Measurement of the 

Remanent Magnetization of 

Igneous Rocks

GEOLOGICAL SURVEY BULLETIN 1203-A

Measurement of the 

Remanent Magnetization of 

Igneous Rocks

By RICHARD R. DOELL and ALLAN COX

EXPERIMENTAL AND THEORETICAL GEOPHYSICS

GEOLOGICAL SURVEY BULLETIN 1203-A

An induction magnetometer, a portable 

drill, and a computer program

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1965
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

The U. S. Geological Survey Library has cataloged this publication as follows:

Doell, Richard Rayman, 1923-

Measurement of the remanent magnetization of igneous 

rocks, by Richard R. Doell and Allan Cox. Washington, 

U. S. Govt. Print. Off., 1965.

iv, 32 p. illus., diagrs., table. 24 cm. (U. S. Geological Survey. 

Bulletin 1208-A)

Theoretical and experimental geophysics. 

Bibliography: p. 32.

1. Rocks, Igneous. 2. Magnetism, Terrestrial. 3. Magnetometer. 

4. Electronic data processing-Magnetometer. I. Cox Allan V 

1926- joint author. II. Title. (Series)

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402 - Price 20 cents (paper cover)
CONTENTS

Abstract__ _______________________________________

Introduction _______________________________________

Acknowledgments. _________________________________

Spinner-type remanent magnetometer_________________

Instrument description._________________________

Alinement and calibration.______________________

Measurement procedure.____________________________

Precision and accuracy of measurement.______________

Specimen-pickup-coil design__________________________

Collection of samples________________________________

Use of a computer to reduce spinner-magnetometer dataCalculation procedure.. _ ________________________

References. ________________________________________

Page 

Al

1

2

2

2

8

11

18

20

22

25

27

32

ILLUSTRATIONS

showing spinner -type remanent 

______________________________

mechanical part of remanent

FIGURE 1. Schematic diagram 

magnetometer ______

2. Photograph showing

magnetom eter _ ___________________________________

3. Diagram showing mechanical details of specimen coil, 

specimen shaft, and reference-signal generator________

4. Schematic diagram showing phase shifter, attenuator, and 

mixing circuits. __________________________________

5. Photograph showing phase-shifter, attenuator, and 

mixing-circuit chassis. _-__________-______-_---____

6-7. Schematic diagrams showing 

6. Band-pass filters- _ __________________-_-_-_-_---

7. Procedure for calibration of spinner magnetometer. 

8-10. Diagrams showing 

8. Rock specimen, specimen holder, and spinner shaft 

in position for first measurement... ___-_____--_

9. Designation of magnetic components within a rock 

specimen.. . __ _ ______________________________

10. Angular relationships in the double-spin procedure..

ni

Page

A3

9

10

12

13

14
IV CONTENTS

Page 

FIGURE 11-12. Graphical calculations showing 

11. Direction of remanent magnetization within a

specimen from spinner-magnetometer data_ _ ___ A16

12. In-place direction of remanent magnetization from 

orientation data and specimen-magnetizationdirection data.-_____-_______-_-_-___-___-__ 17

13-14. Diagrams showing 

13. Relations of position of pickup coil to rotating

specimen__ _______________________________ 20

14. Curves of equal incremental signal-to-noise ratio__ 22 

15. Photograph showing sample-coring drill with water tank

and orienting devices_____--_--_--__-_--_---___--__ 23 

16-17. Diagrams showing 

16. Mechanical details of the core-drill transmission. _ 23

17. Declination gradiometer.______________________ 25

TABLE

Page 

TABLE 1. Specimen orientations for six spins._____-_-__-__--_-____-__ A14
EXPERIMENTAL AND THEORETICAL GEOPHYSICS

MEASUREMENT OF THE REMANENT MAGNETIZATION 

OF IGNEOUS ROCKS

By RICHARD R. DOELL and ALLAN Cox

ABSTRACT

The design of a simple motor-driven spinner magnetometer for measuring 

remanent magnetization in the range 1X10~S to 1.0 emu per cc (electromagnetic 

units per cubic centimeter) is presented; included are practical details of mechanical components and electronic circuits and procedures of operation and calibration. 

In routine use over a 2-year period, two of these instruments have measured 

directions of remanent magnetization of rock specimens with an estimated accuracy of 1 ° and have measured intensities with an estimated accuracy of several 

percent; they have required infrequent calibration and only minor maintenance. 

Computational techniques are given for calculating magnetic moments and directions from magnetometer-output data using either graphical procedures or 

numerical methods suitable for machine calculation. The design of a lightweight portable drill for coring samples in place and procedures for accurately 

orienting cores using a mechanical stage are also given.

INTRODUCTION

Most igneous rocks have natural remanent magnetizations in the 

range 10~4 to 10~2 emu per cc (electromagnetic units per cubic centimeter), although intensities as high as several such units may occur 

near areas where lightning bolts have struck (Cox, 1961; Graham, 

1961). For paleomagnetic research on igneous rocks, an instrument 

with a sensitivity somewhat greater than 10~4 emu per cc is generally 

needed to measure the remanent magnetization of rock specimens 

after they have been partially demagnetized. This report describes a 

spinner-type magnetometer suitable for magnetic analysis of most 

igneous rocks. It is capable of accurately measuring remanent 

magnetizations in the range 1X 10~5 to 1.0 emu per cc with an ultimate 

sensitivity of 10~6 emu per cc. Long-term stability, measurement 

accuracy, and efficiency of operation, rather than high sensitivity, 

were primary considerations in the design of this instrument, which is a 

variation of instruments previously described by Johnson and McNish 

(1938) and by Nagata (1961, p. 58-64).

