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Evoluzione Sistema Terra 2004/2005 Introduzione al problema della variazione di livello marino medio isostasia e movimenti crostali verticali PowerPoint PPT Presentation


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Evoluzione Sistema Terra 2004/2005 Introduzione al problema della variazione di livello marino medio isostasia e movimenti crostali verticali. Carla Braitenberg Dipartimento Scienze della Terra, Università di Trieste, Via Weiss 1, 34100 Trieste [email protected]

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Evoluzione Sistema Terra 2004/2005 Introduzione al problema della variazione di livello marino medio isostasia e movimenti crostali verticali

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Evoluzione sistema terra 2004

Evoluzione Sistema Terra2004/2005Introduzione al problema della variazione di livello marino medio isostasia e movimenti crostali verticali

Carla Braitenberg

Dipartimento Scienze della Terra,

Università di Trieste, Via Weiss 1, 34100 Trieste

[email protected]

Tel +39-040-5582258 fax +39-040-575519


Program exercizes on pc

Program-Exercizes on PC:

  • Scope of exercize: familiarize with flexure response of crust.

  • Load: bathymetry

  • The flexure model is tested trough the observed gravity field. Procedure: Take Bouguer anomaly over sea. This field is representative of crustal thickness variations. Invert field by downward continuation-you obtain first approximation of Moho.


Introduction

Introduction

  • An important question is: how big is the influence of mankind and industrialisation on climate evolution

  • Necessary: separation of the man-induced effect from those effects independent of man, which may be termed “natural”

  • Mean sea level (MSL): tightly tied to the conditions of the global earth climate. Strongly dependent on:

    • mass exchange between ice-sheets and ocean water

    • Thermal expansion


Introduction 2

Introduction 2

  • Impact of sea level rise:

  • Increased erosion of beaches

  • Model of Bruun (1962): beaches erode on the order of 50-200 times the increase of sea level.

    • Example Ocean City, Maryland: erosion 150 times. From tide gauges: increase of sea level is 3.5 mm/yr

    • Erosion/decade=150 * 3.5mm/yr*10yr=5m/decade

  • Major damage for storms and inundations

  • Flooding of low lying flatlands


Introduction 3

Introduction 3

  • Measurement of today’s MSL changes through:

    • Tide-gauges. Time interval: 102 yr

      • Local measurement

    • Satellite altimetry. Time interval: 10 yr

      • Global measurement

    • Geomorphology/geological inferences: 105 yr

      • Local measurement


Msl changes in recent 300 yrs

MSL changes in recent 300 yrs.

Tide gauge measurements. Observations have been corrected for postglatial isostatic movements. (Lambeck und Chappell, 2001)


Short period msl variations

Short period MSL variations:

  • The measurement is influenced by:

  • tides

  • Sea currents

  • Temperature

  • Local subsidence/emergence: tectonic, isostatic, anthropogen

  • Climatic influences


Introduction 4

Introduction 4

  • Present global increase observed with tide-gauges over last 100 yrs is estimated to 2 mm/yr (Douglas et al., 2001)

  • Question: is this increase significative? Is it a fluctuation? Does it comply with an extrapolation of the variations over previous centuries/millennia?

  • Necessary: knowledge of MSL variations in the past:

    • How big were the variations?

    • Are variations local and/or global?

    • Knowledge on geographic distribution of variations


Intro 5

Intro 5

  • Find driving mechanism for the variations

  • What other parameters correlate with the MSL variations

  • Explain past MSL variations in order to predict today’s variations

  • Be able to detect whether today’s MSL increase is accelerated with respect to model.


Msl variations in geologic history

MSL variations in geologic history

  • Time scale of milions of years

  • Results from “seismic sequence stratigraphy”. Combination of local and global variations. Greatest oscillation: connected with plate tectonics (Hallam, Annu. Rev. Earth Planet. Sci., 12, 205, 1984,(Lambeck und Chappell, 2001)


Evoluzione sistema terra 2004

Time scale of 140 000 years: Huon Peninsula Papua New Guinea. Dating of cores from coral reefs. MSL in m. OIS: Oxygen Isotope Stage


Time scale of 140 000 years huon peninsula

Time scale of 140 000 years: Huon Peninsula

  • Measurement: dating of cores from coral riffs

  • Area subject to tectonic uplift. Therefore MSL of LGM (Last Glacial maximum) is in 30-40 m depth.

