J. Volc. Geotherm. Res., 94, 191–218, 1999.

Emter, D., Tidal triggering of earthquakes and volcanic events, Lecturenotes in Earth Sciences, vol. 66, edited by H. Wilhem, W. Zurn, andH.-G. Wenzel, pp. 293–309, Springer-Verlag, Berlin, 1997.

Fonseca, J. F. B. D., B. V. E. Faria, J. N. P. Lima, S. I. N. Heleno,C. Lazaro, N. F. d’Oreye, A. M. G. Ferreira, I. J. M. Barros, P. Santos,Z. Bandomo, S. J. Day, J. P. Osorio, M. Baio, and J. L. G. Matos,Multiparameter Monitoring of Fogo Island, Cape Verde, for VolcanicRisk Mitigation, J. Volc. Geotherm. Res., in press, 2003.

Francis, O., and P. Melchior, Tidal loading in south western Europe: A testarea, Geophys. Res. Lett., 23, 2251–2254, 1996.

Heleno, S. I. N., S. J. Day, and J. F. B. D. Fonseca, Fogo Volcano, CapeVerde Islands: Seismicity-derived constraints on the mechanism of the1995 eruption, J. Volc. Geotherm. Res, 94, pp. 219–231, 1999.

McNutt, S. R., Volcanic tremor from around the world: 1992 update, ActaVulcanologica, 5, 197–200, 1994.

Melchior, P., The Tides of the Planet Earth, Pergamon Press, New York,1983.

Neuberg, J., External modulation of volcanic activity, Geophys. J. Int., 142,232–240, 2000.

Scherneck, H.-G., A parametrized solid Earth tide mode and ocean loadingeffects for global geodetic base-line measurements, Geophys. J. Int., 106,677–694, 1991.

Wenzel, H. G., The nanogal software: Earth tide data processingpackage ETERNA 3.30, Bull. Inf. Marees Terrestres, 124, 9425–9439, 1996.

!!!!!!!!!!!!!!!!!!!!!!!S. I. S. Custodio and J. F. B. D. Fonseca, ICIST, Instituto Superior

Tecnico, Lisbon, Portugal. ([email protected]; [email protected])N. F. d’Oreye, European Center for Geodynamics and Seismology,

Museum of Natural History, Luxembourg, Belgium. ([email protected])B. V. E. Faria, INMG, Mindelo, Republic of Cape Verde. (vigil.isecmar@

cvtelecom.cv)Z. Bandomo, Laboratorio de Engenharia de Cabo Verde, Praia, Republic

of Cape Verde. ([email protected])

Figure 5. Power spectral density of atmospheric pressureand air temperature at Fogo Volcano meteorological station,acquired simultaneously with the seismic data. Semi-diurnalpeaks have a solar frequency of 2.00 cycles per day, andtherefore cannot explain the modulation at 1.93 c.p.d.

Figure 6. Normalized power spectral density of synthetictide gravity potential (dashed), ocean-tide data from SalIsland (dotted) and seismic noise r.m.s. at station FMLN,EW component (solid).

SDE 10 - 4 CUSTODIO ET AL.: TIDAL MODULATION OF SEISMIC NOISE AND VOLCANIC TREMOR

Custódioetal,2003



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Frenchetal,2015

plumes stand out as continuous features confined to well definedvertically oriented columns.

In particular, the Hawaiian plume appears as a separate verticalconduit of varying width (Fig. 2a–c), with a weaker zone at around500 km above the CMB, rooted in its own patch of strongly reducedshear velocity at the base of the mantle. In the transition zone, thisplume appears to be strongly deflected towards the west–southwest(Fig. 3). This morphology is compatible with evidence for a hot uppermantle to the west of Hawaii, based on the analysis of converted waves(that is, receiver functions)22. The presence of bodies with higher-than-average velocity southwest and northeast of the Hawaiian chain is inagreement with regional studies23,24. However, in the lower mantle, theassociated conduit is more vertically oriented in SEMUCB-WM1.Similar broad, vertically oriented low-velocity conduits are found inthe vicinity of some hotspots lying on the border of the African LLSVP(Figs 1e, f and 3d, e and Extended Data Fig. 2).