Al
A2 EXPERIMENTAL AND THEORETICAL GEOPHYSICS 

ACKNOWLEDGMENTS

We wish to thank Major Lillard for construction of the spinner 

magnetometers, field core drills, and associated equipment; we are 

indebted also to Thomas Robinson and Edward Roth for assistance 

with the measurements used for analyzing the operation of the spinner 

magnetometers.

SPINNER-TYPE REMANENT MAGNETOMETER

INSTRUMENT DESCRIPTION

The general arrangement of the apparatus is depicted in figure 1. 

A nonmagnetic shaft, rotated at 109 cps (cycles per second) (6,540 

rpm) by an induction-type electric motor, is fitted with a specimen 

holder at one end and reference magnets at the other. The specimen 

and reference magnets thus induce signals of the same frequency in 

their respective pickup coils. The signal from the reference coils 

passes first through a phase shifter which shifts the output phase at 

angles from 0° to 360° with respect to the input-phase angle; the 

signal then passes through a voltage attenuator which varies the 

reference-signal amplitude over a range of 1X 10~6 to 1.0. The output 

signal from the reference attenuator is added to the signal from the 

specimen pickup coil in a mixing circuit, and the sum is amplified, 

filtered, and displayed on a cathode-ray oscilloscope.

The reference-signal phase shifter and attenuator are so calibrated 

than when the two signals entering the mixing circuit total zero, the 

direction of the specimen's magnetic moment projected normal to the 

shaft axis is read directly from the phase-shifter dial, and the intensity 

of this moment, in electromagnetic units, is read from the attenuator 

dials.

Because the signal coil, reference coils, phase shifter, attenuator, 

and mixing circuits are all passive networks, they are not subject to 

electronic drift and therefore do not need repeated calibration. 

Changes in the electronic circuits of the amplifier, filters, and cathoderay oscilloscope affect only the ease with which null signals can be 

read; they do not affect calibration.

Figure 2 is a photograph of the mechanical parts of the apparatus, 

and figure 3 shows a detailed drawing of the signal-generating part 

of the unit. The specimen, a cylinder 2.49 cm in diameter by 2.28 

cm long, is clamped in a cubical holder of clear plastic, which in turn 

fits into a square indentation at one end of the shaft (fig. 8). The 

other end of the shaft, which is constructed from laminated phenolic 

material, supports two disk-shaped permanent magnets that have 

been magnetized in opposite directions along their diameters. The 

shaft rotates in two bronze bushings mounted in a brass bearing
Belt 

6540 rpm dl"ive

x^s 345V rpm

V.

Drive 

motor

Reference 

magnets

Signal coil Phase 

shifter Attenuator

Mixing 

circuit Amplifier Band-pass filter Cathode-ray oscilloscope

FIGURE 1. Spinner-type remanent magnetometer.
A4 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

FIGURE 2. Mechanical part of remanent magnetometer.

support and is driven by a K-horsepower induction-type electric motor 

through a 2-meter-long shaft and a V-belt drive. The motor is 

sufficiently powerful to operate within 1 percent of its rated speed 

under all normal load and powerline variations and is far enough 

removed from the pickup coils not to induce unwanted signals in the 

detecting units.

The specimen pickup coil is of the balanced type, that is, the outer 

windings are in opposition to the inner windings and are so chosen 

that the net flux linkage from uniform magnetic fields through the 

two coils is zero. The rationale for the shape of the windings is 

described on page A20. On our instrument, the inner winding 

contains 1,800 turns of 26 AWG copper transformer wire, and the 

outer windings have 187 turns of 24 wire. The coil impedance at 

109 cps is 87 ohms. The entire pickup coil is covered by an electrostatic shield constructed of thin aluminum strips, so arranged as 

to form no large current loops.

Because the unknown specimen signal in a magnetometer of this 

type is determined by comparison with a known reference signal 

(Bruckshaw and Robertson, 1948), the measurement accuracy is 

strictly limited by the stability and accuracy of the reference-signal 

system. Ideally, the reference-signal phase angles should be exactly 

equal to the angular position of the dial which indicates the magnetic 

direction, and the output of the attenuator should be exactly pro-
E

FIGURE 3. Mechanical details of specimen coil, specimen shaft, and reference-signal generator (shown about one-half size). 

A, Specimen; B, specimen holder; C, shaft; D, shaft bearings; E, lubrication fittings; F, bearing support; G, drive pulley; H, 

reference magnets; /, reference-coil cores; J, reference-generator support; K, main pickup coil; L, balancing coil.

1 §
A6 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

portional to the position of the dial which indicates magnetic moment. 

The phase shifter and attenuator should also function independently, 

and it is convenient if the reference signal is large enough to measure 

strong magnetic moments directly without attenuation of the signal 

from the specimen pickup coil.

In our instrument a large three-phase reference signal is generated 

by rotating 2 disk-shaped magnets, 19 mm in diameter by 1.25 mm 

thick, near 12 stationary pickup coils. Because the magnets have 

rather large moments, they are alined in opposite directions and 

carefully astaticized to produce no detectable signal in the specimen 

pickup coil. (See p. A8.) The reference coils are placed at 60° 

intervals about the two reference magnets, and each coil contains 

1,500 turns of 44 AWG copper transformer wire wound on a soft 

iron core. Three groups of four coils, each with the same phase 

angle, are connected in series fashion, and at 109 cps each group has 

an impedance of about 280 ohms. The position of each coil can be 

adjusted radially to balance the three-phase signal during the alinement and calibration procedure.