  • Compare to mediterranean: in stable areas this level is at 120 m depth

  • Growing of corals: tied to typical water depth (several cm to several m, depending on species). Therefore index of MSL, Dating with 14C method.


Time scale of 140 000 years huon peninsula1

Time scale of 140 000 years: Huon Peninsula

  • Properties of MSL:

  • Variations due to mass exchange between ice cover and sea water

  • Glatial: MSL Min Interglatial: MSL max

  • Curves affected by local effects


Geographic differences in the msl variation lambeck chappell 2001

Geographic differences in the MSL variation(Lambeck, Chappell 2001)


Description of geographic differences

Description of geographic differences

  • Ångermann- river sediments now in 200 m r.p.s.l.

    • Transgression of sea: change from fresh water to marine sediments

    • Regression: inverse

    • Time scale from dating of sediments or counting seasonal Varves

  • S-England: transition from fresh-water to estuarine deposition

    • In situ tree-stumps: give upper margin to MSL


Description of geographic differences1

Description of geographic differences

  • Sunda Shelf: flooding of shelf

  • Barbados: Fossil corals: age-height relation

    • Dating: Carbon or Uranium series methods

  • North Queensland: Micro-atoll-formation of corals. Today same corals live in 10 cm depth relative to minimum sea level.


Geographic differences description

Geographic differences- Description

  • Classification of observed areas:

  • Central area of former ice-sheet: Ångermann, Hudson Bay

  • Marginal areas of ice-sheet or area of small ice-sheets: Åndoya

  • Medium latitudes, broad area that confined to ice-sheet: South England. The same: Mediterranean, Atlantic coast of SA, Gulf of Mexico.

  • Areas far from ice-sheet-margin: Barbados, Sunda Shelf

  • Most observations regard time after LGM: older traces were cancelled by:

    • A) rising MSL after LGM

    • B) advancing ice-sheet before LGM


Conservation the signatures

Conservation the signatures

  • In areas with uplift: older signatures conserved if now above MSL

  • Example: Huon Peninsula- Papua New Guinea: coral rift up to 1000 m a.s.l. Huon Sequence is an important record for MSL

  • Glatial ice model:

    • Known: geographical extent of ice-sheet in N-Europe and N-America

    • Not clear: extent in E-Siberia and in Shelf-Areas

    • Not clear: thickness and evolution of ice-sheet before LGM


How to recover evolution of ice sheet

How to recover evolution of ice-sheet

  • Method to determine volume of ice-sheet:

  • From the observation of MSL and used as constraints

  • Consider: vertical crust movements due to

    • Isostasy

    • Tectonics


Isostatic model local equilibrium airy and pratt and regional equilibrium flexural isostasy

Isostatic Model: local equilibrium (Airy and Pratt) and regional equilibrium (Flexural Isostasy)

  • Airy: variation of crustal thickness function of topography

  • Pratt: variation of crustal density function of topography


Airy and pratt isostatic models

Airy and Pratt Isostatic models


Examples

Examples

  • In Airy approximation: consider subsidence (r) of crust below iceload of thickness (h):

Maximum icethickness at LGM in Scandinavia and N-America estimated to max 2000-2500 m (Lambeck and Chappell, 2001).

result: r about 600-760 m


Deformation due to the ice load

Deformation due to the ice-load


Example

example

  • Airy isostasy: calculate uprising of crust (r) in the case of a MSL lowstand :

With a measured sealevel change of 120 m, the value of r is about 50 m.

The value corrected for the hydro-isostatic effect would then be:

It should be borne in mind, that the value calculated with the Airy-approximation is generally over-estimated.


Differential sea level change at stable coast and in ocean basin

Differential sea level change at stable coast and in ocean basin


Regional equilibrium flexural isostasy model of the flexure of a thin plate

Regional equilibrium (Flexural Isostasy)Model of the flexure of a thin plate


Regional equilibrium flexural isostasy

Regional equilibrium (Flexural Isostasy)

  • Flexural rigidity:

Typical values:

E= 1011 N/m2

 = 0.25


Regional equilibrium flexural isostasy1

Regional equilibrium (Flexural Isostasy)

  • Insert the expression for p and q:

  • Solution of the equation:

k= wavenumber

We set:

We obtain:


