Conductivity Distribution of the Earth Derived from Long Period Magnetic Data

Transcription

1 Conductivity Distribution of the Earth Derived from Long Period Magnetic Data Nils Olsen Neustadt/Weinstrasse, 27 th June 2009 Nils Olsen (DTU Space) Long Period Transfer Functions 1 / 25

2 Long Period Transfer Functions Derived from Magnetic Data Nils Olsen Neustadt/Weinstrasse, 27 th June 2009 Nils Olsen (DTU Space) Long Period Transfer Functions 1 / 25

3 Outline of Talk 1 Transfer functions 2 Source Fields 3 Transfer functions determinations before Transfer functions determinations Latest attempts and new concepts Nils Olsen (DTU Space) Long Period Transfer Functions 2 / 25

4 Outline of Talk Transfer functions 1 Transfer functions 2 Source Fields 3 Transfer functions determinations before Transfer functions determinations Latest attempts and new concepts Nils Olsen (DTU Space) Long Period Transfer Functions 3 / 25

5 Transfer functions Response functions for induction studies Spherical Harmonic domain Q n (ω) = ιm n (ω) ɛ m n (ω) Spatial domain C(ω) = B z (ω) H B H (ω) ɛ m n and ι m n are spherical harmonic expansion coefficients of external (inducing), resp. internal (induced), sources Nils Olsen (DTU Space) Long Period Transfer Functions 4 / 25

6 Transfer functions Response functions for induction studies Spherical Harmonic domain Q n (ω) = ιm n (ω) ɛ m n (ω) Spatial domain C(ω) = B z (ω) H B H (ω) Q n = n n n+1 a C n 1 + n a C n Earth s radius r = a C n = ɛ m n and ι m n are spherical harmonic expansion coefficients of external (inducing), resp. internal (induced), sources a n + 1 These responses are only valid for 1D Earth, H σ σ/ C 1 n+1 n Q n 1 + Q n Nils Olsen (DTU Space) Long Period Transfer Functions 4 / 25

7 Transfer functions Global vs. regional sounding Spherical Harmonic Domain (global) sounding: Spherical Harmonic analysis of B x, B y, B z yields ɛ m n (ω), ι m n (ω) Q n (ω) = ιm n (ω) ɛ m n (ω) Spatial domain (regional) sounding: C(ω) = B z (ω) H B H (ω) Nils Olsen (DTU Space) Long Period Transfer Functions 5 / 25

8 Transfer functions Global vs. regional sounding Spherical Harmonic Domain (global) sounding: Spherical Harmonic analysis of B x, B y, B z yields ɛ m n (ω), ι m n (ω) Q n (ω) = ιm n (ω) ɛ m n (ω) Both horizontal and vertical components are used globally Spatial domain (regional) sounding: C(ω) = B z (ω) H B H (ω) Vertical component is used locally, horizontal components are used regionally Nils Olsen (DTU Space) Long Period Transfer Functions 5 / 25

9 Transfer functions Two methods for determining H B H (ω) Z/H: Assumption about source structure, e.g. P1 0 for RC or Pm m+1 for mth daily harmonic (Sq) Gradient sounding: Estimation of source structure from observed B H = (B x, B y ) (regional) polynomial fit yields G = H B H Z : Y (global) spherical harmonic fit yields v m n Y = H B H = n,m = ɛ m n + ι m n n(n + 1)v m n P m n e imφ Nils Olsen (DTU Space) Long Period Transfer Functions 6 / 25

10 Transfer functions Two methods for determining H B H (ω) Z/H: Assumption about source structure, e.g. P1 0 for RC or Pm m+1 for mth daily harmonic (Sq) allows determination of response from data of a single site Gradient sounding: Estimation of source structure from observed B H = (B x, B y ) (regional) polynomial fit yields G = H B H Z : Y (global) spherical harmonic fit yields v m n Y = H B H = n,m = ɛ m n + ι m n n(n + 1)v m n P m n e imφ Vertical component is used locally, horizontal components are used regionally Nils Olsen (DTU Space) Long Period Transfer Functions 6 / 25