The phase shifter, attenuator, and mixing circuits, shown schematically in figure 4, are all placed in a single cabinet (fig. 5). The 

phase shifter is a commercial electromechanical unit commonly used 

in servosystem applications. Its three stationary primary windings 

have impedances of about 300 ohms; the secondary winding, a rotating 

armature, has an impedance of 500 ohms. When the primary windings are supplied with the three-phase signal from the reference-signal 

generator, the output of the secondary armature has a constant 

amplitude and a phase angle that varies directly with its angular 

position. The armature is fitted with a dial scribed from 0° to 360°.

The attenuator consists of ganged 10-turn potentiometers K2 (500 

ohms) and K3 (300 ohms) designed to vary linearly the voltage 

appearing across K5 (550 ohms) by a factor of %o to 1. They are 

fitted with a three-digit dial. The unit labeled "decade attenuator" 

is a commercial T-type voltage attenuator (600-ohm impedance) that 

can be set for 0- to 100-db (decibel) attenuation in 20-db steps. Thus, 

voltages as small as 1X 10~6 of the full value may be obtained at the 

output of the decade attenuator and are adjustable to 1 percent of 

the output value. K4 (5K ohms) is a calibrating resistor (see p. As), 

and the switch SI allows either the specimen-coil signal or the attenuator-output signal to be observed independently. These two signals 

are mixed under normal operation in the primary of transformer Tl, 

and the secondary is connected to the voltage amplifier. Tl has a 

primary impedance of 125 ohms, a secondary impedance of 39,000 

ohms, and a turns ratio of 1:18. Resistor Rl has a value of 22 ohms.
From 1 \ 

reference

coils _ \ I

FIGURE 4. Phase shifter, attenuator, and mixing circuits.

C^ «_ From 

SI I \ specimen 

1 I - coil

§

«

§CO

o

O

wco
A8 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

FIGURE 5. Phase-shifter, attenuator, and mixing-circuit chassis.

The amplifier is a commercial unit with low input noise level and 

adjustable gain from 0 to 85 db. Its input impedance is about 1 

megohm, and the output impedance is 3,000 ohms. A schematic 

drawing of the band-pass filters, which are the electronic-feedback 

type (Gray, 1954, p. 682-685), is shown in figure 6. The ganged 

potentiometers R5-R9 and R6-R10 adjust the band-pass center 

frequency (coarse and fine adjustment, respectively), and the resistors 

R13 (fine) and Rl4 (coarse) adjust the width of the pass band and 

the Q of the filter frequency response. The cathode-ray oscilloscope 

used as a null detector is a general-purpose unit that has moderate 

input sensitivity.

ALINEMENT AND CALIBRATION

To astaticize the reference magnets with respect to the specimen 

pickup coil, the inner reference magnet is magnetized to saturation 

along a diameter and then for stability, is partially demagnetized in 

an alternating field of 300-oersted peak value. The outer magnet is 

magnetized to saturation in the opposite sense and then partially 

demagnetized in steps until no signal can be observed at the highest 

sensitivity level of the null-detector system, as described below.
REMANENT MAGNETIZATION OF IGNEOUS ROCKS A9

R1 = 330K

R2=1M

R3=R4=R16=1.8K

R5=R9=500K'

R6=R10=R13=50K

R7=R8=R17=3.9K 

R11 = R15=22K 

R12=5.6K 

R14=250K 

R18=470K

C2=C3=0.005ji

C4=40/i

V1 = V2= V3= V4=K(12AX7)

B+ = 135v regulated

FIGURE 6. Band-pass filters.

After the calibration adjustment resistor K4 has been roughly 

adjusted using either a known test magnet or the calibration circuit 

described below, the three signals from the reference coils are balanced. 

The most sensitive way of adjusting the reference coils is to observe 

the output of the phase shifter rather than to observe the intensity of 

the reference coils directly. A test magnet or rock specimen is placed 

in the specimen holder, measured, rotated within the holder exactly 

30° about the shaft axis, and remeasured; the process is repeated for 

12 measurements. The phase-dial readings and attenuator settings 

are then plotted against the test-magnet angles. Ideally the phasedial reading should be a linear function of the test-magnet angle over 

the entire range of 0° to 360°, and the attenuator settings should be 

constant; by trial and error the coils are moved radially until this 

condition is attained. We have been able to obtain phase linearity 

to about 0.1° and constant amplitude to within 1 percent. After the 

three-phase reference signal is balanced, the phase dial may then be 

so placed on the shaft of the phase shifter that it reads 0° when the 

test specimen has its moment alined with the zero reference mark 

on the specimen holder.

The next step is to adjust exactly the intensity calibration resistor 

R4. The output of the attenuator is linear for all ranges except for 

the 0-db setting of the attenuator. Thus, if a specimen or test 

magnet is available with accurately known moment (less than 1.0 

emu), the 20- to 100-db attenuation ranges of the instrument may be 

calibrated by setting the attenuator to the known moment of the
A10 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

rpm

Magnet

Signal coil

FIGUEE 7. Procedure for calibration of spinner magnetometer.

magnet and adjusting resistor R,4 to give a null on the oscilloscope. 

For the rarely used 0-db attenuation range, a calibration chart must 

be prepared.