The lower-mantle plume conduits described above are rooted inwide patches (of diameter 500–800 km) of strongly negative velocityreduction near the CMB. In at least three cases, these patches coincidein location with large ULVZs previously detected in the vicinity of thecorresponding hotspots: near Hawaii (detected through observationsof post-cursors to diffracted S waves5), and beneath Iceland6 andSamoa7 (found through the study of waveform distortion in the phaseSPdiffKS).

Because of the computational challenges of whole-mantle imagingusing full waveforms and numerical simulations, the resolution of ourmodel is limited by our choice of parametrization and maximumfrequency. However, resolution tests (Methods; Extended Data Figs4–8) clearly indicate that our approach can resolve the vertical con-tinuity of plumes without ray-like smearing or erroneous deflection,and that the variations of the shape and amplitude of the plumes withdepth are likely to be robust features. These tests also indicate (seeSupplementary Information section S1 and Supplementary Figs 1and 2) that our modelling approach can distinguish between hypo-thetical broad superplume-like features and the distinct vertical con-duits that are shown in Fig. 1. Numerical experiments (SupplementaryInformation section S2 and Supplementary Figs 5–9) demonstrate thatplumes of the same scale as are seen in Fig. 1 and used in our testsshould be readily detectable in the waveform data used by our inver-sion. Furthermore, on the basis of relative amplitude recovery alone,our resolution tests also show that in order to obtain a velocity reduc-tion of 2% or more over the major part of the lower mantle—as seen inour model—a narrow plume would have to be very strong (that is,.10% reduction in shear-wave velocity for a plume of width ,200 km;see Methods and Extended Data Fig. 4). Such a strong velocity contrastwould translate into unrealistically high25 effective temperatureexcesses of 1,500–2,000 uC. In contrast, for a 2% velocity anomaly overa width of 800–1,000 km, as imaged in SEMUCB-WM1 under Hawaii

Samoa SamoaTahiti

Marquesas

GuadalupePitcairn

+2.0–2.0

δVs/Vs (%)

a b

dcMacDonald

Yellowstone

Balleny

1,00

02,

000

500

1,50

02,

500 CMB

Depth km

Galapagos

Cape Verdee

CanaryIceland

Jan Mayen

f

Figure 1 | Whole-mantle depth cross-sections of relative shear-velocityvariations in model SEMUCB-WM14, in the vicinity of major hotspots. Thesections are shown in the inset maps, with the direction of the projectionindicated by the position of the purple dot in both map and cross-section views(black boxes correspond to the three-dimensional rendering regions in Fig. 2).Green dots and triangles mark the locations of hotspots27. The referencemodel is the corresponding global one-dimensional average shear-wavevelocity (Vs) profile of SEMUCB-WM1. The colour scale has been chosen toemphasize lower-mantle structures, resulting in substantial saturation inthe upper mantle. Broken lines indicate depths of 410 km, 660 km and1,000 km. Focused, quasi-vertical, broad plumes extend continuously from

patches of strongly reduced Vs at the base of the mantle to depths of at least1,000 km in the vicinity of: a, Samoa; b, Tahiti, the Marquesas, the Galapagosand Samoa; c, Pitcairn; d, MacDonald; e, Cape Verde; and f, the Canary Islands.These plumes stand out from other low-velocity features in these cross-sections, which span nearly half of Earth. d, Note the absence of a noticeableanomaly in the lower mantle immediately beneath the Yellowstone hotspot.However, a faint low-velocity conduit appears to the southwest (offshore ofNorth America), anchored by a low-velocity patch in the D0 mantle region. It isbeyond the resolution of our study to verify whether this feature is related to theYellowstone or the Guadalupe (c) hotspot.

