ESA training. Gravity, magnetics and gradients for mapping and modelling. Jörg Ebbing. Department of Geosciences Kiel University

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1 ESA training Gravity, magnetics and gradients for mapping and modelling Jörg Ebbing Department of Geosciences Kiel University Contributions from: Eldar Baykiev (Trondheim), Des Fitzgerald (Melbourne), Nils Holzrichter (Kiel), Nils Olsen (Copenhagen), Wolfgang Szwillus (Kiel)

2 Some considerations: Coordinate systems GOCE - NWU (north, west, up) (Des Fitzgerald, 2011) 2

3 Application of satellite gradients How can we model satellite data? Is a topographic reduction necessary? Is there any additional benefit using (satellite) gradients? All signal is theoretically in the potential? At which height should I use the data? Downward continued to surface? At satellite height? How to use data for regional modelling? Do we need to consider a spherical (ellipsoidal) Earth, if using satellites? Do satellite gradients have a sensitivity beyond global models or terrestrial data? 3

4 Flat Earth vs. Spherical calculations 4

5 Flat Earth vs. Spherical calculations 5

6 Flat Earth vs. Spherical calculations Uieda & Braitenberg 2015 Tesseroids modelling tool: Gravity: available from Magnetics (Baykiev): soon to be released, see slim.dgfi.tum.de

7 Curie temperature isotherm Moho Δρ Crust Lithospheric mantle Asthenospheric mantle

8 The Magnetic Field from Space: Swarm Launched: 22 November 2013

450km) 24 hours LT coverage within 7-10 months to avoid seasonal or yearly periods (near polar) Inclination difference: drift

9 Constellation of Satellites 4 years operational phase Low altitude down to 300km (or lower) and pair of satellites for zoom on crustal signal Altitude difference: higher (app. 530km) & lower satellites (app. 450km) 24 hours LT coverage within 7-10 months to avoid seasonal or yearly periods (near polar) Inclination difference: drift between orbital planes towards 9 hours LT Credits: J.E. Rasmussen DNSC launch after 1.5 yr after 3 yrs after 4.5 yrs launch after 4.5 years red (C) 530 km 500 km yellow (A,B) 450 km 300 km

10 Swarm - Mission Aim The Swarm mission will provide the best ever survey of the geomagnetic field and its temporal evolution, in order to gain new insights into the Earth system by improving our understanding of the Earth s interior and physical climate.

.. and with Swarm N = 133, resolution: 300 km

11 Improvement of Lithospheric Field Model Before Ørsted... N = 30, resolution: 1330 km... with present satellites Ørsted and CHAMP... N = 60, resolution: 670 km... and with Swarm N = 133, resolution: 300 km Magnetic field of Earth s crust radial component at 10 km altitude

12 Sources of the Earth s Magnetic Field (DTU Space)

13 Radial magnetic component at satellite altitude (DTU Space)

14 (DTU Space)

15 Magnetic field strength Changes in 6 months (December 2013 to June 2014) J (DTU Space)

Global modelling A first example CRUST1.0 (Laske et al., 2013) is a 1 o x1 o degree global crustal model comprising several crustal and sedimentary layers.

16 Global modelling A first example CRUST1.0 (Laske et al., 2013) is a 1 o x1 o degree global crustal model comprising several crustal and sedimentary layers. For our model, each 1 o x1 o cell that describes a layer element was converted to a single tesseroid. Following Purucker et. al (2002) the susceptibility of the oceanic crust was set as 0.04 SI, and of the continental crust SI Ambient field IGRF11 (Finlay et al., 2010) Computation grid resolution 2 x2 Computation grid altitude 400 km Eldar Baykiev

17 Global modelling A first example CRUST1.0 (Laske et al., 2013) is a 1 o x1 o degree global crustal model comprising several crustal and sedimentary layers. For our model, each 1 o x1 o cell that describes a layer element was converted to a single tesseroid. Difference between spherical and ellipsoidal shape of the Earth on data in Swarm orbit Eldar Baykiev

18 Gravity gradients

19 Magnetic gradients (Inclination: 90 ) Txx Txy Txz Tzz Tzx Tzy Tyz Txz Tyy Tyx Tyy Tyz Txx Txy Tzz Susceptibility: 0.02 SI Similar for magnetics, but direction of external field is important..

20 Magnetic gradients (Inclination: 45 ) Txx Txy Txz Tzz Tzx Tzy Tyz Txz Tyy Tyx Tyy Tyz Txx Txy Tzz Susceptibility: 0.02 SI Declination=0

21 Magnetic gradients (Inclination: 0 ) Txx Txy Txz Tzz Tzx Tzy Tyz Txz Tyy Tyx Tyy Tyz Txx Txy Tzz Susceptibility: 0.02 SI Declination=0, anomalies at magnetic equator!