Regional equilibrium flexural isostasy2

Regional equilibrium (Flexural Isostasy)

An arbitrary topography can be expressed as the sum of sine-functions (Fourier-Transformation)

The flexure of the plate is then:


Regional equilibrium flexural isostasy3

Regional equilibrium (Flexural Isostasy)

  • k= wave number

  • W(k)= FT(w(x)) H(k)= FT (h(x))

  • To the same result one can arrive by applying the Fourier Transform to the above equation:


Transition to local compensation

Transition to local compensation:

With very low flexural rigidity or for very small wave numbers (long wavelengths) the regional isostasy goes over into local Airy type compensation:

With very high flexural rigidity or for very great wave numbers (short wavelengths) the loading does not deform the plate.


Flexure of the plate by point like loading te 1 3 5 10 15 25 40 km

Flexure of the plate by point-like loading Te=1,3,5,10,15,25,40 km


Properties of the flexure of the plate

Properties of the flexure of the plate:

  • Below the load: maximum downward flexure

  • In the limiting areas of the load: flexural bulge

  • With decreasing elastic thickness of the plate:

    • greater amplitude of flexure

    • smaller wavelength of flexure

  • At great distances from load: no effect


Mean sea level mis 5 5 along italian coast

Mean sea level MIS 5.5 along italian coast

  • Lambeck et al., 2004


Loading with volcanic masses

Loading with volcanic masses

Parameter:

Elastic thickness

Laureanda: Patrizia Maraini


Deformation along the coast

Deformation along the coast

  • Curves for different Te (km)


Glacial hydro isostatic model of lambeck

Glacial-hydro-isostatic model of Lambeck


Glatial hydro isostatic model of lambeck

Glatial-hydro-isostatic model of Lambeck


Model parameters

Model-parameters

  • Mantle: divided in 3 spherical shells

    • Elastic lithosphere with effective elastic thickness H1

    • Upper mantle: from base of lithosphere to 670 km depth. Medium viscosity um

    • Lower mantle: Medium viscosity lm


Ice equivalent msl

Ice-equivalent MSL

From the observations of MSL recover the ice-equivalent MSL variations. Necessary: isostatic correction


Some examples of geological markers

Some examples of geological markers

  • Categories:

    • Biological, Sedimentological, Erosional, archaeological

  • Morpho-stratigraphic markers:

    • Notches

    • Lagoonal sedimentary facies

    • Fossil beaches and terraces


Some examples of geological markers courtesy dr f antonioli

Some examples of geological markers(courtesy Dr. F. Antonioli)

  • Biological markers: the living habits must be tied to a certain range from the sea level surface

  • Vermetids: reef building species of Gastropods. Reefs are submerged during high tide, exposed during low tide

  • Lithophaga: bivalves living in calcareous rock. 90% live in the upper 2m of sea.


Some examples of geological markers courtesy dr f antonioli1

Some examples of geological markers(courtesy Dr. F. Antonioli)

  • Speleothems with marine overgrowth:on speleothems in flooded caves, alternation of speleothem growth and encrustments of colonies of marine worm Serpula massiliensis can be found. The worm forms calcitic tubes.

  • Mediterranean: Strombus bubonus. Gastropod now living in tropical seas. Lived in Medit. only during the Last Interglacial (124 000 ± 2000 ys BP). A marker for this event in the Medit.


Some examples of geological markers courtesy dr f antonioli2

Some examples of geological markers(courtesy Dr. F. Antonioli)

Core samples: analyzed for biological markers. For example fluvial and marine environments are detected

Beach rock: shoreline deposits cemented by calcitic-magnesitic or aragonitic-carbonates in or near the intertidal zone, at the interface of freshwater-marine phreatic flow

Coral reefs: height-age dependence of core sample.

Coral algea: algae that form features similar to coral. Living habitat in tidal range.


Example for vermetid reef dr f antonioli enea

Example for Vermetid reef (Dr. F. Antonioli, ENEA)


Example for vermetid dendropoma dr f antonioli enea

Example for vermetid dendropoma(Dr. F. Antonioli, ENEA)


Evoluzione sistema terra 2004

Example for present marine notch.Dark part: coralline algal rim. Max 1.90 m from base of algal rim top of notch, Maxwell coast, Barbados (Dr. F. Antonioli, ENEA)


Grotta argentaorla 22 m antonioli

Grotta Argentaorla -22 m (Antonioli)


S vito lo capo vermetide reef antonioli

S. Vito Lo Capo, Vermetide Reef(Antonioli)


Sea level curve with italian archeological markers

Sea level curve with italian archeological markers

(Antonioli e Leoni, 1998, Il Quaternario).


