Investigation of local geodynamic effects using repeated gravity gradient measuements

1. Budapest University of Technology and Economics Department of Geodesy and Surveying Investigation of local geodynamic effects using repeated gravity gradient measuements Gy. Tóth Budapest University of Technology Department of Geodesy and Surveying, Budapest, Hungary

2. Overview • Geodynamic processes • Measurement techniques • Gravity and gravity gradients of deformable polyhedral bodies • Separating local effects by gravity gradiometry

3. Geodynamic processes • Regional effects • co-seismic/post-seismic dislocations & gravity changes • tidal deformation • Local effects • oil/gas reservoirs (Groningen, subsidence ~50 cm) • groundwater flow & soil consolidation • anthropogenic effects

4. Example of regional effect:Surface vertical displacements due the 1999 Izmit earthquake, Turkey (Wang et al. 2003)

5. Measurement techniques • Near-surface deformations • GPS, leveling • satellite-based radar techniques (InSAR) • extensometers, tiltmeters • Gravity • gravimetry (absolute, relative) • airborne gravity and gravity gradiometry (FALCON)

6. Gravity effect of polyhedral bodies • Several formulations for homogeneous & linearly varying density • Okabe (1979), Götze and Lahmeyer (1988), Pohánka(1988), Holstein and Ketteridge (1996), … • Computation of gravity gradient tensor (second potential derivatives)

7. Formulation (Holstein, 1996) P bij orthonormal edge triad: r2ij r1ij ni ni∙ri ( hij , tij ,ni) edge j hij = tij× ni tij hij∙rij potential face i gravity gravity gradient

8. Deformable polyhedral bodies • reference (initial) configuration B0 at t =0 • reference gravity field G0(B0) • deformed configuration Bt of vertices of the polyhedra at t • gravity field Gt (Bt ) of the deformed configuration • displacement of observation positions ut (Bt ,B0 ) leads to gravity changes Gu (Bt ) • observable gravity effect Gobs (Bt ) is Gt (Bt ) + Gu (Bt ) • suitable for realistic FEM/BEM modeling

9. Separating local effects by gravity gradiometry - illustrative example • deformable polyhedral body of size 20 m, composed of 12 tetrahedra • its 2400 t mass is buried at ~40 m depth • random vertex deformation of the body is ~25 cm on average • surface subsidence (=displacements of observation positions) is max. 5 cm 600 kgm-3 20 m

10. surface deformation gz surface deformation induced gravity change subsurface body deformation induced gravity change

11. measureable gravity variation due to subsurface + surface deformation the total gravity variation is largely determined by the pattern of vertical surface deformation

12. surface deformation Vzz surface deformation induced gravity gradient change subsurface body deformation induced gravity gradient change

13. measureable gravity gradient variation due to subsurface + surface deformation the total gravity gradient variation is largely determined by the pattern of subsurface body deformation

14. What this example shows The gravity field variationpattern of gravity and gravity gradient is similar, but the signal to noise ratio is better for gradiometry: 3 μGal vs. 6 Eötvös, for near-surface deformation

15. What this example shows - contd • Gravity measurements have to be accompanied by (vertical) surface deformation measurements (e.g. GPS) in order to reveal subsurface mass variation, whereas • Gravity gradients are insensitive to a small dislocation of the measurement position

16. Conclusions • The gravity field of polyhedral targets can be calculated easily and the formulation is suitable for FEM modeling • Gravity gradients are useful in separating/eliminating near-surface/surface deformation from deeper one, because of O(1/r3) dependence instead of O(1/r2) • More complex and realistic situations should be investigated with FEM/BEM modeling

17. Thank you for your attention! ?