Cooperative Magnetic Inversion. Dom Fournier, PhD. Student * Kristofer Davis, Research Associate Doug W Oldenburg, Professor

Transcription

1 Cooperative Magnetic Inversion Dom Fournier, PhD. Student * Kristofer Davis, Research Associate Doug W Oldenburg, Professor October 17 th, 2016

2 Outline Review on magnetics Effect of remanence Review on algorithms Amplitude Inversion Magnetic Vector Inversion Cooperative strategy Ongoing research

3 Magnetic Data Magnetization H 0 MLi nrm M H s κ H 0 κ

4 simpeg.xyz Magnetic Data Magnetic Data Powered by:

5 Magnetic Inversion Inverse Problem This talk this Data misfit Regularization Next talk!! (4:10 pm)

6 Magnetic Susceptibility Inversion Induced assumption: (Li & Oldenburg 1996) M = H 0 κ

7 Induced assumption M = H 0 κ Magnetic Susceptibility Inversion Stable and robust for any inducing field orientation Several commercial (MAG3D) and open-source codes available Extensively Li used by the mineral exploration sector.

8 Magnetic Susceptibility Inversion Complication with remanence M = H 0 κ + M nrm

9 Complication with remanence Magnetic Susceptibility Inversion M = H 0 κ + M nrm Wrong assumption results in severe distortion Common for many types of mineral deposits (Kimberlite, BIF, VMS)

10 Previous Work Data processing Fourier domain (Roest et al. 1992) Helbig s method (Phillips 2003) Cross-correlation (Dannmiller & Li 2006) Simple and fast Becomes hard for multiple anomalies and requires gridding

11 Previous Work Amplitude Inversion Invert data weakly sensitive to magnetization M H 0 κ e Major work from CSM Sarah Shearer, MSc. Thesis (2005) Li et al Li & Li 2014 Li

12 Previous Work Amplitude Inversion: Li et al M H 0 κ e Sensitivity weights applied nd W r = J [i:] 2 1/2 i=1

13 Previous Work Amplitude Inversion Robust recovery of effective susceptibility Requires pre-processing for amplitude data Li

14 Previous Work Magnetic Vector Inversion, Cartesian (MVI-C) Directly for the components of magnetization t s p Li Lelievre & Oldenburg (2009) Geosoft VOXI

15 Magnetic Inversion Magnetization Vector Inversion, Cartesian (MVI-C) φ m = φ p + φ s + φ t = p p ref 2 + p 2 + s s ref 2 + s 2 + t t ref 2 + t 2

16 Previous Work Magnetic Vector Inversion, Cartesian (MVI-C) t s p Recovers both amplitude and orientation Largely underdetermined, relies heavily on regularization Models too smooth for easy interpretation Clustering methods (FMC) (Li & Sun 2016) Li

17 Parallel research Compact Norms (Next 4:10 pm) M = H 0 κ

18 Parallel research Limitations with current formulation Sparsity imposed on individual components favoring magnetization along single component: p s t Difficult to incorporate borehole constraints (koenigsberger ratio) Li

19 Cooperative Strategy Cooperative Magnetic Inversion (CMI) Fournier, MSc Liu et al Susceptibility Inversion Equivalent Source 2 Amplitude Inversion Effective Susceptibility 3 MVI

20 Cooperative Strategy Cooperative Magnetic Inversion (CMI) Weighted regularization φ m = W m W s (m m ref ) i=x,y,z W m W i G i m 2 2 Model weight 1 κ e W m = max(κ e ) + ε

21 Cooperative Strategy Cooperative Magnetic Inversion (CMI) Able to apply sparsity Recover both the amplitude and direction 1 Susceptibility Inversion Equivalent Source Minimum of 3 inversions required Dependents on the ability of extracting amplitude data Can t apply sparsity on the orientation Li 2 3 Amplitude Inversion MVI Effective Susceptibility

22 Ongoing research Magnetic Vector Inversion, Spherical (MVI-S) Separate the amplitude and direction z a y θ φ x x = a cos φ cos θ y = a cos φ sin θ z Ƹ = a sin φ Li Lelievre s PhD. (2009) Put aside due to high non-linearity

23 Ongoing research Magnetic Vector Inversion, Spherical (MVI-S) Natural separate the amplitude and direction a y θ φ x x = a cos φ cos θ y = a cos φ sin θ z Ƹ = a sin φ Solved issues regarding the non-linearity Sensitivity: φ m = φ a + φ t + φ p = a a ref 2 + a 2 + t t ref 2 + t 2 + p p ref 2 + p 2 Li S = J = d = SG m cos φ cos θ a sin φ cos θ a cos φ sin θ cos φ sin θ a sin φ sin θ a cos φ cos θ sin φ cos φ 0

24 Ongoing research Magnetic Vector Inversion, Spherical (MVI-S) Apply Koenigsberger ratio constraints φ m = a a ref 2 + a 2 + t 2 + p 2 Li

25 Ongoing research Magnetic Vector Inversion, Spherical (MVI-S) Sparsity on amplitude φ m = a a ref p + a p + t 2 + p 2 Li

26 Ongoing research Magnetic Vector Inversion, Spherical (MVI-S) Sparsity on angles φ m = a a ref p + a p + t p + p p Li

27 Case History Osborne Cu-Au deposit, Queensland Airborne mag discovery in 1974 (Newmont Pty Ltd) Magnetite-rich Ironstones layers within metasediments of Mt Isa quartzite. Li

28 Case History Strong self-demagnetization effects as studied by Logan & Anderson (1992) Li

29 Case History Conventional Inversions Induced Assumption MVI-C Li

30 Case History Conventional Inversions Amplitude Inversion CMI Li

31 Summary Managed to reduce the non-uniqueness of usual MVI-Cartesian formulation Allow to apply sparse norms Promising results with MVI-Spherical formulation Requires more work to improve performance Li

32 Thank you!