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POTENTIAL METHODS 2018-2019 Part 4 Rock Densites

POTENTIAL METHODS 2018-2019 Part 4 Rock Densites. Carla Braitenberg Trieste University, DMG Home page: http://www2.units.it/~braitenberg/ e-mail: berg@units.it Tutor Tommaso Pivetta Email: tommasopivetta@yahoo.it. Overview.

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POTENTIAL METHODS 2018-2019 Part 4 Rock Densites

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  1. POTENTIAL METHODS2018-2019Part 4Rock Densites Carla Braitenberg Trieste University, DMG Home page: http://www2.units.it/~braitenberg/ e-mail: berg@units.it Tutor TommasoPivetta Email: tommasopivetta@yahoo.it

  2. Overview Chapterrefers to Chapter 4 of textbookHinze et al, 2013. The density of earthmaterialsisdefined, sinceitis the basicparameternecessary for modeling. The densityisdiscussed for: rock type, depthdependence, agedependence, temperature and pressure effect.

  3. Density of inomogeneous rock • Grain density of rock made of ndifferentmineralconstituents, with vi the volume fraction of ithmineral, and ρi the mineraldensity: • Presence of voidspaces (fractures, porosity with vp volume fraction of void) reduce the density- bulk density: • If the voids are partiallyfilledwith fluid, with density

  4. Density in earthInterior • Averagedensity, from total mass and averageradius of earth: • =M/(4/3 pi R3) • (GRS80): GM=398600.5 10^9 m3s-2 • Ravg=(a+b)/2=(6378137+6356752.3141)/2 m= 6367444.657 m • G=6.674 08 x 10-11 m3 kg-1s-2 • M=5.9724 1024 kg; Volume= 1.0814 1021 m3 • =5522.8 kg m-3 Moment of inertia of solidsphere: I=8/15 pi R5 With the abovevalues for density and Radius the intertial moment for a homogeneousearthwould be: 9.6858 1037 m2 kg Compare to value of moment of inertia of earth : A=8.008 1037 m2kg (Lambeck, 1980) C=8.034 1037 m2 kg

  5. Moment of inertia of the Earth issmallerthanexpected for a homogeneoussphereos the same mass. therefore mass isconcentratedtowards the center of the earth.

  6. Rock density dependance: which are the primarycontrols of rock density 1) mineralcomposition 2) percentage of voidspace • Depending on: lithology, secondarychemical and physicaleffects (fracturing, dissolution, chemicalalteration of minerals). • Mineraldensity: majority 2500 to 3500 kg/m3 • Ore minerals: 4000-6000 kg/m3 • Density of mineralsdecreases with increase of SiO2 content. Alsodecreases with increase of H2O content. • Mineralsthatformed under high pressure in metamorphicrockshavehigherdensity • Non-metalliferousresources (coal, salt,clay) havelowdensity • Metalliferousores: higherdensity • Lithostatic pressure increase: higherdensity • Temperature increase: lowerdensity

  7. Classification of rocksused for densityvaluesdiscussion. Crystalline Rocks SedimentaryRocks UnconsolidatedSediments Igneousrocks MetamaorphicRocks - Plutonic - Volcanic

  8. CrystallineRocks • Unalteredplutonicrocks: only 1% voids, due to weathering, faulting. Fracturesclose due to lithostatic pressure. Densities and velocitiesapproachconstantvaluesatpressures > 600MPa, reachedat 15-20km of depth. • Densityisgoverned by the mineralcomposition. • Felsic to mafic: increase of density, due to smallerportion of SiO2, and higherportion of Ca, Fe and Mg.

  9. Crystallinecrust- Continental Crust • Compositionbecomes more mafic with depth, so densityincreases. Thisisonly a general rule- strong lateraldensitycontrasts can be presentalso in mid-crust. For instance due to large strike-skipfualts. Seeexample in next slide. Overallaverage of uppercrustis 2670 kg/m3. thereforethisvalueisusedas standard for the topographicreduction to obtain the Bougeranomaly. • According to a global analysis of Christensen and Mooney (1995) the averagecrustaldensityis 2830 kg/m3. • Lower crust: averagecomposition of Gabbro. Base of crust: maficgarnet granulite

  10. Averagecrustalprofileaccording to Christens and Mooney (1995)

  11. Density for Oceaniccrust • Layering: Sediments, maficextrusiverocks, maficintrusicerocks. • Variations due to: age, metamorphic grade • Layerbelowsediments: lavasextruded on seafloor (density 2620 -2690 kg/m3) • Lowermostcrustallayer: 1920 to 2970 kg/m3

  12. Density of Uppermantle • Ultramaficuppermantle: 3270-3320 kg/m3, on average: 3300 kg/m3 • Peridotite: principallithology • Eclogite: 3500 kg/m3 • Depletedmantlerocks, thathaveundergonepartialmelting, depleted in Ca, Fe, Al, Ti, and are rich in olivine and Mg contenthavelowerdensity. • Compositionaldifferences to densityvariation. Example SW USA, 3% densityvariation (100kg/m3). • Thermal-petrologic-seismological model. Allows to calculatedensity and seismicvelocity for crust and mantleconditions of pressure and temperature: Hacker et al, 2003; 2004; New version: Abers and Hacker, 2016, JGR. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2015GC006171

  13. Illustration of a crustalsection with densityincrease with depth, butalso with strong lateralvariation due to crustal fault.

  14. Moho- crust-mantlediscontinuity • Moho is an importantdensityboundary- itisresponsible of a strong gravitysignal. • Densityjumpacrossboundary: 200 to 450 kg/m3. • Gravitysignal due to depthvariations of Moho. Shallow Moho equivalent to mass increase- deep Moho corresponds to mass deficit due to crustalroot. Responsible of mass compensationbeloworogens.

