Anisotropy of Magnetic Remanence: Empirical Guidelines Towards an Efficient Acquisition Protocol

Martin Chadima

AGICO Inc., Brno, Czech Republic ([email protected]) Institute of Geology of the Czech Academy of Sciences, Prague, Czech Republic Agenda 2

1. Theoretical background for AMR

2. Instruments and data acquisition techniques

3. Empirical guidelines demonstrated on test samples Theoretical background 3

Introduction

• Rocks and sediments display a magnetic anisotropy when constituent mineral grains have a preferred orientation. • Magnetic fabric is usually described by the anisotropy of magnetic susceptibility (AMS). As all minerals in a rock or sediment (diamagnetic, paramagnetic, ferromagnetic /sensu lato/) contribute to the susceptibility; the observed anisotropy is the sum of the individual mineral components, their specific susceptibility anisotropy and their preferred alignment. • The anisotropy of magnetic remanence (AMR) is only dependent on the ferromagnetic grains (s.l.) in a rock. Since the number of different ferromagnetic phases is more limited, the source of the AMR is easier to distinguish, and the degree of anisotropy is less sensitive to mineral variation.

Theoretical background 4

Application

• Tool to study rock texture (Petrofabric) • Compared to the other methods of fabric analysis (U-stage, X-ray texture goniometry, neutron texture goniometry, EBSD), AMS is fast, cheap, high- resolution, non-destructive. • It can be applied to many samples covering whole outcrops, drill cores, or geological units. • Application in structural geology and tectonics, volcanology, sedimentology, and paleomagnetism. Theoretical background 5

Hysteresis loop

M = Mi + Mr Mi = k  H Magnetic susceptibility Induced magnetization Remanent magnetization

Mr = kr  H Remanent susceptiblity Theoretical background 6

Susceptibility vs. Remanence Diamagnetism Paramagnetism Ferromagnetism (s.l.) M M M

k < 0 k > 0 k >> 0

Induced magnetization antiparallel to the Induced magnetization parallel to the Complex relationship between external external field external field field and induced magnetization: hysteresis curve Magnetic susceptibility relatively low and Magnetic susceptibility relatively low and Magnetic susceptibiliy relatively high negative positive No remanence No remanence Remanent magnetization

quartz pyroxene iron calcite hornblende (titano-) magnetite aragonite olivine pyrrhotite micas hematite Theoretical background 7

Tensor notation of AMR (or AMS)

Magnetically isotropic material

Mr1 = kr H1 Mr2 = kr H2 Mr3 = kr H3

Magnetization of anisotropic materials

Mr1 = kr11 H1 + kr12 H2 + kr13 H3 Mr2 = kr21 H1 + kr22 H2 + kr23 H3 Mr3 = kr31 H1 + kr32 H2 + kr33 H3

Mat rix notation

Mr1 kr11 kr12 kr13 H1 Mr2 = kr21 kr22 kr23 H2 Mr3 kr31 kr32 kr33 H3

Vector of Remanebility tensor Vector of field intensity magnetization Theoretical background 8

Concept of magnetic fabric X

Principal remanebilities

k1  k2  k3 Mean remanebility Shape parameter

km = (k1 + k2 + k3) / 3 T = (2h2 - h1 - h3) / (h1 - h3) where h = ln k , h = ln k , h = ln k Degree of anisotropy 1 1 2 2 3 3

+1 > T > 0 oblate (planar) fabric P = k1 / k3 -1 < T < 0 prolate (linear) fabric Theoretical background 9

Shapes of fabric ellipsoids

Triaxial prolate Rotational prolate

Neutral

Triaxial oblate Rotational oblate Theoretical background 10

Flinn diagram (L-F plot) Theoretical background 11

Jelinek diagram (Pj-T plot) Theoretical background 12

Acquisition of isothermal remanence

Butler 1992 Theoretical background 13

Types of anisotropy of magnetic remanence (AMR)

• Anisotropy of Anhysteretic Remanent Magnetization (AARM) Anisotropy of partial ARM (ApARM)

• Anisotropy of Isothermal Remanent Magnetization (AIRM) low field IRM high field IRM or saturation IRM (SIRM)

• Anisotropy of Thermal Remanent Magnetization (ATRM) Anisotropy of partial TRM (ApTRM) Theoretical background 14