Grotta argentarola 18 5 m mrs antonioli

Grotta Argentarola -18.5 m(Mrs. Antonioli)


Example french coast lambeck bard 2000

Example: French coast (Lambeck & Bard, 2000)

  • Observations are based on:

    • archeology: coast was lived before and afterLGM

    • sedimentation: Estuarine and fluvial Deposits

  • values for time before 6000 14C yr BP (radiocarbon before present) are only upper or lower limts


Shells as geological markers

Shells as geological markers

  • Shells in silty sands on continental slope:give minimum sea level, unter the hypothesis that shells are found at the position of growth (see P1-P4 in figure). The same mollusks of same age were also found some tens of m lower.

    Shells in silty sands from caves give lower limits (V1,V2)

(Lambeck & Bard, 2000)


Geologic markers at french coast

Geologic markers at French coast

Fluvial-paludal deposits: upper limit (BA1-9)

Estuarine deposits: lower limit

Coralline algal deposits (C3,C4) from Cosquer cave

estimated uncertainty: 5 m

In the graph: calibrated time scale or radiocarbon time scale

(Lambeck & Bard, 2000)


Observations for the time after 7000 14 c

Observations for the time after 7000 14C

Beach deposits (upper limit)

Estuarine and fluvial peats (lower limit)

Archaeological observations of ancient harbour constructions from Marseille region

best data: coralline algae

Gastropod vermetid

Lithophyllum lichenoides: lives in 0.1m-0.2 m depth

(Lambeck und Bard, 2000)


Error budget

Error budget

The global error on the MSL is given by the uncertainty on:

Habitat-depth,

Tidal amplitudes,

Position of sample.

In the order of 0.3m-0.5m

(Lambeck und Bard, 2000)


Map with position of sampled areas

Map with position of sampled areas

Location map for the French Mediterranean and adjoining areas. 1 =Nice, 2 =Cap d'Antibes, 3 =Cannes, 4 =Fre¨jus,

5 =St. Tropez, 6 =Cosquer Cave, 7 =Cap Romarin, 8 =Villefranche, 9 =Cap Corse, 10 =Scandola, 11 =Giens.

(Lambeck und Bard, 2000)


Sources for sea level data from the french mediterranean coast

Sources for sea-level data from the French Mediterranean coast

Area Figure reference Identification point Data type Reference

Roussillon 2AR1-R6 Shelly sands and marine shells [2,13]

Golfe du Lion 2A L1-L3 Shells [13]

Grotte Huet

(Cannes) 2A Ca1, Ca2 Terrestrial and marine cave deposits [13]

Villefranche 2A V1, V2 Marine cave deposits [13]

Provence 2A P1-P4 Shells in silty sands [13]

Marseille 2A M Bryozoans [14]

St. Tropez 2A T Shells in shelly sand [13,16]

Fre¨jus 2A F Shells in silty sand [16,17]

Cap d'Antibes 2A A Shells in silty sand [15]

Cosquer 2A C1 Shell fragments (Mytilus galloprovencialis) [18]

C3, C4 Coralline algae [19]

Baie des Anges 2A BA1-BA9 Fluvial-paludal and estuarine deposits [5]

Corsica 9 Vermetid and coralline algae [6]


Sources for sea level data from the french mediterranean coast1

Sources for sea-level data from the French Mediterranean coast

Area Figure reference Identification point Data type Reference

Marseille 2B Archaeological data [12]

La Ciotat 2B Vermetid and coralline algae [6]

Giens 2B Vermetid and coralline algae [12]

Port Cros 2B Vermetid and coralline algae [6]

Baie des Anges 2BEstuarine, fluvial and beach deposits [5]

Corsica 9 Vermetid and coralline algae [6]


A sea level evolution along french coast from 35 kys 5kys

A) Sea level evolution along French coast from 35 kys-5kys

(Lambeck and Bard, 2000)


Evoluzione sistema terra 2004

A


B sea level evolution along french coast from 8 kys present

B) Sea level evolution along French coast from 8 kys-present

(Lambeck and Bard, 2000)


Evoluzione sistema terra 2004

B


Evoluzione sistema terra 2004

Predicted isostatic contributions to sea-level change for a site near Cannes on the French Mediterranean margin.