Standard magnetic specimens may be used to prepare this calibration chart and to check the linearity of the instrument. An alternative 

calibration method which uses an alternating-current meter as a 

primary standard is shown in figure 7. The specimen pickup coil is 

replaced by an auxiliary coil, and a magnet is rotated in the specimen 

holder. The signal induced in the auxiliary coil is amplified by a 

power amplifier and supplied to a test coil through an accurate 

current meter. Our test coil consists of a single layer of 39 turns of 

24 AWG copper transformer wire wound on a cylindrical form 2.49 

cm in diameter and 2.28 cm long (the specimen size). During the 

test, its axis is alined along the specimen-pickup-coil axis, and it is 

placed at the same distance from the pickup coil that a specimen 

would have during normal operation. The test coil induces a signal 

in the specimen pickup coil equivalent to a specimen of magnetic 

moment :

M (eum)=25.53irms (amperes),

where irms is the root-mean-square current supplied to the test coil. 

Thus, signals equivalent to any desired specimen magnetic moment
REMANENT MAGNETIZATION OF IGNEOUS ROCKS All

may be induced in the pickup coil and nullified with the reference 

signal in the manner used for normal operation.

Because the filters are the feedback type, resistors R13 and R14 

(fig. 6) can be so adjusted that the units go into a self-sustained oscillation. For optimum filtering (smallest band-pass width), Rl3 and R14 

are adjusted so that the filters are just below the point where sustained 

oscillation occurs. Then when the spinner is running and a signal 

appears on the oscilloscope, the resistors R5-R9 and R6-R10 are 

adjusted to give a maximum signal on the oscilloscope. When so 

adjusted, the band-pass peak is at the operating frequency of the 

spinner. Unless the specimens being measured have magnetic moments near the minimum values measurable on these instruments, it is 

not necessary to use an extremely narrow pass band, and adjustments 

need be made only a few times each week.

During several years of operation, in which two different standard 

specimens were measured each week to test the operation and calibration of the magnetometers, it has not been necessary to change any of 

the adjustments described above or to change the adjustment of the 

calibration resistor. Although it is necessary occasionally to adjust 

the filter circuits to improve noise rejection, it should be noted that 

these adjustments do not affect the calibration.

MEASUREMENT PROCEDURE

Attenuator and phase-dial readings recorded by spinning about one 

axis of the specimen determine only the component of the magnetic 

moment normal to the axis of spinning. At least one more datum 

must therefore be obtained by spinning the specimen about a different 

axis to determine the total magnetic moment and its direction within 

the specimen. Several additional measurements are desirable to 

minimize effects of induced magnetic anisotropy and specimen inhomogeneity and to estimate the precision of a single determination of 

the remanent magnetism of a specimen.

In our system for obtaining oriented samples in the form of cores 

(described on p. A22), the specimens later cut from these samples are 

assigned right-handed orthogonal axes x, y, and z. The z axis is along 

the specimen cylinder axis, the y axis is along the specimen diameter 

that was horizontal in the in-place position, and the x axis is along the 

diameter normal to the y axis. When a specimen is placed in a specimen holder (fig. 8), each of the three axes is parallel to one of the cube 

edges of the holder. The square indentation in the spinner shaft is 

arranged so that one of the axes of the specimen is in the zero position; 

this direction is marked "I" on the shaft, and the direction 90° 

clockwise is marked "II".
A12 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

After the unit is properly calibrated and the filters adjusted, a 

single measurement can be made by the following procedure:

1. Place the specimen holder in the shaft in the desired position and 

start the shaft spinning.

2. Short out the reference signal with the switch Si and adjust the 

amplifier gain so that a convenient signal from the specimen 

appears on the cathode-ray oscilloscope.

3. Leaving the amplifier gain unchanged, move switch SI to short out 

the signal from the specimen and adjust the attenuator until a 

signal of similar size from the reference magnets appears on the 

cathode-ray oscilloscope.

4. Move switch Si to its center position and alternately adjust the 

phase dial and attenuator until no signal appears on the cathoderay oscilloscope; as the null is approached, the amplifier gain 

should be increased so that small adjustments of the phase dial 

and the attenuator away from the null settings cause easily 

recognizable signals to appear on the cathode-ray oscilloscope. 

The setting on the phase dial is the angle of the component of 

magnetization normal to the spin axis measured clockwise from 

the I mark on the shaft, and the attenuator settings record its 

magnetic moment in electromagnetic units. Nulls usually can 

be easily achieved without use of the shorting switch unless 

intensities vary greatly between measurements.

FIGURE 8. Rock specimen, specimen holder, and spinner shaft in position for 

first measurement (spin 1 in table 1).
REMANENT MAGNETIZATION OF IGNEOUS ROCKS

A-x

A13

+2 (specimen-cylinder axis)

FIGURE 9. Designation of magnetic components 

within a rock specimen.

For the complete determination of remanent magnetization of a 

specimen, we routinely make six different single measurements, or 

spins. These spins are in pairs about the three axes, hence two separate determinations of the intensity and direction of each of the three 

components normal to the three axes are obtained. The component 

normal to the z axis is labeled Mz, and its direction is <j>z, measured 

clockwise from the plus-x direction (fig. 9). The other two components are determined by Mx, <t>x , and My, <j>v for spins about the x 

and y axes, respectively.