RESEARCH LETTER

G2015 Macmillan Publishers Limited. All rights reserved

9 6 | N A T U R E | V O L 5 2 5 | 3 S E P T E M B E R 2 0 1 5

Referências bibliográficas

1.  Notasdasaulas,Fénix.

2.  NumericalRecipes,Pressetal,CambridgePress.

Avaliação

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•  Osprojectosserãofeitosemgruposde2alunos.•  Os3projectosserãoentreguesparaavaliação.•  Osprojectosincluemasoluçãodeumproblemaeasua

apresentaçãográfica.•  Cadagrupodefenderáoralmenteosprojectos(ppt).

2a-f,Entregas 3a-f,T21 4a-f,T21 5a-f,PL22 5a-f,PL24 5a-f,PL23 6a-f,PL25 6a-f,PL2114/Fev 15/Fev 16/Fev 16/Fev 16/Fev 17/Fev 17/FevT1 T2 Intro-1 Intro-1 Intro-1 Intro-1 Intro-121/Fev 22/Fev 23/Fev 23/Fev 23/Fev 24/Fev 24/FevT3 T4 Intro-2 Intro-2 Intro-2 Intro-2 Intro-228/Fev 1/Março 2/Março 2/Março 2/Março 3/Março 3/MarçoCarnaval T5,Protoc. Ex1-1 Ex1-1 Ex1-1 Ex1-1 Ex1-17/Março 8/Março 9/Março 9/Março 9/Março 10/Março 10/MarçoT6 T7 Ex1-2 Ex1-2 Ex1-2 Ex1-2 Ex1-214/Março 15/Março 16/Março 16/Março 16/Março 17/Março 17/MarçoT8 T9 Ex1-3 Ex1-3 Ex1-3 Ex1-3 Ex1-3

20/Março,17:00 21/Março 22/Março 23/Março 23/Março 23/Março 24/Março 24/Março ApresentaçõesEntregaEx1 T10 T11 Ex1-4 Ex1-4 Ex1-4 Ex1-4 Ex1-4

28/Março 29/Março 30/Março 30/Março 30/Março 31/Março 31/MarçoT12 T13,Protoc. Ex2-1 Ex2-1 Ex2-1 Ex2-1 Ex2-14/Abr 5/Abr 6/Abr 6/Abr 6/Abr 7/Abr 7/AbrT14 T15 Ex2-2 Ex2-2 Ex2-2 Ex2-2 Ex2-211/Abr 12/Abr 13/Abr 13/Abr 13/Abr 14/Abr 14/AbrT16 Páscoa Páscoa Páscoa Páscoa Páscoa Páscoa18/Abr 19/Abr 20/Abr 20/Abr 20/Abr 21/Abr 21/AbrPáscoa DiaCiências Ex2-3 Ex2-3 Ex2-3 Ex2-3 Ex2-3

26/Abr,9:00 25/Abr 26/Abr 27/Abr 27/Abr 27/Abr 28/Abr 28/Abr ApresentaçõesEntregaEx2 Feriado T18 Ex2-4 Ex2-4 Ex2-4 Ex2-4 Ex2-4

2/Mai 3/Mai 4/Mai 4/Mai 4/Mai 5/Mai 5/MaiT19 T20,Protoc. Ex3-1 Ex3-1 Ex3-1 Ex3-1 Ex3-19/Mai 10/Mai 11/Mai 11/Mai 11/Mai 12/Mai 12/MaiT21 T22 Ex3-2 Ex3-2 Ex3-2 Ex3-2 Ex3-216/Mai 17/Mai 18/Mai 18/Mai 18/Mai 19/Mai 19/MaiT23 T24 Ex3-3 Ex3-3 Ex3-3 Ex3-3 Ex3-3

22/Mai,17:00 23/Mai 24/Mai 25/Mai 25/Mai 25/Mai 26/Mai 26/Mai ApresentaçõesEntregaEx3 T25 T26 Ex3-4 Ex3-4 Ex3-4 Ex3-4 Ex3-4

30/MaiT27

Trabalhos práJcos

•  Serãoelaborados3projectospráfcos,umsobrecadaumdostemasabordadosnacadeira.