11 The C-Response Transfer functions Nils Olsen (DTU Space) Long Period Transfer Functions 7 / 25

12 The C-Response Transfer functions Nils Olsen (DTU Space) Long Period Transfer Functions 7 / 25

13 The C-Response Transfer functions Nils Olsen (DTU Space) Long Period Transfer Functions 7 / 25

14 The C-Response Transfer functions Nils Olsen (DTU Space) Long Period Transfer Functions 7 / 25

15 The C-Response Transfer functions Nils Olsen (DTU Space) Long Period Transfer Functions 7 / 25

16 Outline of Talk Source Fields 1 Transfer functions 2 Source Fields 3 Transfer functions determinations before Transfer functions determinations Latest attempts and new concepts Nils Olsen (DTU Space) Long Period Transfer Functions 8 / 25

17 Source Fields RC, the magnetospheric ring-current Source structure is mainly given by P 0 1 = cos θ d (θ d is dipole co-latitude) Period range between a few hours and 100 days Depth range 300 km to 1500 km Can be used for induction studies with satellite data (source is external to observation point!) Nils Olsen (DTU Space) Long Period Transfer Functions 9 / 25

18 Source Fields Sq, the ionospheric regular daily variation Source structure of mth daily harmonic (m = 1, ) dominated by P m m+1 eimt with local time T Period range between 4 hrs (for m = 6 ) and 24 hours (m = 1) Depth range 300 to 600 km Nils Olsen (DTU Space) Long Period Transfer Functions 10 / 25

19 Outline of Talk Transfer functions determinations before Transfer functions 2 Source Fields 3 Transfer functions determinations before Transfer functions determinations Latest attempts and new concepts Nils Olsen (DTU Space) Long Period Transfer Functions 11 / 25

20 Transfer functions determinations before 1985 Transfer functions determinations before 1985 Important publications by Ulrich Schmucker: Erdmagnetische Variationen und die elektrische Leitfähigkeit in tieferen Schichten der Erde, Sitzungsbericht und Mitteilungen Braunschweigische Wiss. Gesellschaft, Sonderheft, Band 4, p , 1979 Magnetic and electric fields due to electromagnetic induction by external sources, Landolt-Börnstein, Springer Verlag, 1985 Development of Z : Y method (spherical version of gradient method) Application of the various methods to observatory hourly mean values Nils Olsen (DTU Space) Long Period Transfer Functions 12 / 25

21 Transfer functions determinations before 1985 Ulrich Schmucker s Responses as of Z/H, Sq Z:Y, Sq Z/H, Sq Z:Y, RC 12 hours 1 day 1 week 1 month 3 months 1000 [km] 500 Re{C} 0 Im{C} period [secs] Nils Olsen (DTU Space) Long Period Transfer Functions 13 / 25

22 Transfer functions determinations before 1985 Ulrich Schmucker s Responses as of 1985 ρ (ω) = 2µ 0 ω Im{C(ω)} 2 z (ω) = Re{C(ω)} after U. Schmucker, Landolt-Börnstein, Z/H, Sq Z:Y, Sq Z/H, Sq Z:Y, RC 500 ρ * [Ωm] z * [km] Nils Olsen (DTU Space) Long Period Transfer Functions 13 / 25

23 Outline of Talk Transfer functions determinations Transfer functions 2 Source Fields 3 Transfer functions determinations before Transfer functions determinations Latest attempts and new concepts Nils Olsen (DTU Space) Long Period Transfer Functions 14 / 25

24 Transfer functions determinations Transfer functions determinations Data mining: recovery of old data sets Hourly mean values of IGY/C ( Chapman-Gupta collection ) Throughout quality check of data from observatories from (IGY/C), (IQSY), and (IMS) These hourly mean values became basis for digital data collection at WDC-C (Copenhagen, now Edinburgh) Nils Olsen (DTU Space) Long Period Transfer Functions 15 / 25

25 Transfer functions determinations Transfer functions determinations Data mining: recovery of old data sets Hourly mean values of IGY/C ( Chapman-Gupta collection ) Throughout quality check of data from observatories from (IGY/C), (IQSY), and (IMS) These hourly mean values became basis for digital data collection at WDC-C (Copenhagen, now Edinburgh) Accounting for day-to-day variability when estimating transfer functions Sq analysis using potential and Z : Y method (Schmucker 1999) Sq and RC analysis using Z : Y-method (Olsen 1992, 1998, 1999) Nils Olsen (DTU Space) Long Period Transfer Functions 15 / 25