22 Magnetic gradients from MF7 SH=1-120 at surface Br_θ Br_φ Bθ_θ B φ _ θ Stavros Kotsiaros

23 Korhonen et al. 2007

24 Magnetic satellite data Lithospheric signal is small compared to normal (core) field Swarm satellite fly in ~400 and 550 km height Noise/disturbing signal Polar regions are affected by ionospheric turbulences Equatorial jet currents Tesseroids modelling tool available

25 GOCE & Swarm

GOCE -Gravity field and steadystate Ocean Circulation Explorer Mission period 17 March 2009 11 November 2013 Gradiometer; 3 pairs of 3-axis, servocontrolled,

26 GOCE -Gravity field and steadystate Ocean Circulation Explorer Mission period 17 March November 2013 Gradiometer; 3 pairs of 3-axis, servocontrolled, capacitive accelerometers (each pair separated by a distance of about 0.5 m). Orbit height: 225 to 255 km Grids can be downloaded from

Gravity gradient grids @ 255 km height North-north

27 Gravity gradient 255 km height North-north North-east North-radial East-east East-radial Radial-radial

28 Topographic and Bouguer correction Complete Bouguer correction is defined as 1) Gravity effect of Bouguer slab 2) spherical correction 3) Terrain correction

29 Topographic and Bouguer correction Complete Bouguer correction is defined as 1) Gravity effect of Bouguer slab 2) spherical correction 3) Terrain correction h h describes height above reference level or water depth and is different for each station.

30 Topographic and Bouguer correction Complete Bouguer correction is defined as 1) Gravity effect of Bouguer slab 2) spherical correction 3) Terrain correction

31 Topographic and Bouguer correction Complete Bouguer correction is defined as 1) Gravity effect of Bouguer slab 2) spherical correction 3) Terrain correction

32 Topographic and Bouguer correction Bouguer calculation is always possible if only station height is known, can be quickly calculated. Terrain correction requires high-resolution topography for surface data (25 or 50 m for local sources which have highest effect)

33 Topographic and Bouguer correction BUT: NOT WORKING WELL FOR GRADIENTS (Slab of constant thickness has not effect on gradients, terrain important) =>TOPOGRAPHIC MASS REDUCTION (Computational demanding)

34 Topographic and Bouguer correction For satellites: point of obervation above topography (e.g. 250 km) => no high-resolution topography needed

35 Topographic and Bouguer correction TOPOGRAPHIC MASS REDUCTION (for gravity and gradients) possible

36 Global or local topographic correction? Surface Topo Full effect Topo distant effect (1.5 degree) Wolfgang Szwillus

37 Global or local topographic correction? Surface Topo Full effect Satellite height Topo Full effect Topo distant effect (1.5 degree) Topo distant effect (1.5 degree) Wolfgang Szwillus

38 Global or local topographic correction? Surface Topo Full effect Satellite height Topo Full effect Topo distant effect (1.5 degree) Topo distant effect (1.5 degree) Topo distant effect (5 degree) Wolfgang Szwillus

39 Global or local topographic correction? Far field effect of topography is significant Do we have always to calculate globally? Regional modelling only possible, if using global model as reference model for surrounding? But how to treat uncertainties or which model is best suited: Crust 5.0, Crust2.0, Crust1.0, GEMMA? A simple alternative: Use isostatic reference model

40 Isostasy: A justified assumption? Isostatic anomaly GEMMA crustal thickness Moho => Crust Base lithosphere => Lith. Mantle 42

41 Topographic-isostatic correction for Full effect Distant (1.5 degree) Wolfgang Szwillus

42 Remaining distant RIE as function of correction radius for ground stations 5 degrees might be enough, if you want to avoid long computations or Extend your model by 5 degrees during modelling Wolfgang Szwillus

Topographic-isostatic correction for gravity @Surface @Satellite height Full

43 Topographic-isostatic correction height Full effect Full effect Distant (1.5 degree) Distant (5 degree) Wolfgang Szwillus

44 Remaining distant RIE as a function of correction radius for satellite stations 5 degrees might be enough?? or Extend your model by 5 degrees during modelling or Maybe gradients are better suited? Wolfgang Szwillus

45 Topographic-isostatic correction for gravity gradients at satellite height Full effect Distant (5 degrees) Wolfgang Szwillus

46 Remaining distant RIE gradient component at satellite height <-Vertical gradient Wolfgang Szwillus

47 Remaining distant RIE gradient component at satellite height NE gradient -> <-Vertical gradient Wolfgang Szwillus

48 Topographic reduction of satellite data Replace Bouguer correction with topographic mass reduction Topographic mass reduction of gravity gradients Satellite height: Low resolution topography (4 min) sufficient Global topographic models with 30s are available (SRTM) 10 km height: Omission error of topographic reduction is challenging Extension radius of 5 degrees is sufficient, but use topography over same area as model definition

49 GEMMA project 51

50 GOCE satellite altitude / Earth s surface satellite altitude is smooth Downward continuation enhances signal power & details

51 Comparison GOCE and EGM2008 EGM2008 GOCO3S EGM2008-GOCO3S Free-air anomaly Free-air anomaly Difference Comparison untill spherical harmonic degree 200

Note: Gxz and Gyz are even constant to zero which is in

52 Crust 1.0: A test for the Arabian pensinsula The Crust 1.0 model cannot explain the measured gravity gradients Note: Gxz and Gyz are even constant to zero which is in large disagreement to the measurements. Observed From Crust1.0