Acquisition of ARM (pARM) and IRM Theoretical background 15

Application of AMR

• Preferential orientation of ferromagnetic (remanence-carrying) minerals • Coaxial and non-coaxial fabrics • Timing of mineral formation • Change is strain field • Deflection of paleomagnetic vectors • Paleointensity • Paleopole – plate reconstruction

Gilder, S.A., K. He, M. Wack, and J. Ježek (2019), Relative paleointensity estimates from magnetic anisotropy: Proof of concept, Earth and Planetary Science Letters, 519, 83-91 Theoretical background 16

Pros & Cons (advantages & disadvantages)

• AARM: easy to apply and remove, but limited in coercivity range • AIRM: useful for high coercivity minerals, but question about repeatability of acquired magnetization. • ATRM: useful for low and high coercivity minerals, but rocks cannot produce new ferromagnetic phases with heating.

Instruments and Techniques 17

Directional schemes for AMR acquisition Instruments and Techniques 18 SushiBar Munich Instruments and Techniques 19 AGICO LDA5/PAM1 Magnetizer & JR-6(A) Magnetometer

• Both instruments controlled from one computer • Timer starts when magnetization pulse terminates • Repeated measurement of viscous decay of IRM Instruments and Techniques 20

Rema6 LDA5 Instrument control SW for JR-6(A) Instrument control SW for LDA5 Instruments and Techniques 21

1. 2.

3. 4. Instruments and Techniques 22

Even a small baby can handle anisotropy of magnetic remanence (with AGICO instruments)! Samples 23

Name Rock type Location Ferromagnetic Magnetic carrier (?) susceptibility AS32 Limestone Italy Magnetite ca. 10 E-6

CS34 Camptonite Czech Republic Titanomagnetite ca. 150 E-3 (volcanic rock) JH10 Shale Czech Republic Pyrrhotite ca. 800 E-6

VIK01 Mudstone Svalbard Magnetite ca. 300 E-6 Samples 24

Name Rock type

AS32 Limestone

CS34 Camptonite (volcanic rock) JH10 Shale

VIK01 Mudstone Example 1: AS32 – Limestone at the Assergi Fault 25 AS32 – Rock characteristics 26

Ultracataclastic talus breccia. The fault rock is polymict and has the strongest susceptibility in this dataset. Nevertheless the magnetic fabric is not stronger or better constrained than in the other sites. K3 axes plot perfectly in the fault plane pole, whereas K1 and K2 are nearly undefined. Weak positive susceptibility.

Courtesy of Hannah Pomella, Insbruck, Austria AS32 – AMS vs. AAMR 27

AMS AAMR 0 0 Geographic Equal-Area Geographic Equal-Area Coordinate Projection Coordinate Projection System N = 10 System N = 7

270 90 270 90

Max F Max D Int Int Min 180 Min 180

1.0 14.0 1.0

13.0

12.0

0.5 0.5

11.0 06 SI] 06

- 10.0

T T 0.0 0.0 9.0

8.0 -0.5 [E Kmean -0.5 7.0

6.0

-1.0 5.0 -1.0 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.00 1.05 1.10 1.15 1.20 1.25 1.30 P P AS32 – Magnetic characteristics 28 AS32 – Directional Acquisition of ARM 29 Weak magnetization HAC = 20 - 40 mT, HDC = 0.5 mT Weak anisotropy

Magnetizing directions Residuals A mode AARM tensors B mode 0 0 C mode 0 D mode P mode

270 90 270 90 270 90

Max Down Down Int Up Up Min 180 180 180 1.0 M [E-06 A/m] 50.0 45.0 0.5 40.0 35.0

30.0

25.0 T 0.0 20.0 15.0 10.0 -0.5 5.0 0.0 0 5 10 15 20 25 30 # -1.0 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 P Example 2: CS34 – Site location 30 CS34 – Site view 31 CS34 – AMS vs. AAMR 32

AMS AAMR 0 0 Geographic Equal-Area Geographic Equal-Area Coordinate Projection Coordinate Projection System N = 28 System N = 10

270 90 270 90

Max D Max D Int Int Min 180 Min 180

1.0 125 1.0 120 115

0.5 110 0.5

105 03 SI] 03

- 100

T T 0.0 0.0 95 90

-0.5 [E Kmean 85 -0.5 80 75 -1.0 70 -1.0 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 P P CS34 – Magnetic characteristics 33 CS34 – Directional Acquisition of ARM 34 Very strong magnetization! HAC = 0 - 40 mT, HDC = 0.5 mT Weak anisotropy

