1. Western Balkans Moho Depth and Crustal Structure Exploiting GOCE Data
D. Sampietro(1), M. Reguzzoni(1,2)
(1) GReD s.r.l. – Geomatics Research & Development
Spin-off del Politecnico di Milano
(2) Department of Civil and Environmental Engineering – Politecnico di Milano

2. The Western Balkan Area
While the crustal structure of the Pannonian, Transilvanian, Adriatic, and Carpathian basins is reasonably well know thanks to the exploration of oil companies the Dinarides and the surrounding areas suffer from lack of measurements, which results in high uncertainties in the estimations of the Moho depths.
Well known provinces
Raykova, R., & Nikolova, S. (2007). Studia Geophysica et Geodaetica, 51(1),
In the present work we will study the Moho depth of the Western Balkan Region by exploiting GOCE data.
The Western Balkan area, basically the region laying between Bulgaria
and the Adriatic Sea, is one of the most complex and active
European tectonic setting. The area is located in the correspondence
of the collision between the African and Eurasian plates
and is characterized by the of the Alpine-Himalayan orogenic
Belt and by the opening of the Pannpresence onian Basin see Fig. 1.
In particular, due to the thrusting of the Adria Plate into the European
lithosphere, the Alps,the Dinarics and the Albanides was
formed. According to latest studies, mainly based on the analysis
of velocities retrieve from permanent GNSS networks, and on passive
seismic methods Adria is now seen as a set of two or even
three smaller units moving northward with velocity of the order of
35 mm/year (Oldow et al. 2002; Herak et al. 2005).On the contrary
the Southern Carpathian and East part of Balkan Peninsula show
southward oriented movement with magnitude of about 3 mm/year.

3. Geological provinces class.
The Inversion Procedure
The Inversion procedure is composed by two main steps the data reduction and the inversion of the residual field.
GOCE data are used in both steps:
In the former they are used to classify the area in geological homogeneous patches;
In the latter they are used as observation to apply the inversion algorithm.
Sediment, ocean, and ice models
GOCE data
Geological provinces class.
Crystalline crust model
Data stripping
Data reduction
Reduced data
Mantle effect
Seismic
combination
Inversion Δρ
Linearization point
Inversion operator
Density functions D ρ D
Convergence?
model
Crustal no
yes ρ

4. Step 1: Data Reduction
Removed with geometry from ETOPO1 and fixed density.
Removed with geometry from ETOPO1 and fixed density.
Crystalline crust represents the most important contribute. Its density defines the gravitational effect to be removed and the density contrast at the Moho discontinuity.
Unknown geometry, density from crystalline crust and upper mantle models.
Removed with geometry and density from Laske & Masters, EOS Trans. AGU, 78, F483, 1997).
Removed with geometry defined by the mean Moho depth and density from GyPSuM model (Simmons et al. Journal of Geophysical Research: Solid Earth 2010)

5. The Importance of Geological Provinces for Moho Depth Determination
Christensen and Mooney, J GEOPHYS RES, 100(B7), PP. 9768, JUNE 10, 1995.
𝜌=𝑎+ b 𝑉 𝑝
Note that the definition of the geological provinces is crucial to correctly reduce the data and invert the residual signal.

6. The Importance of Geological Provinces for Moho Depth Determination
[km]
GEMMA1.0[1]
[1] M. Reguzzoni, D. Sampietro. GEMMA: An Earth crustal model based on GOCE satellite data, Int J Appl Earth Obs, doi: /j.jag

7. Bayesian Estimation of Geological Provinces Boundaries
We suppose to have a rough geological provinces model and that the geological province Gi of a pixel i can be either the a-priori one or the ones of its neighborhood Δi.
THE PRIOR probability of Gi is computed by defining a weight-matrix W, e.g. the probability that the geological province Gi is G1 is equal to:
where:
Geologic Province and Thermo-Tectonic Age Maps (Exxon, Technical Report, 1995) .
e.g.