•  Osprojectosserãofeitosemgruposde2alunos.•  Os3projectosserãoentreguesparaavaliação.•  Osprojectosincluemasoluçãodeumproblemaeasua

apresentaçãográfica.•  Cadagrupodefenderáoralmenteosprojectos(ppt).

•  Asprimeirasduassemanasdepráfcasnãotêmavaliação.•  Consftuiçãodosgruposna1aPL(estasemana).•  PensemnaconsftuiçãodosgruposantesdasPLs.

Trabalhos práJcos - Avaliação

•  Relatórioentreguenaformade2ficheiros:-Exemplo:EX1PL25G08.py,EX1PL25G08.pptx(Projecto1,PL25,Grupo8)-Nointeriordosficheirosdevemestaranotadososnomesdosautores).

•  Entrega,pore-mailparaoprofessordaTP

-Assuntodoe-mail:ModNum2017-Entrega:2a-fdasemanadasdiscussões,atéàs17:00.-Cadadiadeatrasodesconta1valor.-Excepção:25/Abril.Entregadia26/Abril,9:00.

•  Nota:SóumdosmembrosdogrupoapresentaráoProjecto1(10min).AmbosapresentamoProjecto2(2×5min).OoutromembroapresentaráoProjecto3(10min).Aescolhaédosgrupos.

O que é um modelo?

Representação(simplificada)darealidade.

(Oconhecimentobaseia-sesempreem“modelos”.)

O que é um modelo?

•  Modelosconceptuais(qualitafvos,esquemáfcos,idenfficandocausaseefeitose/ouevoluçãoppica).

NASA

O que é um modelo?

•  Modelosteóricos(e.g.traduzidosemequaçõesanalífcasentrevariáveis).Porvezesnãotêmsolução…

EquaçõesdaMeteorologia:Equações da meteorologia


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w � � � � �

wEuler, 1755

2vK� �Navier-Stokes 1822

2 v� :uCoriolis 1835

3 equações5 incógnitas

� � 2. Radiativo Latentev Q QtT T N Tw � � � � � �

wconvecção condução

� �. vtU Uw ��

w� �, , , 2

, , , , , ,.v l g cTransiçãode fasev l g c D v l g c

qv q q

tN

w � � � � �

w910 equações910 incógnitas

Mas, não existe solução analítica!

(1 0.61 )p R T qU �00

kpTp

T�

§ · ¨ ¸

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Fase transitions

Simplificações:Geometriacartesiana…(montanhas?Planeta esférico?)

O que é um modelo?

•  Modelosanalógicos(túneldevento,tanquehidráulico,sandbox).

2 F.M. Rosas et al. / Tectonophysics 548–549 (2012) 1–21


Rosasetal.,2012

O que é um modelo?

•  Modelosanalógicos(túneldevento,tanquehidráulico,sandbox).


Rosasetal.,2012

O que é um modelo?

Representação(simplificada)darealidade.

(Oconhecimentobaseia-sesempreem“modelos”)

•  Modelosnuméricos(traduzidosemrelaçõesmatemáfcasdiscretasentrevariáveis).

ECMWF

Caltech

ObjecJvos

•  Experiências“controladas”(oqueacontecese…)

•  Trabalharna“escalalaboratorial”(noespaçoenotempo):omodelosóéúflseforrealizável…

•  Exemplos:modelosdedoençashumanasemcobaias;túneldevento(modelosanalógicos)…

•  Caracterizarprocessosindividuais(isolarcausaseefeitos).

•  Preverofuturo.

Documents

Modelação Numérica 2017 - ULisboa · Susana I. S. Custodio,1 Joao F. B. D. Fonseca,1 Nicolas F. d’Oreye,2 Bruno V. E. Faria,3 and Zuleyka Bandomo 4 Received 27 January 2003;