53 Arabian Peninsula Seismological results Hansen et al Bouguer anomaly (EGM2008) A-A Hansen et al. 2007

54 Arabian Peninsula Seismological results Hansen et al Bouguer anomaly (EGM2008) Gravity gradients at orbital height:260 km

55 Moho depth by satellite gravity gradient inversion Inversion Gzz=Full Z 0 =30 km Dr= 350 kg/m 3

56 Hansen et al. 2007

57 Sensitivity to intra-crustal sources: lower crust Observed Modelled Gxx Gxy Gxz Gyy Gyz Gzz

58 Lithospheric sensitivity LAB depth Artemieva & Thybo (2008) Full geoid Artemieva & Thybo (2008) Bouguer anomaly

Use of GOCE gravity gradient data for lithospheric modeling and geophysical exploration Data sets from the GOCE mission have two main advantages compared with earlier global gravity models: (1) The

59 Use of GOCE gravity gradient data for lithospheric modeling and geophysical exploration Data sets from the GOCE mission have two main advantages compared with earlier global gravity models: (1) The GOCE gravity model has higher resolution in the transitional wavelength between earlier satellite and terrestrial gravity data. Only based on GOCE gravity data, it would be feasible to provide a gravity field with 80 km resolution (2) The second and more revolutionary novelty is that GOCE measures gravity gradients. How useful for geophysical research and exploration?

60 Depth sensitivity of GOCE gravity gradients What is the depth extent visible in gravity gradient data? Model signal mostly related to crustal thickness? What is the effect of other sources in crust and mantle? 62

61 Sensitivity of satellite gradients => Vertical components good fit, but not non-vertical components? Sensitivity kernels for spherical gravity gradients Z. Martinec 2013

62 Effect of uncertainties of Moho depth and density contrast Density contrast at Moho can vary with respect to upper crust and lower mantle density Typically a range from 300 to 500 kg/m 3 is applied

63 Effect of Moho depth Moho depth (Grad et al. 2009)

64 Effect of Moho depth uncertainty

65 Effect of density uncertainty

66 Lithospheric model set-up < Moho Lith. mantle Asthenosphere Piece-wise calculations for depth slices through 3D model Thickness of depth slices similar to resolution of other geophysical methods

67 0-2.5 km height

68 2.5-5 km height

69 5-7.5 km height

70 km height

71 10-15 km height

72 15-20 km height

73 20-25 km height

74 25-30 km height

75 30-35 km height

76 35-40 km height

77 40-45 km height

78 45-50 km height

79 Sensitivity analysis on the scale of NE Atlantic We use density contrast of -20 to -40 kg/m 3 at base lithosphere Temperature-dependent upper mantle density 81

80 km depth

81 km depth

82 km depth

83 km depth

84 km depth

85 km depth

86 km depth

87 km depth

88 Lithospheric sensitivity GOCE gravity gradients are sensitive to upper 100 km of the lithosphere low sensitivity to thickness of the lithosphere Not affected by regional trends GOCE gradients can complement seismic tomography Seismic tomography has low resolution from Moho to 100 km depth where GOCE gradients are sensitive True on a larger scale? Yes, if realistic density structure is used Simplification by lateral varying density blocks leads to large errors 90

89 Relative signal km height for Model A

90 Relative signal km height for Model A

91 Relative signal km height for Model A

92 Relative signal km height for model A

93 Relative signal km height for model A I2 I1

94 Gradient data and rotational invariants Gradients are dependent on the orientation of the coordinate system, which may differ from the orientation of random geological features Invariants have the advantage to be independent from the coordinate system and help to delineate the outline of density contrasts. Pedersen and Rasmussen (1990) demonstrated the use of rotational invariants of the gravity tensor: I1: contraction invariant deep sources I2: determinant shallow sources 9 6 These rotational invariants are independent from the orientation of the flight lines and facilitate to detect sources randomly orientated in any coordinate system

95 Example: Bedrock/ice corrected gradients for Antarctica

96 Example from an airborne survey E.g. Model interaction often requires profile modelling How to model out of plane components? Solution: Modelling of invariants!

Summary: Lithospheric modelling GOCE gravity models provide the most homogeneous global data set Downward continuation possible, but be aware of omission error Satellite gravity gradients help to

97 Summary: Lithospheric modelling GOCE gravity models provide the most homogeneous global data set Downward continuation possible, but be aware of omission error Satellite gravity gradients help to validate regional crustal setting Non-vertical tensor components are sensitive to subtle lateral density variations Satellite gradients should be used jointly with gravity data to model the entire lithosphere

98 Comparison to global Vs tomography

Geophysik mittels Satellitenbeobachtungen - Von der Struktur zur dynamischen Betrachtung der Erde

Geophysik mittels Satellitenbeobachtungen - Von der Struktur zur dynamischen Betrachtung der Erde Jörg Ebbing Institut für Geowissenschaften Christian-Albrechts-Universität zu Kiel 102. Sitzung des FKPE