Magnetizing directions Residuals A mode AARM tensors B mode 0 0 C mode 0 D mode P mode

270 90 270 90 270 90

Down Down Max Up Up Int Min 180 180 180

1.0

M/Mmax Mmax = 25.62E+00 A/m M [E-03 A/m] 1.0 350.0 0.5 0.9 300.0 0.8

0.7 250.0

T 0.0 0.6 200.0 0.5 0.4 150.0 -0.5 0.3 100.0 0.2 50.0 0.1 0.0 0.0 -1.0 0 2 4 6 8 10 12 14 16 18 20 0 5 10 15 20 25 # 1.00 1.02 1.04 1.06 1.08 1.10 1.12 P Example 3: JH10 – Location 35 JH10 – Site characteristics 36

Courtesy of Jaroslava Hajna, Prague JH10 – Magnetic susceptibility 37 JH10 – AMS vs. AAMR 38

AMS AAMR 0 0 Geographic Equal-Area Geographic Equal-Area Coordinate Projection Coordinate Projection System N = 14 System N = 9

270 90 270 90

Max C Max D Int Int Min 180 Min 180

1.0 900 1.0

800

0.5 0.5

700 06 SI] 06

- 600

T T 0.0 0.0 500

Kmean [E Kmean 400 -0.5 -0.5 300

-1.0 200 -1.0 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 P P JH10 – Magnetic characteristics 39 JH10 – Directional Acquisition of ARM 40 Strong magnetization HAC = 10 - 40 mT, HDC = 0.5 mT Very strong anisotropy!

Magnetizing directions Residuals A mode AARM tensors B mode 0 0 C mode 0 D mode P mode

270 90 270 90 270 90

Max Down Down Int Up Up Min 180 180 180

1.0

M [E-03 A/m] 30.0 0.5

25.0

20.0

T 0.0

15.0

10.0 -0.5

5.0

0.0 -1.0 0 2 4 6 8 10 12 14 16 18 20 # 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 P JH10 – AARM in various bias DC field 41

0 Geographic Equal-Area Coordinate Projection System N = 6

270 90 550 500 450 400 350 300 250 200

Field [A/m] Field 150 Max D 100 Int 50 0 Min 180

1.0 550 500 450 0.5 400 350

300

T 0.0 250

Field [A/m] Field 200 -0.5 150 100 50 -1.0 0 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 P JH10 – AIRM in various DC field 42

0 Geographic Equal-Area Coordinate Projection System N = 6

270 90 25000

20000

15000

10000 Field [A/m] Field Max D 5000 Int 0 Min 180

1.0 25000

20000

0.5

15000

T 0.0

10000 Field [A/m] Field

-0.5 5000

-1.0 0 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 P Example 4: VIK01 – Location 43 VIK01 – Site view 44

Courtesy of Katarzina Dudzisz, Warsaw, Poland VIK01 – AMS vs. AAMR 45

AMS AAMR 0 0 Geographic Equal-Area Geographic Equal-Area Coordinate Projection Coordinate Projection System N = 42 System N = 18

270 90 270 90

Max B Max B Int Int Min 180 Min 180

1.0 310 1.0

300

0.5 0.5

290 06 SI] 06

- 280

T T 0.0 0.0 270

Kmean [E Kmean 260 -0.5 -0.5 250

-1.0 240 -1.0 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 P P VIK01 – Inverse fabric carried by siderite 46 VIK01 – Magnetic characteristics 47 VIK01 – Directional Acquisition of ARM 48 Moderate magnetization HAC = 10 - 40 mT, HDC = 0.05 & 0.5 mT Weak anisotropy

Magnetizing directions Residuals A mode AARM tensors B mode 0 0 C mode 0 D mode P mode

270 90 270 90 270 90

Down Max Down Int Up Up Min 180 180 180 1.0 HAC = 10 - 40 mT, HDC = 0.5 mT M/Mmax Mmax = 47.28E-03 A/m M [E-06 A/m] 1.0 180.0 0.5 0.9 160.0 0.8 140.0 0.7

120.0

T 0.0 0.6 100.0 0.5 80.0 0.4 0.3 60.0 -0.5 0.2 40.0 0.1 20.0 0.0 0.0 -1.0 0 2 4 6 8 10 12 14 16 18 20 0 10 20 30 40 50 60 70 80 # 1.00 1.02 1.04 1.06 1.08 1.10 1.12 P VIK01 – Directional Acquisition of ARM 49 Strong residual artifact! HAC = 10 - 40 mT, HDC = 0.5 mT