The first or a spin is made with the plus-2 axis directed into the shaft, 

the plus-a; axis directed toward the I position, and the plus-?/ axis 

directed toward the II position. The phase dial reads the angle 4>z>a 

(see fig. 10), and the attenuator reads the magnetic moment Mz, a . 

The second or b spin is made with the plus-s axis directed out from the 

shaft, the plus-z axis directed toward I, and the minus-?/ axis directed 

toward the II position. The phase-dial reading is (f>Zi B and the attenuator reads M2>6 . Ideally, Mz, a and MZi 6 are both equal to the true 

moment Mz ; <f> s>a is equal to <£«; and <£ a, 6 is related to (f>z by the 

relation:

$3=360 $2, B . (1)

These relations are shown in figure 10. Similar measurements are 

made by spinning about the x and y axes as summarized in table 1.

745-239 O 64 3
A14 EXPERIMENTAL AND THEORETICAL GEOPHYSICS 

SPIN 1 SPIN 2

, a

FIGURE 10. Angular relationships in the double-spin procedure.

TABLE 1. Specimen orientations for six spins

Spin

1... . -.. ... .... ..

2

3

4. .._... -

5

6

Axis directed 

into shaft

+2 

 2

+z

 X

+y -v

Axis towards 

I direction

+x 

+x

+y 

+y

+2 

+2

Axis towards 

II direction

+V -V

+z 

 z 

+x

 X

Data obtained

Moment

M, 

M2 6

MX a 

MX 6

My a 

My b

Angle

 ©- ©- ©-«-«- ©-

Measurements about the z, x, and y axes are combined in pairs as 

follows:

(2a)

(2b)

Use of these averages rather than a single measurement about each 

axis reduces possible errors due to inhomogeneity or anisotropy in the 

specimen, and provides redundant data to check measurement accuracy and precision. Averaging also automatically corrects for any 

possible systematic error in phase-angle measurement, inasmuch as 

the same error angle is added to both 02 , a and <f>z, 6 , for example, and
REMANENT MAGNETIZATION OF IGNEOUS ROCKS A15

drops out in step 2b above. When the direction of the component 

normal to the spin axis falls near the I position, both 0g( and 02> 6 , 

for example, may fall on the same side of the zero-phase reading. 

This may be caused by small measurement errors or by the systematic 

errors mentioned above. When both phase angles fall on the same 

side of zero, the expressions (2b) should be replaced by

(2c)

t)j

The total magnetic moment is given by

(3a) 

,)» (3b)

The key to finding the direction of magnetization from spinnermagnetometer measurements lies in noting that during each spin the 

component of magnetization parallel to the rotation axis does not 

contribute to the signal generated in the pickup coil. Thus the 

angle 02 is consistent with any vector lying in a half plane having an 

edge along the rotation axis and extending in the direction 02 ; the same 

applies for <f>x and <£ . One method of determining the direction of 

magnetization in a specimen uses phase angles and intensities in 

combination. The component of the total magnetization along the 

z direction is given by Mx sin 4>x My cos <j> y, and similarly for the components along the x and y directions. These pairs of values may 

then be averaged and the direction and intensity of magnetization in 

the specimen calculated from these three vector components.

An alternative method using only phase angles is preferable for 

most purposes because phase angles can be measured with greater 

precision than intensities and can easily be checked for internal consistency. As previously noted, the 0Z measurement is consistent 

with all vectors lying in a half plane passing through the z axis, and 

the 0X measurement is consistent with all vectors in a plane passing 

through the x axis; therefore the only vector consistent with both 

measurements is along the intersection of these two planes. The 

4>x and <j> y measurements similarly define a unique vector consistent 

with both measurements, as do the <f>v and <f> z measurements. The 

mean of these three vectors may be taken as the direction of magnetization of the specimen, and the angular differences between the 

vectors as a measure of the precision of the measurement.

A graphical technique using an equal-area or stereographic projection has been given by Graham (1949). The planes defined by 0,,
A16 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

FIGURE 11. Calculation of the direction of remanent magnetization within a 

specimen from spinner-magnetometer data.

<t>x, and <£ are drawn as great circles on the projection (fig. 11) and 

usually intersect to form a small-error triangle. The radius of the 

circle inscribed in this triangle is commonly used to check the precision, and its center, defined by the angles 0Z and ~dz, is commonly 

used as the best estimate of the direction of magnetization. A minor 

difficulty in using this method for determining the mean direction 

arises when the magnetization of the specimen is nearly parallel to a 

rotation axis. Signals which are weaker and less well defined than 

the others are generated by spinning about that axis, but the plane 

defined by these weaker spins is given nearly equal weight if the 

center of the inscribed circle is taken as the direction of magnetization. 

This factor can be qualitatively considered by taking the best estimate 

of the magnetic direction nearer the intersection of the two planes 

defined by the stronger signals. A quantitative analytical method for
REMANENT MAGNETIZATION OF IGNEOUS ROCKS A17

weighting the stronger and more reliable measurements is given on 

page A25.

To find the magnetic declination D and inclination / corresponding 

to the original orientation of the specimen, let a be the geographic 

azimuth of the horizontal y axis, /3, the plunge of the z axis, 4>g , the 

azimuth of the magnetic vector reckoned clockwise from x in the xy 

plane, and 0Z, the inclination of the magnetic vector above ( ) or 

below (+) the xy plane, as shown in figure 12. The -\-z axis is first 

rotated (90 /3)° toward the -\-x axis, and the magnetic vector is 

rotated the same angular displacement along a small circle having the y 

axis as its center. The plane of projection thus becomes the horizonta 

plane corresponding to the original orientation of the specimen. If 

geographic north is marked at an angle a counterclockwise from y, then 

D and / may be read directly from the projection, as indicated in 

figure 12.

