v It appears that under their own units the gravity gradient is a million times worse than the gravity. v In reality this is not the case.

Transcription

1 v It appears that under their own units the gravity gradient is a million times worse than the gravity. v In reality this is not the case. v In particular, the opposite is true in terms of dealing with the nuisance of elevation corrections.

2 h R E = x 10 6 meter, The average radius of the Earth g = μgal g z h R? = B E h R?

3 h R E = x 10 6 meter, The average radius of the Earth g = μgal g z h R? = B E h R? The gradient has ~ Million times smaller elevation corrections than the gravity (under their own units)

4 Contents 1. Static mass anomaly with gravity gradient (a brief review) 2. Deformation related gravity gradients (Preliminary modeling) Ø Traditional gas deposit and production Ø Hydraulic cracking for shale gas

5 Gravity gradient tensor " $ $ $ G = $ $ $ $ # g 1 x 1 g 1 x 2 g 1 x 3 g 2 x 1 g 2 x 2 g 2 x 3 g 3 x 1 g 3 x 2 g 3 x 3 % ' ' ' ' ' ' ' & Symmetric G i, j = 2 Φ x i x j Zero trace 3 3 G = 2 Φ i,i 2 x i=1 i=1 i = 0

6 Gradient is sensitive to shallow and sharp structures g(x) ~ sinωx, G z,x = ω cosωx Gradient Gravity G z,z ( 0) = 1 z 3 g( 0) ~ 1 z 2 x Depth of penetration Potential Φ( 0) ~ 1 z z

7 A big nuisance for airborne gravity is the height correction for repeated flyby h 0.3 m for 0.1mgal Hajkova et al, 2010

8 For airborne gravity gradient the accuracy of aircraft height is much less important h 350 m for 0.5E

9 Probe the static structure: the double rings of Vredefort Crater, South Africa, with Gravity Gradient

10 Artistic Reconstruction of the Crater from geological evidence

11 Investigating area by airborne gradiometer Beiki at al. (2010)

12 g z z Beiki at al. (2010)

13 Probe natural gas production

14 Traditional natural gas production Gravity can be used to monitor the underground mass changes. We will show that the gravity signal is mostly dominated by the land subsidence /uplift, while the gravity gradient is land- subsidence/uplift proof.

15 Self-gravitating elastic half space model set up u h Displacement φ Perturbed gravitational potential e z e r Free surface Half- space 2 u h σ u h ρ 0 µ φ + ρ 0g ( µ e z u h e z u h ) = 0 2 φ = 4πGρ 0 u h lim R z + ( u h,φ) 0

16 Poroelastic ball embedded in a selfgravitating half space p Incremental pressure variation β Poroelastic expansion coefficient e z e r Free surface pβ Decoupled pore mechanics λ H u + μ H u + u 3λ + 2μ β p = 0

17 Gravity and gravitational gradient from selfgravitation on the free surface φ = φ x, φ y, φ z φ = P φ x P P φ x y P φ x z P φ x y P φ y P P φ y z P φ x z P φ y z P φ z P

18 Perturbed gravity Pore expansion coefficient B z 100 m " 1 β p 1+σ % Normalized to ' 1 σ & 0.5 p $ # µgal Contribution from surface uplifting A = 0.18 μ = Pa = kg/m 3 b = 1 (100 m) h = 1.2 b Deformed surface of the poroelastic reservoir

19 Perturbed gravity gradient g z z B Density perturbation Normalized to x100m δρ ρ Contribution from surface uplifting 10 3 E Pore expansion coefficient Normalized to " β p 1+σ % $ ' # 1 σ & Red: Density change Green: Self gravitation x100m A σ = 0.18 μ = Pa ρ = kg/m 3 b = 1 (100 m) h = 1.2 θ b Deformed surface of the Poroelastic reservoir

20 Hydraulic fracturing for shale gas

21 Perturbed gravity gradient from density (red) selfgravitation (blue) and surface uplift (black) g z z km Normalized to δρ ρ Eotovs " β p 1+σ % Normalized to $ ' # 1 σ & km 3200 m 2900 m Sources s = 0.25 μ = Pa ρ = kg/m 3 b = 100 m

22 Conclusions The gravity gradient can effectively denuisance the ground subsidence/uplift effect in deformation- related time- varying gravity variations.