26 Transfer functions determinations Responses as of hours 1 day 1 week 1 month 3 months coh Potential method, Sq (Schmucker 1999) Z:Y, Sq (Schmucker 1999) Z:Y, Sq+RC (Olsen 1999) [km] 500 Re{C} 0 Im{C} period [secs] Nils Olsen (DTU Space) Long Period Transfer Functions 16 / 25

27 Transfer functions determinations Responses as of 1999 ρ * [Ωm] Potential method, Sq (Schmucker 1999) Z:Y, Sq (Schmucker 1999) Z:Y, Sq+RC (Olsen 1999) 500 ρ (ω) = 2µ 0 ω Im{C(ω)} 2 z (ω) = Re{C(ω)} z * [km] Nils Olsen (DTU Space) Long Period Transfer Functions 16 / 25

28 Outline of Talk Latest attempts and new concepts 1 Transfer functions 2 Source Fields 3 Transfer functions determinations before Transfer functions determinations Latest attempts and new concepts Nils Olsen (DTU Space) Long Period Transfer Functions 17 / 25

29 Latest attempts and new concepts Two incompatible approaches Z/H method, assumption about source structure (here: P 0 1 = cos θ) B z (ω) = +C(ω) G(ω) = C(ω) a tan θ B x (ω) 2 with G = H B H = a tan θ 2 B x Assumption: 1D Earth (no lateral variation of conductivity) Induction arrows, to detect lateral conductivity variations B z (ω) = T x (ω) B x (ω) + T y (ω) B y (ω) Assumption: homogeneous source ( k, n 0) Nils Olsen (DTU Space) Long Period Transfer Functions 18 / 25

30 Latest attempts and new concepts Two incompatible approaches Z/H method, assumption about source structure (here: P 0 1 = cos θ) B z (ω) = +C(ω) G(ω) = C(ω) a tan θ B x (ω) 2 with G = H B H = a tan θ 2 B x Assumption: 1D Earth (no lateral variation of conductivity) Induction arrows, to detect lateral conductivity variations B z (ω) = T x (ω) B x (ω) + T y (ω) B y (ω) Assumption: homogeneous source ( k, n 0) In both approaches B z B x Interpretation depends on chosen assumptions Nils Olsen (DTU Space) Long Period Transfer Functions 18 / 25

31 Latest attempts and new concepts How to make them compatible... Observed vertical magnetic field B z = B nz + B az consists of normal part B nz and anomalous part B az B nz = C G, G = H B nh B az = T x B nx + T y B ny B z = B nz + B az = C G + T x B nx + T y B ny U. Schmucker, Ein Kontinent erwacht, EMTF 2005 Nils Olsen (DTU Space) Long Period Transfer Functions 19 / 25

32 Latest attempts and new concepts Generalized Gradient Sounding 1/3 U. Schmucker: Electromagnetic induction studies with long-periodic geomagnetic variations in Europe 1. Methods, unpublished manuscript, 2004 Lateral variation of conductivity: E H = ZB nh [ E] z = iωb z B z = C xx B nx y + C xx y B nx +... with C-response tensor C = iωz Eight terms on right side Nils Olsen (DTU Space) Long Period Transfer Functions 20 / 25

33 Latest attempts and new concepts Generalized Gradient Sounding 2/3 Using B = 0 and rearranging reduces this to five terms: ( Bnx B z = C 1 x + B ) ( ny Bny + C 2 B ) nx B nx + C 3 y y x y with C 1 = C xy C yx 2 C 2 = C xy + C yx 2 C 3 = C xx C yy 2 T x = C xx y T y = C xy y C yx x C yy x + T xb nx + T y B ny Nils Olsen (DTU Space) Long Period Transfer Functions 21 / 25

34 Latest attempts and new concepts Generalized Gradient Sounding 2/3 Using B = 0 and rearranging reduces this to five terms: ( Bnx B z = C 1 x + B ) ( ny Bny + C 2 B ) nx B nx + C 3 y y x y with C 1 = C xy C yx 2 C 2 = C xy + C yx 2 C 3 = C xx C yy 2 T x = C xx y T y = C xy y C yx x C yy x 5 transfer functions, collected in C and T + T xb nx + T y B ny Nils Olsen (DTU Space) Long Period Transfer Functions 21 / 25

35 Latest attempts and new concepts Generalized Gradient Sounding 3/3 B z = C 0 G univariate corresponds to 1D isotropic conductivity G = G 1 = ( Bnx x ) + Bny y Nils Olsen (DTU Space) Long Period Transfer Functions 22 / 25