FIGURE 12. Calculation of in-place direction of remanent magnetization from 

orientation data and specimen-magnetization-direction data.
A18 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

A program for carrying out on a digital computer all of the calculations described in this section, along with additional calculations 

designed to check the internal consistency of the phase-angle and 

intensity measurements is given'on page A27.

PRECISION AND ACCURACY OF MEASUREMENT

Instrumental precision was determined by making nine measurements in succession on a specimen having an intensity of magnetization 

of 1.5X10" 3 emu per cc. When the specimen was removed from the 

holder between successive measurements, the direction of magnetization could be measured with a reproducibility of 0.7° sd (standard 

deviation) and the intensities to 1.1 percent (Doell and Cox, 1963). 

When the specimen was left in the holder between successive measurements, the reproducibility was 0.2°sd. Thus measurement precision 

is primarily limited by the accuracy with which specimens can be 

alined in the holder.

The measurement accuracy of these instruments can be conveniently 

separated into several parts: (1) the accuracy of the original calibrations, (2) the rate of drift or change in this calibration with time, and 

(3) the amount of error introduced in the measurements by such factors 

as specimen shape, specimen inhomogeneity, and susceptibility anisotropy.

During the original alinement and calibration procedures set forth 

above, the reference-signal system may be adjusted so that a phase 

angle, corresponding to a magnetic-component direction, is determined 

to within ±0.1°. The accuracy of the intensity determination depends on the linearity of the attenuator units, rated at 1 percent, and 

on the accuracy of the alternating-current meter used in setting the 

calibration resistor R4. Our meter is rated at 1 percent.

Any change in the output signal from the reference system between 

calibration checks will reduce the accuracy of the measurements, and 

small changes are expected if the magnetic moments of the reference 

magnets change, if the rotation frequency changes, or if the shaft 

changes alinement owing to bearing wear. As a routine check on 

instrument performance, a small bar magnet (2.1 X10" 2 emu) has been 

measured at weekly intervals, and these data may be used to provide 

an estimate of the drift. Independent measurements by two operators 

using two magnetometers evaluated over a 1-year period showed a 

standard deviation of 1.8° in direction and 2.4 percent in intensity. 

These values are not very much larger than the precision values and 

may in part be due to drift in the bar magnets rather than instrumental 

drift,

The accuracy of measurements may also be affected by the shape 

of the specimens inasmuch as, for a cylindrical specimen, the magnetic
REMANENT MAGNETIZATION OF IGNEOUS ROCKS A19

field sensed at the pickup coil depends not only on the direction and 

intensity of the remanent magnetization but also on the orientation 

of the cylinder axis in the specimen holder. It should be noted that 

this effect is quite different from the change in magnetization of a 

specimen due to the internal demagnetizing field, which also depends 

on the shape of the specimen; the first effect represents the nondipolar 

part of the field outside the specimen due to its shape, and the second 

change represents the effects of the influence of the demagnetizing 

field inside the specimen. To determine the magnitude of the externalshape effect on the present instrument, each of four specimens from 

different lava flows was magnetized to saturation along 11 different 

directions in a constant magnetic field of 7,000 oersteds. The measured directions of these saturation remanent magnetizations differed 

from the known directions of the applied field by average angles of 

0.65°, 0.69°, 0.99°, and 1.04° for the four specimens, and intensity 

variations were well under 1 percent. Because individual angular 

errors showed no systematic relationship to the directions of the 

applied field, they are not due to the external-shape effect; they are 

probably due to errors in measurement and errors in alining the 

specimen in the 7,000-oe magnetic field. From these and other 

related experiments, we conclude that the effect of specimen shape 

is negligible and that the calibration procedure previously described 

may be used for specimens magnetized in any direction, even when 

the geometry of the calibration coil corresponds to a specimen magnetized along its axis.

To test the influence of specimen inhomogeneity on the accuracy 

of measurement, a test specimen was assembled from 10 thin cylindrical disks cut from a homogeneous basalt. The test specimen was 

given a saturation remanent magnetization along its axis and was 

then repeatedly measured after various disks had been replaced by 

nonmagnetic blanks. These measurements were also repeated using 

the same specimen magnetized to saturation along a diameter and 

along a direction 45° to the cylindrical axis. In all, 98 configurations 

were investigated, some consisting almost entirely of blanks and others 

almost entirely of magnetic disks. The results of these experiments 

may be summarized as follows: No systematic differences in direction 

greater than about 1 ° were observed, nor were there intensity differences greater than several percent. Moreover, errors this large were 

observed only for the more extreme configurations. Measurement 

errors due to inhomogeneities commonly found in rock specimens 

thus appear to be negligible.

Anisotropy of susceptibility may also give rise to spinner-magnetometer measurement errors. An analysis of this problem is beyond 

the scope of the present report; however, it can be shown that the
A20 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

double-spin procedure for measurements about each axis reduces errors 

of this type to a point where they are negligible for rocks commonly 

used in paleomagnetic research.

SPECIMEN-PICKUP-COIL DESIGN

The equations derived here were used to design a spinner-magnetometer specimen pickup coil that would have a maximum signal-tonoise ratio; given the present mechanical configuration. The coilresponse equations are expressed in differential forms so that the total 

response of a coil of any desired shape may be obtained by integrating 

the appropriate equations over the total cross-sectional area of the 

coil.

