POLITECNICO DI MILANO,
POLO REGIONALE DI COMO
GOCE EXPLOITATION FOR
MOHO MODELING AND
APPLICATIONS
D. Sampietro
POLITECNICO DI MILANO, POLO REGIONALE DI COMO
Department of Hydraulic, Environmental, Infrastructure and Surveying
Engineering
The present research has been partially funded by ESA through the
GEMMA project.
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
PROBLEM STATEMENT AND SCIENTIFIC CHALLENGE
The Moho is a physical discontinuity between the Earth crust and the upper part
of the mantle separating rocks with different densities.
Moho estimation is traditionally based on:
- seismic data (profiles)
- ground gravity data (points)
Andrija Mohorovičić
POLITECNICO DI MILANO,
POLO REGIONALE DI COMO
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
PROBLEM STATEMENT AND SCIENTIFIC CHALLENGE
CRUST2.0 Bassin et Al., 2000
•Data from 1950 to nowdays;
•Older profiles were digitized by hand from published
papers;
•For some areas regional Moho depth maps, compiled
using deep seismic data have been used;
•In large areas of South America, Africa, Antartica and
part of the Ocean models are based only on few and
poor quality data;
from Tsoulis, 2004
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Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
PROBLEM STATEMENT AND SCIENTIFIC CHALLENGE
The GOCE mission is observing the
Earth’s
gravitational
field
with
unprecedented accuracy and resolution.
The solution of inverse gravimetric
problems can benefit from GOCE.
The GOCE mission can be used to
improve the existing model or to
estimate the Moho in large areas from a
homogeneous dataset.
The main objective of the GOCE EXPLOITATION FOR MOHO
MODELING AND APPLICATIONS (GEMMA) project is to improve
the knowledge of the crust-mantle discontinuity surface by
using data coming from satellite mission.
POLITECNICO DI MILANO,
POLO REGIONALE DI COMO
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
AREA OF STUDY
1. Improvement of a global reference Earth Moho Model
A model with only the low frequencies, based on very simply approximations to be used as
a-priori information for local moho studies.
2. Local studies in critical regions such as:
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Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
DATA SET
GOCE data (potential and second radial derivative) on a grid at satellite altitude with
stationary noise.
Observations used:
gridded values of
- Potential
- Second radial derivatives
POLITECNICO DI MILANO,
POLO REGIONALE DI COMO
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
DATA SET
Geological information (where available) to constrain the model e.g.:
- Local sediment models;
- Local crust density models ;
We do not know the error structure of
these data.
- Seismic profiles;
- Ground gravity anomalies
POLITECNICO DI MILANO,
POLO REGIONALE DI COMO
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
THE PROPOSED APPROACH: HYPOTHESES
To guarantee the uniqueness of the solution for the inverse gravimetric problem
some simplifying hypotheses are required.
Hypotheses
two-layer model:
1) from topography to Moho
2) from Moho to the bottom
of the lithosphere
Problems:
 Regularity of the Moho
Effect of anomalous masses
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POLO REGIONALE DI COMO
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
METHODOLOGY (GLOBAL MODELS)
Global models of the Earth gravitational potential are typically expressed
as a spherical harmonic expansion:
GM
V (r , ,  ) 
R
 1
R
  Vm Ym ( ,  )

 0 m 0  r 
L

spherical harmonics of
degree  and order m
Gravitational potential
coefficients
  10 , m  0
  10 , m  2
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  10 , m  5
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
METHODOLOGY (GLOBAL MODELS)
GOCE OBSERVATIONS
DATA REDUCTION
SPHERICAL
GM
V (r , ,  ) 
R
HARMONIC ANALYSIS
 1
R
  Vm Ym ( ,  )

 0 m 0  r 
L

Sediments do not look significant at
global scale.
LINEARIZED RELATION BETWEEN GRAVITATIONAL
POTENTIAL COEFFICIENTS AND MOHO COEFFICIENTS
SPHERICAL
L
 M ( ,  )    M
0 m0
m
Y m ( ,  )
HARMONIC SYNTHESIS
GLOBAL
MOHO
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Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
PRELIMINARY RESULTS (GLOBAL MODELS)
A GOCE only global Moho model, based on very simple hypotheses, to be used as
preliminar model for local studies.
Hypotheses
- Reduction only for topography
- Constant density contrast
- GO_CONS_GFC_2_SPW_R2 model
- Mean Moho depth from CRUST2.0
POLITECNICO DI MILANO,
POLO REGIONALE DI COMO
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
PRELIMINARY RESULTS (GLOBAL MODELS)
Improvement of the CRUST2.0 global Moho model.
Empirical error maps
Original and corrected models
The gravitational signal generated from the updated model is consistent with the actual
gravitational field observed by GOCE.
POLITECNICO DI MILANO,
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Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
METHODOLOGY (LOCAL MODELS)
D  D  
T( x ) 
 dd 
x  2  2   2
h
2
Tzz ( x )  2
z
Observables

G
h  D  D  
dd

G
x  2  2  z   2
h
Wiener filter
d
prediction
D̂T , Tzz f   T̂0  T̂zz 0
d
z 0

SD k̂ T S zz
S zz S  k̂ T2 zz SD S  k̂ T2 SD S zz
Linearization
Convolutions
Tx   Tx   Tx  

 k x  Dd
T

Tzz x   Tzz x   T zz x  

k
Tzz

Error Szz S 
spectra
S T ,T (f ) 
zz
SD k̂ T zz S
2
k̂ Tzz SD S  k̂ T2 SD S zz
SD S zz S
S zz S  k̂ T2 zz SD S  k̂ T2 SD S zz
x  Dd