(i) The hydro-isostatic contribution resulting from the global changes in ocean volume

(ii) the ice-equivalent sea-level change correspondingto the totality of the continent-based ice sheets

.


Predicted isostatic contributions to sea level change continued

Predicted isostatic contributions to sea-level change continued

(iii) the glacio-isostatic contribution from the former northern hemisphereice sheets

(iv) the total sea-level change.

(Lambeck and Bard, 2000)


The graph of prediced sea level change

The graph of prediced sea level change

(a) (i) The hydro-isostatic (ii) the ice-equivalent (iii) the glacio-isostatic

(iv) the total sea-level change.

(b) The Holocene part of thesame predictions but drawn onexpanded scales.


Evoluzione sistema terra 2004

The contributions of the different components of MSL change (see previous figure (Lambeck aund Bard, 2000):

Hydro-isostatic effect (i): positive

Glatial-isostatic effect (ii): negative. Greater than hydrostatic effect

Eis-equivalent (iii): greatest contribution. Goes to zero at 6000 BP. Successive rising due to isostatic movements. Around 6000 BP most of the glacial ice is melted

Total curve (iv): deviates from ice-equivalent by about 10 m


Temporal evolution of msl

Temporal evolution of MSL

MSL was never higher than now since 20000 yr BP

By comparison with the MSL curves from other areas of the world: vertical movements in Provence were less than 0.02 mm/yr.

Further evidence for max. sea level: paintings of Cosquer cave


Cosquer cave

Cosquer Cave

Entrance of Cosquer cave: now at –37m with respct to SL

  • 2 cave chambers above SL

  • Paintings reproduce fauna of last glacial period

  • Dating of paintings (14C Method):

  • 33 000-16 500 cal. yr. BP

  • Paintings below SL are washed away

  • MSL was never higher than now since LGM.

  • Last access to cave:

    • 9800-13 000 cal. yr. BP


  • Cosquer cave1

    Cosquer Cave


    Cosquer cave2

    Cosquer cave


    Cosquer cave3

    Cosquer cave


    Evoluzione sistema terra 2004

    Observed sea levels corrected for the glacio-hydro-isostatic contributions for the past 50 000 calibrated years

    • Ice-equivalent sea-level change from the French Mediterranean area

    • Error bars on points: include both observational uncertainties and themodel uncertainties for the isostatic correction terms


    Corrected msl continues

    Corrected MSL continues

    • Curves (i) and (ii):

      • equivalent functions inferred from a more extensive and homogeneous data base (see ref. in paper).

    • Curve (iii):

      • estimate inferred from oxygen isotope record, calibrated against height-age relationship of coral reefs ion Huon Peninsula


    I ce equivalent sea level change from the french mediterranean area compared to global curves

    Ice-equivalent sea-level change,from the French Mediterranean area compared to global curves


    Evoluzione sistema terra 2004

    Ice-equivalent sea-level change,from the French Mediterranean area for late-Holocene time. The continuous curve is same as (i) in (a)

    (Lambeck and Bard, 2000)


    The ice volume equivalent sea level function

    The ice-volume equivalent sea level function

    • The ice-volume equivalent sea level function e(t) estimated from observations of local sea level change for three time intervals (Lambeck und Chappell, 2001).

    • (A) The interval between the last two glacial maxima at about 140,000 and 25,000 years ago, respectively

    • (B) The interval from the LGM to the end of major ice sheet decay


    The ice volume equivalent sea level function1

    The ice-volume equivalent sea level function

    • The ice-volume equivalent sea level function e(t) estimated from observations of local sea level change for three time intervals (Lambeck und Chappell, 2001).

    • (C) The past 7000 years

      • The isostatic corrections i (t) are based on continental margin response parameters where appropriate and on oceanic mantle parameters for the islands of Tahiti and Barbados.


    The ice volume equivalent sea level function2

    The ice-volume equivalent sea level function


    Evoluzione sistema terra 2004

    Time scale of 450 000 years relative MSL in m Composite: Dating of cores from coral reefs (Huon Penins)and Oxygen isotope ratio. .