FIGURE 13. Relations of position of pickup coil to rotating 

specimen (« 2-n-f).

The flux linkage of an incremental cross-sectional area, dA, of the 

coil at radius r and distance z from the center of the specimen (here 

approximated by a magnetic dipole: fig. 13) is

dct>=2irMinr2/(r2 -\-22') 3/2dA, (4)

where M* is the component of the magnetic moment of the specimen 

normal to the spin axis, here alined along the coil axis, and n is the 

number of turns per unit cross section of the coil.

If n is replaced by (7r/4)(l/a), where a is the cross-sectional area of 

the wire used to wind the coil (?r/4 is a winding factor), and the specimen rotates with angular frequency /, then the incremental rootmean-square voltage induced in the coil is

The root-mean-square thermal noise voltage of such a coil is 

(Gray, 1954, p. 494-499)

de t=(4kTRAf) 1/2 , (6)
REMANENT MAGNETIZATION OF IGNEOUS ROCKS A21

where k is Boltzmann's constant, T the absolute temperature, A/ the 

pass band over which de t is measured, and R is the total resistance of 

the incremental cross-sectional area, dA, of the coil. Replacing R 

by 2irrp(n/a) dA = (ir2rp)/(2a2), where p is the resistivity of the wire, 

equation 6 becomes

de t=(Tr/a)(2kTrptf) 1/2dA. (7)

Another source of noise arises from voltages induced in the coil 

from ambient alternating fields in the laboratory. Assuming that 

there are no gradients in such fields over the area bounded by the 

coil, the root-mean-square voltage in the incremental cross-sectional 

area of the coil from these fields is «

= WHtf (WdA, (8)

where Hf is the effective peak field strength of the component of the 

ambient alternating field at frequency/ along the coil axis. 

Forming signal-to-noise ratios, we find :

de t 

and

de, TtMt r r T'2

J

T'2

'

The total ratio of e s/ef for a coil is commonly increased either by 

placing a larger coaxial balancing coil in series opposition with the 

main coil (with a slight reduction in e s and e s/e t) or by placing the 

unit in a magnetic shield.

Lines of equal de s/de t determined from equation 9 are circles 

centered on the axis of rotation and passing through the center of the 

specimen, as shown in figure 14.

These considerations and the relations in equations 5, 9, and 10 

can then be used to design an optimum coil. The significant requirements are:

1 . The main coil should be as close to the sample as possible, its outer 

cross-sectional shape bounded by a circle of equal de s/de t (equation 9).

2. The coil should be no larger than necessary (equation 10), but it 

must be large enough to yield a signal sufficient to drive the 

detecting units (the integral of equation 5) over the cross section 

of the coil. (Note also that the overall coil size and wire crosssectional area, I/a, will determine the coil impedance, which
A22 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

FIGURE 14. Curves of equal incremental signal-to-noise ratio (desfde t). Dotted 

line shows outline of rotating equipment: A, optimum shape for the main coil; 

B, optimum shape of the balancing coil for the spinner magnetometer described 

in this paper.

should be matched to the detecting unit.) Figure 14 also shows 

the optimum shape of a detecting coil for the spinner magnetometer described above.

The equations also suggest high angular-rotation velocities and 

narrow pass bands; these factors can be considered along with others 

such as the desired sensitivity, ease of operation, and stability of the 

detecting units in the overall design of a spinner magnetometer.

COLLECTION OF SAMPLES

Although irregularly shaped samples broken from outcrops may be 

oriented in a variety of ways, it is often more efficient to obtain 

oriented samples by drilling short cores in place with portable coring 

equipment. The regularly shaped cores can be routinely oriented 

with an accuracy of 2°, and sampling need not be restricted to the 

edges of joint blocks.

The drilling unit we employ (fig. 15) consists of the power unit 

from a small commercial chain saw, a special transmission (details
REMANENT MAGNETIZATION OF IGNEOUS ROCKS A23

FIGURE 15. Sample-coring drill with water tank and orienting device.

FIGURE 16. Mechanical details of the core-drill transmission (shown about 

one-half size). A, Case; B, shaft; C, water inlet; D, grease fittings; E, bearings; 

F, seals; G, adapter to fit core drill; H, adapter to fit clutch plate; /, drill with 

fitting.

shown in fig. 16), a commercial sintered diamond masonry-coring 

drill, and pressure-type garden-insecticide spray tanks for supplying 

cooling water to the diamond drill. Cores 2.49 cm in diameter and 

from 10 to 20 cm long can be drilled from most extrusive igneous
A24 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

rocks with little difficulty unless the rock is highly fractured. Hard 

rocks that require long drilling time may be more easily drilled by 

fitting the coring equipment to a tripod, or similar device, that will 

support the weight of the unit as well as guide the core drill. Without 

water in the tanks, the unit weighs about 10 kilograms.

The cores are oriented by means of slotted tubes that can be slipped 

over the core before it is separated from the outcrop (fig. 15). The 

slotted tubes are fitted with a level so that the slot may be placed 

along the uppermost edge of the core (intersection of the core surface 

with the vertical plane passing through the core axis); they are also 

fitted with a magnetic compass, an inclinometer, and sighting blades 

for transit operation. Properly fitted, a geologist's pocket transit 

may also fulfill all these needs.

