1. A spherical Fourier approach to estimate the Moho from GOCE data Mirko Reguzzoni 1, Daniele Sampietro 2 2 POLITECNICO DI MILANO, POLO REGIONALE DI COMO Department of Hydraulic, Environmental, Infrastructure and Surveying Engineering 1 ITALIAN NATIONAL INSTITUTE OF OCEANOGRAPHY AND APPLIED GEOPHYSICS Department of Geophysics of the Lithosphere. The present research has been partially funded by ASI through the GOCE ITALY project.

2. AN EXAMPLE: The first digital, high-resolution map of the Moho depth for the whole European Plate, extending from the mid-Atlantic ridge in the west to the Ural Mountains in the east, and from the Mediterranean Sea in the south to the Barents Sea and Spitsbergen in the Arctic in the north. MOTIVATION Moho estimation is traditionally based on: - seismic data (profiles) - ground gravity data (points) accurate information at local scale Andrija Mohorovičić

3. MOHO DEPTH OF EUROPEAN PLATE

4. Data come from early the 1970s and the 1980s to 2007. Older profiles were digitized by hand from published papers. For some areas regional Moho depth maps, compiled using deep seismic data have been used. MOHO DEPTH OF EUROPEAN PLATE

5. THE GOAL The GOCE mission promises to estimate 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 an homogeneous dataset.

6. We consider a mean reference Moho (computed for example from a isostasy model). THE HYPOTHESES We suppose to know (and subtract from the observations) the gravitational effect of the layers from the center of the Earth to bottom of the lithosphere (e.g. using a Preliminar Reference Earth Model). We neglect the effect of the Atmosphere.

7. Hypotheses: - two-layer model: 1) from topography to moho 2) from moho to the bottom of the lithosphere - layers with constant density: 1) ρ c =2670 kg m -3 2) ρ m =3300 kg m -3 Topography Moho Lithosphere THE HYPOTHESES Unique solution (Barzaghi and Sansò 1988)

8. THE HYPOTHESES Hypotheses: - GOCE data (potential and second radial derivative) on a grid at satellite altitude with stationary noise. - Ground gravity anomalies. 250 km Space-wise approach

9. THE METHOD (GOCE-ONLY, PLANAR APPROXIMATION) Linearization Fourier transform Inverse Fourier Transform Estimated Moho Error cov-matrix 2D collocation convolution error spectrum prediction observables

10. THE METHOD (PLANAR APPROXIMATION) Point-wise ground observations can be added to the system to improve the the estimation of the high frequency of the model. The collocation system can be partitioned as: Gridded satellite observations Ground point-wise gravity anomalies The system can be efficiently solved

11. EDGE EFFECTS Convolution kernelBording area Δφ Δλ Correct convolutionEdge effect In the case of moho estimation: Potential: Δφ =25°, Δλ=45° First radial derivative (at ground level): Δφ=2°, Δλ=3° Second radial derivative: Δφ=5°, Δλ=9° MISO approach: Δφ=12°, Δλ=22°

12. EDGE EFFECTS In the case of moho estimation: Potential: Δφ =25°, Δλ=45° First radial derivative (at ground level): Δφ=2°, Δλ=3° Second radial derivative: Δφ=5°, Δλ=9° MISO approach: Δφ=12°, Δλ=22° Convolution kernelBording area Δφ Δλ Correct convolutionEdge effect We have to consider wide areas Generalize the method to spherical approximation

13. SPHERICAL APPROXIMATION Moho Topography (H Q ) (M Q ) We start from the potential in spherical coordinates: and introduce the coordinates system: We approximate the distance between P and Q as: where

14. The potential can be linearized with respect to the variable r around Convolution kernel SPHERICAL APPROXIMATION

15. A SIMPLE EXAMPLE φ=27° φ=81° λ=-41° λ=71° h=10km km Errors from 0.5 km to 1 km Errors from 0.2km – 0.7km Estimated model in spherical approximation Estimated model in planar approximation

16. SIMULATED MOHO IN CENTRAL EUROPE 66° 112° The final moho will be estimated in an area of 42°x75° with a resolution of 0.25° Bording area for T rr convolution Bording area for T convolution The considered region Bording area for MISO approach

17. SIMULATED MOHO IN CENTRAL EUROPE Reference moho Estimated model in spherical approximation km Low-medium fequencies are well estimated using GOCE only observations. As expected details are not recovered by observations at satellite altitude.

18. SIMULATED MOHO IN CENTRAL EUROPE Differences between the starting moho model and the estimated one Difference between reference and estimated model (Spherical approach) Mean [km] -0.3 r.m.s. [km] 0.5 Details are not recovered from GOCE observations km

19. SIMULATED MOHO IN CENTRAL EUROPE Differences between planar and spherical approches km ReferenceEstimated Spherical Estimated Planar Mean [km] 31.230.930.8 r.m.s [km] 1.702.333.3

20. SIMULATED MOHO IN CENTRAL EUROPE Error map obtained with potential, second derivative and adding 50 ground observations. Adding ground observations also high frequency can be recovered. Estimation error decrease to 0.3km (r.m.s.) km

21. CONCLUSIONS The general problem of estimating the discontinuity surface between two layers of different constant density was investigated. A method based on collocation and FFT has been implemented to evaluate the contribution of GOCE data in the Moho estimation. The integration between satellite and ground data has been studied. The method has been generalized to spherical approximation. Convolution kernels have been modified in order to consider the effect of spherical approximation.

22. CONCLUSIONS FUTURE WORK Apply the method to real data (GOCE-ITALY project). Open issue: how to disentangle the different gravimetric signals that are mixed up into the data? combination with geological models and conditions The method has been tested on simulated data for the estimation of the Moho depth in the central Europe, showing that GOCE observation can improve our knowledge of the crust structure.