36 Latest attempts and new concepts Generalized Gradient Sounding 3/3 B z = C 0 G univariate corresponds to 1D isotropic conductivity B z = C 1 G 1 + C 2 G 2 + C 3 G 3 + T x B nx + T y B ny 5-variate general 3D anisotropic conductivity G = G 1 = G 2 = ( Bnx x ( Bnx x G 3 = Bnx y ) + Bny y ) Bny y Nils Olsen (DTU Space) Long Period Transfer Functions 22 / 25

37 Latest attempts and new concepts Generalized Gradient Sounding 3/3 B z = C 0 G univariate corresponds to 1D isotropic conductivity B z = C 1 G 1 + C 2 G 2 + C 3 G 3 tri-variate corresponds to 1D anisotropic conductivity B z = C 1 G 1 + C 2 G 2 + C 3 G 3 + T x B nx + T y B ny 5-variate general 3D anisotropic conductivity G = G 1 = G 2 = ( Bnx x ( Bnx x G 3 = Bnx y ) + Bny y ) Bny y Nils Olsen (DTU Space) Long Period Transfer Functions 22 / 25

38 Latest attempts and new concepts Generalized Gradient Sounding 3/3 B z = C 0 G univariate corresponds to 1D isotropic conductivity B z = C 1 G 1 + C 2 G 2 + C 3 G 3 tri-variate corresponds to 1D anisotropic conductivity B z = C 0 G + T x B nx + T y B ny tri-variate corresponds to moderate deviation from 1D conductivity B z = C 1 G 1 + C 2 G 2 + C 3 G 3 + T x B nx + T y B ny 5-variate general 3D anisotropic conductivity G = G 1 = G 2 = ( Bnx x ( Bnx x G 3 = Bnx y ) + Bny y ) Bny y Nils Olsen (DTU Space) Long Period Transfer Functions 22 / 25

39 U. Schmucker: Electromagnetic induction studies with long-periodic geomagnetic variations in Europe 1. Methods, Nilsunpublished Olsen (DTU Space) manuscript, 2004 Long Period Transfer Functions 23 / 25 Latest attempts and new concepts Application to European Hourly Mean Values Observatory Wingst (near Hamburg/Germany) C 2 show systematic non-zero values, increasing with frequency indicate anisotropy of the C-response at Wingst

40 Latest attempts and new concepts Long-period induction arrows 7.5 cpd, T = 3.3 hrs, z = 260 km U. Schmucker, Ein Kontinent erwacht, EMTF 2005 Nils Olsen (DTU Space) Long Period Transfer Functions 24 / 25

41 Latest attempts and new concepts Long-period induction arrows 6.5 cpd, T = 3.7 hrs, z = 280 km U. Schmucker, Ein Kontinent erwacht, EMTF 2005 Nils Olsen (DTU Space) Long Period Transfer Functions 24 / 25

42 Latest attempts and new concepts Long-period induction arrows 5.5 cpd, T = 4.4 hrs, z = 315 km U. Schmucker, Ein Kontinent erwacht, EMTF 2005 Nils Olsen (DTU Space) Long Period Transfer Functions 24 / 25

43 Latest attempts and new concepts Long-period induction arrows 4.5 cpd, T = 5.3 hrs, z = 360 km U. Schmucker, Ein Kontinent erwacht, EMTF 2005 Nils Olsen (DTU Space) Long Period Transfer Functions 24 / 25

44 Latest attempts and new concepts Long-period induction arrows 3.5 cpd, T = 6.9 hrs, z = 415 km U. Schmucker, Ein Kontinent erwacht, EMTF 2005 Nils Olsen (DTU Space) Long Period Transfer Functions 24 / 25

45 Latest attempts and new concepts Long-period induction arrows 2.5 cpd, T = 9.6 hrs, z = 500 km U. Schmucker, Ein Kontinent erwacht, EMTF 2005 Nils Olsen (DTU Space) Long Period Transfer Functions 24 / 25

46 Latest attempts and new concepts Long-period induction arrows 1.5 cpd, T = 16 hrs, z = 610 km U. Schmucker, Ein Kontinent erwacht, EMTF 2005 Nils Olsen (DTU Space) Long Period Transfer Functions 24 / 25

47 Latest attempts and new concepts Nils Olsen (DTU Space) Long Period Transfer Functions 25 / 25