Inverse Fourier Transform
Fourier Transform
T̂0 f   k̂ T f D̂f   ˆ f 
T̂zz 0 f   k̂ Tzz f D̂f   ˆ zz f 
Moho
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Error covariance
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
PRELIMINARY RESULTS (LOCAL MODELS)
THE GOCE ESTIMATED MOHO BENEATH THE TIBETAN PLATEAU AND
HIMALAYAS
General good agreement between GOCE Moho model and seismic profiles at low frequencies .
Discrepancies between GOCE model and seismic profiles can be used to detect anomalies into the
Moho.
 Smoothing effect due to the presence of a very deep Moho with high variability. Better results are
expected in other regions of the world.
POLITECNICO DI MILANO,
POLO REGIONALE DI COMO
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
PRELIMINARY RESULTS (LOCAL MODELS)
PROFILE 2 (WEST-EAST)
Very large differences (about 10km) between 300
and 450 km in corrispondence of the collision
between Indian and Eurasian plates.
DISCREPANCIES BETWEEN GOCE AND SEISMIC CAN BE
USED TO DETECT ANOMALIES INTO THE MOHO
GOCE-only Moho
GOCE + Seimic profiles
Moho
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POLO REGIONALE DI COMO
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
PRELIMINARY RESULTS (LOCAL MODELS)
TIBETAN PLATEAU AND HIMALAYAS
ITALY
PARANÀ BASIN
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Sci_Net 2011 workshop
October, 20 – 21, 2011
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RESULTS
1) AN INVERSE GRAVIMETRIC PROBLEM WITH GOCE DATA.
M. Reguzzoni, D. Sampietro – International Association of Geodesy Symposia, “Gravity, Geoid and Earth Observation”, IAG Commission 2:
Gravity Field (oral presentation and contribute published in the proceedings);
2) MOHO ESTIMATION USING GOCE DATA: A NUMERICAL SIMULATION.
M. Reguzzoni, D. Sampietro, (in print). Presented to “Geodesy for Planet Earth”, 31 August – 4 September 2009, Buenos Aires, Argentina
(oral presentation and contribute published in the proceedings);
3) UNIQUENESS THEOREMS FOR INVERSE GRAVIMETRIC PROBLEMS.
D. Sampietro and F. Sansó, (in print). Presented to “VII Hotine- Marussi Symposium”. Rome, 6-10 June, 2009 (poster presentation and
contribute published in the proceedings)
4) A STUDY ON THE AUSTRIAN MOHO FROM GOCE DATA;
M. Reguzzoni, D. Sampietro – EGU General Assembly 2011,Vienna (poster presentation);
5) GOCE EXPLOITATION FOR MOHO MODELING AND APPLICATIONS;
D. Sampietro, – 4th International GOCE User Workshops, Munich. Proceedings of the 4th GOCE user workshop, 31 March – 1 April 2011,
Technische Universitat Munchen (TUM), Germany (oral presentation and contribute published in the proceedings);
6) THE GOCE ESTIMATED MOHO BENEATH THE TIBETAN PLATEAU AND HIMALAYAS;
D. Sampietro, M. Reguzzoni, C. Braitenberg – XXV IUGG General Assembly 2011, Melbourne. (oral presentation and contribute published
in the proceedings);
7) GLOBAL MOHO ESTIMATE FROM GOCE SPACE-WISE SOLUTION AND A LOCAL APPLICATION IN THE MEDITERRANEAN AREA;
D. Sampietro, R. Barzaghi, A. Borghi, M. Reguzzoni – AGU Fall meeting 2011 (accepted as oral presentation).
8)GLOBAL MOHO FROM THE COMBINATION OF THE CRUST2.0 MODEL AND GOCE DATA.
D. Sampietro, M. Reguzzoni – GNGTS 2011, (oral presentation and contribute published in the proceedings);
Selected for the AGLC prize
POLITECNICO DI MILANO,
POLO REGIONALE DI COMO
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
RESULTS
http://geomatica.como.polimi.it/elab/gemma/
- Presentation of the project
- Downloadable material
- Global and local Moho models (asci grid)
- presentations, posters, etc…
POLITECNICO DI MILANO,
POLO REGIONALE DI COMO
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
CONCLUSIONS
A method to locally model the Moho discontinuity, based on
collocation and FFT, has been implemented;
The method has been applied to estimate local Moho models in
the Tibetan region, Italy and Paranà basin (south America) giving
good results;
Discrepancies between GOCE model and seismic profiles can be
used to detect anomalies into the Moho;
A reference GOCE-only global Moho model with a resolution of
1°x1° has been computed;
A correction to the CRUST2.0 model has been computed from
GOCE data;
Estimation error is available for all the computed models;
POLITECNICO DI MILANO,
POLO REGIONALE DI COMO
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati
FUTURE WORKS
The GEMMA project has been funded by ESA and Politecnico di Milano and has a
duration of 2 years.
WP0000 Project management
GENERALIZATION OF THE PROPOSE APPROACH TO SPHERICAL APPROXIMATION.
WP1000
WP2000
ASSESSMENT OF THE COVARIANCE FUNCTIONS AND OF THE ESTIMATION ERROR.
WP3000
ISOLATION OF THE GRAVIMETRIC SIGNAL
ICE SHEET ESTIMATION
WP4000
ON-LINE SOFTWARE AND MAP GENERATION
POLITECNICO DI MILANO,
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WP5000
Sci_Net 2011 workshop
October, 20 – 21, 2011
Frascati