    (Waelbroeck et al., 2002)


    Mean sea level at the time of the lgm

    Mean Sea level at the time of the LGM.

    Lambeck and Bard, 2000


    Dating of msl highstand with stalagmites of argentarola i cave

    Dating of MSL highstand with stalagmites of Argentarola (I) cave

    • Argentarola cave: presently below MSL. Spetial: different continental-marine transitions recorded in the stalagmites

    • Stalagmite sample (ASI): now at –18.5 m b.m.s.l.

    • Tidal amplitude: 0.14 m

    • Stalagmite:

      • Yellow-brown parts with laminations: Speleothem Calcite- were formed at the time of MSL low-stands.

      • White parts: colonies of marine worm Serpula Massiliensis. Forms thick crust composed of Calcitic tubes. Index of flooding of cave.


    Dating of msl highstand with stalagmites of argentarola i cave1

    Dating of MSL highstand with stalagmites of Argentarola (I) cave

    • Area is tectonically stable during last glacial cycle. Visible from the level of the MSL highstand during the penultimate interglacial period (MIS 5.5, about 128-136 kyr BP)

    • See figure, where thw height of maximum highstand is plotted allong the coast.

    • MIS marine isotope stage. Pair number: cold period. Impair number: warm period. Divided into sub-stages:

    • e.g. 5.1,5.3 (also 5.A, 5.C): warm stage; 5.2, 5.4 (5.B, 5.D): cold stages

    • OIS oxygen isotope stage (goes back to Shackleton, 1973)


    Msl highstand mis 5 5 along the coast bard et al 2002

    MSL highstand MIS 5.5 along the coast (Bard et al.,2002)

    Marker show that MSL highstands during MIS M5.5 were about 4-6 m above present MSL at the coast N and S of Argentarola cave (precisely: 5.3 m, 6 m and 4 m for Stations 2, 3 and 4). This confirms tectonic stability in the studied time period.


    Section across the stalagmite from argentarola cave

    Section across the stalagmite from Argentarola cave

    Absolute dating of the MSL highstand is possible: transition from the speleothem to the fossile Serpula. Dating with U/Th Method.

    Age of the transition at rising MSL: 202 kyr

    Age at falling MSL: 190 kyr.

    Bard et al., 2002


    Msl highstand mis 5 5 along the coast bard et al 20021

    MSL highstand MIS 5.5 along the coast (Bard et al.,2002)

    230 Th/ 234 U ages with errors at 2along the length of ASI. From the oldest to the youngest part of ASI, the straight lines define growth rates of 17, 3, 7 and 0.6 mm/kyr, respectively. The growth rate of ASI probably varied in phase with climate and precipitation because these phases broadly correspond to MIS 7.2, 6.6, 6.5 and 6.4.


    Comparison to global curves

    Comparison to global curves

    • The continuous curves in next graph:

    • based on 18 O measurements: SPECMAP curve: blue

    • benthic stack in green

    • ice volume component in black.

    • 18 O curves were converted to sea-level using two fixed points for MIS 5.5 (+7 m r.p.s.l.) and MIS 2 (-120 m r.p.s.l.).

    • Dashed black curve shows the summer insolation at 65°N used to tune 18 O curves in the framework of the classical Milankovitch theory.


    Description of next figure

    Description of next figure

    • Thick horizontal bars:

      • continuous growth of speleothems:

    • ASI: red,

    • DWBAH flowstone: light blue

    • Individual U/Th ages shown as filled circles.

    • Yellow horizontal bar: marine crust filling the 1 cm gap between two main parts of ASI.

    • Blacktriangles: the few A. palmata samples from Barbados corresponding to MIS 7.1.

    • The apparent misfit can be accounted for by the uncertainty on the Barbados uplift rate which may have varied slightly during the past.


    Sea level curve during penultimate glacial cycle derived from oxygen isotopes bard et al 2002

    Sea level curve during penultimate glacial cycle. derived from oxygen isotopes. (Bard et al., 2002)


    Overview

    Overview

    • MSL- change since 140 000 years: Results from geomorphology. Local and global signal

    • model isostatic vertical movements in order to determine the global signal

    • MSL in historic times: direct tide gauge measurements. Distinguish local and global signal

    • MSL fom satellite observations: global signal

    • Bathymetry from satellite observations. Isostasy models are a usful tool to extract long-wavelength gravity field.


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