A spherical Fourier approach to estimate the Moho from GOCE data

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

2. MOTIVATION • Moho estimation is traditionally based on: • - seismic data (profiles) • - ground gravity data (points) accurate information at local scale AndrijaMohorovičić 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.

3. MOHO DEPTH OF EUROPEAN PLATE

4. MOHO DEPTH OF EUROPEAN PLATE • Data come from early the 1970s and the 1980s to 2007. • Older profiles were digitized by hand frompublishedpapers . • For some areas regional Moho depth maps, compiled usingdeepseismic data havebeenused.

5. 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. THE GOAL

6. THE HYPOTHESES Weneglect the effectof the Atmosphere. Weconsider a meanreference Moho (computedforexamplefrom a isostasymodel). 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).

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

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

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

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 The system can be efficiently solved Ground point-wise gravity anomalies

11. EDGE EFFECTS Bording area Convolutionkernel In the case of moho estimation: Potential: Δφ =25°, Δλ=45° First radial derivative (at ground level): Δφ=2°, Δλ=3° Secondradial derivative: Δφ=5°, Δλ=9° MISO approach: Δφ=12°, Δλ=22° Δφ Δλ Correctconvolution Edgeeffect

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

13. SPHERICAL APPROXIMATION We start from the potential in sphericalcoordinates: and introduce the coordinates system: (HQ) Topography Moho (MQ) Weapproximate the distancebetween P and Q as: where

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

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

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

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

18. SIMULATED MOHO IN CENTRAL EUROPE Differences between the starting moho model and the estimated one km Details are not recovered from GOCE observations

19. SIMULATED MOHO IN CENTRAL EUROPE Differencesbetween planar and sphericalapproches km

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

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 • 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. FUTURE WORK • Apply the method to real data (GOCE-ITALY project). Openissue: how to disentangle the different gravimetric signals that are mixed up into the data? combination with geological models and conditions