  15. Igneousrocks • Volcanic and extrusiveigneousrocks: more fine grainedcompared to intrusive plutonicrocks. Fine grainedtexturetends to havelowerdensity, buteffectislessthan 10% for equalcomposition. • Volcanicash: highlyporous. Deeperlevels are more compacted (see figure of nevadatuffs)

  16. Densityincrease due to compaction.

  17. Metamorphicrocks • Densityreflectsoriginalmineralcomposition of rocks • Dependsalso on T and P conditionsthat rock underwent. • In general the highercontent in iron and calciumincreasesdensity.

  18. Sedimentaryrocks and unconsolidatedsediments • Density of sedimentsiscontrolled by the amount of voidspace. • Overburdenleads to compaction and poreand cracksclosure. • The variation of densityiswellrepresented by an exponentialfunction. For shallowdepthsitisapproximated by a linear variation. The linear variationshouldnot be extrapolated to depthshigherthan a few km.

  19. DENSITY AS A FUNCTION OF DEPTHDensity driven by compaction, not lithology Due to the depositional environment and tectonic history of the Gulf of Mexico (and other similar basins), rock densities of the sedimentary section have been found to vary primarily as a function of burial depth. This density-depth relationship is attributed to the very thick (~6000m) pile of clastic sediments that comprise the Gulf basin onshore and offshore. This density-depth relationships have been extensively used to model gravity anomalies and to identify salt structures in the subsurface. DENSITY VS. DEPTH CROSSPLOT FOR OFFSHORE GULF OF MEXICO STUDY AREA. NOTE THE PRESENCE OF SALT AT 750 TO 1000 METERS DEPTH.

  20. Porosity= pore volume / bulk volume Density= bulk density * (1-porosity) From: Allen, P.A. and Allen, J.R., 2005.Basin Analysis: Principles and Applications, 2. ed.,Blackwell Publishing, 549 pp.

  21. Giles, M.R., 1997. Diagenesis: A quantitative perspective. For basin modeling and rock property prediction. Kluwer academic Publisher, Dordrecht. Copied from Allen, P.A. and Allen, J.R., 2005. Basin Analysis: Principles and Applications, 2. ed.,Blackwell Publishing, 549 pp.

  22. In LithoFlex(after Braitenberg et al. 2006, Wienecke 2006): Thereby is z the depth and Ф0 the initial [Porosity] of the sediments at the surface. The bulk density of a rock is composed of the [Fluid density] ρf and the [Grain/Rock density] ρs related to the porosity of the sediments.

  23. Measurements of Rocks’ density Procedure: 1) Measureweight of rock in air on the plate of the scale Weight=P1 2) Measureweight of rock in water by hangingit with a chainbelow the scale Weight=P2 3) Repeat the measurements so astoabletocalculate the repeatabilityof the measurementthrough the standard deviation. Note: P2 islighter due to Archimede’s force. The equivalentweightisequal to the weight of the water displaced by the rock. P2 isequal to the rock’s volume (V) multiplied by the water density (ρw) V = Rock’sdensity: Mean: xm=(x1+x2+x3+x4+x5)/5 Standard Deviation: s2=((x1-xm)2+(x2-xm)2+(x3-xm)2+(x4-xm)2+(x5-xm)2)/5 P2=P1-Vρacqua The precisionof the density measurementisinverselyproportionalto the volume of the rock sample and proportionalto the precisionof the scale.

  24. Densitydependence on temperature and pressure • Lithostatic pressure haseffect of increasingdensityalso in crystallinerocks. Increaseisrelated to elastic bulk modulus • Rho(P2)=Rho(P1)(1+(P2-P1)/K) • P2, P1: pressure values. K: bulk modulus in Gpa (for uppercrust: K=52 Gpa, lowercrust: 75 Gpa, uppermantle: 130GPa, Dziewonski and Anderson, 1981). • Temperature has a minor role. Volume thermalexpansioncoefficients are 20-40 10^-6/°C . • Oneexample of modification of the pressure equation, takinginto account the temperature variation: • Rho(P2)=Rho(P1)( 1+ (P2-P1)/K – αΔT) • αis the coefficient of thermalexpanion, and ΔTis the change in temperature. (AfterRavat et al. 1999)

  25. Density from seismicmethods • Seismicmodels are used to constraindensitymodels due to the goodcorrelationbetweendensity and seismicvelocity. • The relation betweendensity and velocityisdescribed with empirical relations based on laboratorymeasurements of rock specimens. In practiceitisnecessary to correct the density for the in situ cinditions of temperature and pressure. • The empricial relations havebeencompiled for certainrocks by differentauthors. Care should be taken to analyze the probablerockspresent in the model and choose the right relation.

  26. Examples of famous relations M: meanatomicweight of rock. A(M) and b are the parameters. Vp: compressionalvelocity in km/sec Ρ: density in kg/m^3 • Birch (1961). Relation for crystallinerocks Christensen and Mooney (1995). Veryimportantpaper. Crustalrocks linear relation: Dortmann(1976). Compilation of igneous and metamorphicrocks. Linear relation by Schön (1996): Brocher(2005) made an importantpaper with a broad compilation of existing relations and defined a new relation for the velocityrange 1.5 to 8.5 km/s . Garnder et al. (1974) defined a relation for sedimentaryrocks:

  27. Non-linear relationbetweendensityandvelocityforigneousandmetamoprohicrocks.

  28. Density vs. velocity after Brocher Density ρ and velocity have in isotrope, elastic media simple relations: κ: compressibility modus μ: shear (rigidity) modus E: elasticity module ν: Poisson ratio Brocher 2005

  29. Natural density (saturated bulk density of igneous, metamorphic, sedimentaryrocks, and sediments and soils.

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