Magnetizing directions Residuals A mode AARM tensors B mode 0 0 C mode 0 D mode P mode

270 90 270 90 270 90

Max Down Down Int Up Up Min 180 180 180 1.0 M/Mmax Mmax = 80.87E-03 A/m M [E-03 A/m] 1.0 40.0

0.9 35.0 0.5 0.8 30.0 0.7

0.6 25.0

T 0.0 0.5 20.0

0.4 15.0 0.3 10.0 0.2 -0.5 0.1 5.0 0.0 0.0 0 5 10 15 20 25 30 35 40 45 50 55 0 2 4 6 8 10 12 14 16 18 20 # -1.0 1.0 1.5 2.0 2.5 3.0 3.5 P VIK01 – AARM in various coercivity windows 50

0 Geographic Equal-Area Coordinate Projection System N = 5

270 90

Max D Min 180

1.0

0.5

T 0.0

-0.5

-1.0 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 P VIK01 – AARM in various bias DC fields 51

0 Geographic Equal-Area Coordinate Projection System N = 6

270 90 550 500 450 400 350 300 250 200

Field [A/m] Field 150 Max 100 Min 50 0 180

1.0 550 500 450 0.5 400 350

300

T 0.0 250

Field [A/m] Field 200 -0.5 150 100 50 -1.0 0 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 P VIK0103 – AIRM in various DC fields 52

0 Geographic Equal-Area Coordinate Projection System N = 6

270 90 25000

] 20000 uT 15000

10000 DC Field [ Field DC Max D 5000 Min 0 180

1.0 25000

20000

0.5

15000

T 0.0

10000 Field [A/m] Field

-0.5 5000

-1.0 0 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 P Some empirical guidelines 53

1. Acquire a coercivity spectrum of some representative sample(s) to decide which coercivity window is of interest (controlled by AC field). 2. DC bias field controls how much a particular coercivity sub-population is magnetized. Test whether acquired ARM is linear as a function of DC field and try to set the highest DC field which still falls within a linear range. Note that by selecting higher DC field, one may reach up to two orders of magnitude difference between the magnetized and demagnetized states. 3. Test whether acquired ARM is stable in time (effect of viscous decay), if not, each directional ARM should be measured in the same time after ARM has been acquired or long time after that to allow the viscous magnetization to relax. 4. Try to reach the optimum balance between precision and speed (number of magnetizing directions). The precise fitting of AARM tensor strongly depends on the residual magnetization. Prior to any directional ARM acquisition, demagnetize a sample using the highest AC field possible. If the strength of the residual magnetization is in the same order of magnitude as that of magnetized states, one is strongly advised to use magnetizing design employing pairs of antipodal magnetizing directions (A- or C- modes) where the constant residue is compensated. 5. If the residual magnetization is comparable or higher than that of magnetized states, AAMR tensor fitting may be very imprecise even when the antipodal magnetizing directions are used. Literature 54

Tarling, D.H. & Hrouda, F. 1993. The Magnetic Anisotropy of Rock. Chapman & Hall, 217 pp. Lanza, R. & Meloni, A. 2006. The Earth’s Magnetism: An Introduction for Geologist. Springer, 278 pp. (Chapter 5). Jackson, M., 1991. Anisotropy of magnetic remanence: a brief review of mineralogical sources, physical origins, and geological applications, and comparison with susceptibility anisotropy. Pure and Applied Geophysics, 136: 1–28. Hirt, A. 2007. Magnetic Remanence, Anisotropy. Encyclopedia of Geomagnetism and Paleomagnetism. Springer. 535-540. Jackson, M. 2007. Magnetization, Isothermal Remanent. Encyclopedia of Geomagnetism and Paleomagnetism. Springer. 589-594. Moskowitz, B. 2007. Magnetization, Anhysteretic Remanent. Encyclopedia of Geomagnetism and Paleomagnetism. Springer. 572-580. Gilder, S.A., K. He, M. Wack, and J. Ježek (2019), Relative paleointensity estimates from magnetic anisotropy: Proof of concept, Earth and Planetary Science Letters, 519, 83-91.

Cautionary note!!! 55 Thanks for your attention!