8. Bayesian Estimation of Geological Provinces Boundaries
THE LIKELIHOOD is defined by supposing an isostatic Moho depth (Airy model)
in planar approximation (with hi topography) and considering at each pixel the gravitational effect of a Bouguer plate of thickness , so that:
Under these assumptions an approximated relation between ρc,i and δgi holds:
𝜌 𝑐,𝑖 =𝑓 𝛿𝑔 𝑖
The likelihood is supposed to be normally distributed with a mean given by 𝝁 𝜌 𝑐 𝑮 𝓵
and a standard deviation 𝝈 𝜌 𝑐 𝑮 𝓵
Where 𝜇 𝜌 𝑐 𝐺 𝓁 is the mean value of 𝜌 𝑐,𝑖 𝐺 𝓁 computed for the geological province 𝐺 𝓁
and 𝜎 𝜌 𝑐 𝐺 𝓁 is its standard deviation.

9. Bayesian Estimation of Geological Provinces Boundaries
𝜌 𝑐,𝑖
[kg/m3]
GOCE gravity disturbances
[m/s2] 𝛿𝑔
Approximated density variation used for the Bayesian classification

10. Max of the posterior probability
Bayesian Estimation of Geological Provinces Boundaries
THE POSTERIOR distribution of Gi is computed by applying the well known Bayes theorem. Finally the geological province of the pixel is chosen by maximizing the posterior distribution (MAP).
Initial model
Adjusted model
Bada et al. (1998). Geophysical Journal International, 134(1),
Max of the posterior probability
The algorithm allows to compute also the probability that a pixel belongs to a geological province

11. Step 2: Inversion
Basically the solution is based on the same procedure developed to compute the GEMMA1.0 global model but the global inversion in terms of spherical harmonic is here substituted by the regional inversion in terms of Wiener deconvolution.
The Inversion procedure allows:
- to estimate the mean Moho depth even once the normal field is removed;
- to take into account the crustal density variation in the radial direction;
- to correct the a-priori density for scale factors;

12. Step 2: Inversion no yes Reduced GOCE data GEMMA1.0 model
Fast Fourier Transform
Linearization
𝛿𝑔 𝑥 = 𝑘 𝑥 − 𝜉 𝛿𝐷 𝜉 Δ𝜌 𝜉 𝑑 𝜉
𝑘=𝑘 𝐷
GEMMA1.0 model
Wiener Filter
Signal Power spectrum
Local seismic
model
Average Moho depth for each geological province
Seismic combination
Convergence?
Crustal model
Δρ, δD no Δρ
yes
Final model

13. Results [km] Local Moho model from seismic observations Local solution
Crust 1.0
ESC Moho
GEMMA1.0
Moho depth from seismic observation developed in the framework of IUGG upper mantle program.

14. Results [km] Difference Mean [km] Std Crust 1.0 -2.3 2.6 ESC -5.3 2.9
Local Moho model from seismic observations
[km]
Local solution
Difference
Mean
[km]
Std
Crust 1.0
-2.3
2.6
ESC
-5.3
2.9
GEMMA 1.0
-0.1
2.5
Local Solution
-0.7
0.9
Crust 1.0
ESC Moho
GEMMA1.0
Moho depth from seismic observation developed in the framework of IUGG upper mantle program.

15. Conclusions
In the present work an algorithm to refine the shape of the main geological provinces driven by GOCE data in a Bayesian scheme has been studied and implemented.
First tests (on real data) seem to prove the reliability of this Bayesian method thus encouraging possible applications of GOCE observations in this field.
An improved procedure to estimate Moho depth from GOCE data at local scale has been studied and implemented.
Results in terms of geological provinces modelling and Moho depth estimation shown the reliability of the method giving results comparable with those obtained from seismic profiles.
The use of gravity gradients can improve the geological provinces modelling. This should be investigated in future studies

16. Thanks for your attention
GReD s.r.l. – Geomatics Research & Development
Spin-off del Politecnico di Milano
Department of Civil and Environmental Engineering – Politecnico di Milano