In our system, the core axis is the z axis, positive from the surface 

into the outcrop, and the x and y axes define an orthogonal system, 

in which y always lies in the horizontal and the -\-x direction is always 

inclined above the horizontal; right-handed coordinates are used, 

so that the -\-y axis (horizontal) is directed to the right as one looks 

down the core axis (direction of +2).

A mark corresponding to the z axis is made along the upper edge of 

the core by slipping a brass or copper wire down the slot. The plunge 

of this line below (+) or above ( ) the horizontal is read from the 

inclinometer and recorded, as is the geographic azimuth of the -\-y 

direction, which is determined by triangulation prior to removing the 

core from the outcrop.

After the above operations and measurements have been repeated 

by normal field checking procedures, the core is removed from the 

outcrop and the mark along the edge is immediately made permanent 

by marking with a diamond scribe. At the same time, the -\-y direction is indicated by permanent short marks on the right side of the 

orientation line along the entire length of the core. In this manner 

each specimen later cut from the core for measurement (fig. 8) retains 

a complete orientation, and there is no chance of errors arising during 

transfer of orientation marks.

We have estimated from mechanical considerations that cores of 

the size described here may be routinely oriented to within ±2° using 

a simple slotted tube and geologist's pocket transit. If required, 

accuracies of ±0.5° can be achieved with cores of this size by using 

sufficiently precise measuring devices and by using care in placing the 

orientation line on the core before it is removed from the outcrop.

An additional piece of field equipment that has proved useful in 

collecting samples for paleomagnetic investigation is the declination 

gradiometer shown in figure 17 (Doell and Cox, 1962). Two small 

oil-damped magnetic compasses mounted in gimbals at opposite ends
REMANENT MAGNETIZATION OF IGNEOUS EOCKS A25

FIGURE 17. Declination gradiometer.

of a rigid rod half a meter in length are arranged with their index marks 

parallel, so that the declination difference at opposite ends of the rod 

may easily'be read as the rod is moved along an outcrop. The gradiometer is used to identify parts of an outcrop where lightning has struck, 

inasmuch as the strong magnetic fields associated with lightning bolts 

may give igneous rocks a very strong isothermal remanent magnetization and render them useless for paleomagnetic study (Cox, 1961; 

Graham, 1961). Such places can be readily recognized by the local 

gradients in the magnetic field adjacent to the outcrop. Experience 

with lava flows has shown that declination gradients of less than 5° 

per meter, measured with one compass held within 10 cm of the outcrop over an area several meters across, indicates that samples from 

the center of the area are sufficiently free from the effects of lightning 

to be suitable for paleomagnetic analysis. Declination gradients 

near outcrops may also be measured using a geologist's compass.

USE OF A COMPUTER TO REDUCE SPINNERMAGNETOMETER DATA

A program for reducing spinner-magnetometer data with a digital 

computer is outlined below. The following conventions are used to 

identify the input of this program:

4> n ,m(n = x, y, z; m=a, b), phase angles between 0° and 359.9° as 

described in table 1. (Systematic instrumental phase-angle 

errors as large as 90° are corrected under the assumption that 

the phase error for both spins about a given axis remains the 

same.)

Mn, m, magnetic intensities as described in table 1.

V, volume of the specimen, in cubic centimeters.

a, in-place geographic azimuth (0°-359.9°) of the y reference axis.

(3, in-place plunge of the z axis below (+) or above ( ) the 

horizontal.
A26 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

7, quadrant of the horizontal projection of the z axis, according 

to the following convention:

Azimuth y

z vertical._____________________________________ 0

0.1°- 89.9°_--___--____-----_-___---___-____- 1

90.0°-179.9 0 -____ ______- ---____-_--____-_--- 2

180.0°-269.9° _-_______----____-_--__-__--_-- 3

270.0°-359.9° ____-_--_-___-___---_-___------ 4

The following conventions are used to identify the output of this 

program:

D, declination, that is, azimuth of the horizontal component of 

of the remanent-magnetization vector restored to its in-place 

orientation. 

/, inclination, that is, in-place plunge of the magnetic vector

below the horizontal.

M, total magnetic moment of the specimen. 

J, M/V, the magnetic intensity, in electromagnetic units per

cubic centimeter.

A, an analogue of the radius of the error triangle formed by the 

three great circles defined by the phase angles, as discussed 

below.

MM, the root mean square of the differences between the six 

measured magnetic intensities, Mi>a , MZi1> , and so forth, 

and the ideal intensities that would be expected if the 

specimen acted as an ideal dipole with moment M and 

direction of magnetization as calculated.

To find the mean direction from the three phase-angle great circles, 

a comparison is first made to determine whether the three circles 

intersect within 0.1°. If not, an increment is added to each phase 

angle inversely proportional to the A"th power of the corresponding 

intensity Mg , Mx, or Mv , where N is retained as a parameter to be 

specified in the program. This process is reiterated until the common 

intersection is found to within 0.1°. To obtain higher precision, only 

the single constant in step 21 (see below) needs to be changed. As a 

measure of the lack of closure of the original error triangle, the 

average total increment added to the phase angles corresponding to 

the two strongest intensities is recorded as the quantity A.

The best value for the parameter N depends on the relation of the 

accuracy of phase-angle measurements to the magnetic intensities. 

This relation, in turn, depends largely on physical considerations. 

If N is set equal to 0, all phase angles are weighted equally and the 

computer solution is the center of a circle inscribed in the error triangle. This solution is undesirable because it gives too much weight 

to phase angles associated with very weak intensities, which tend to
REMANENT MAGNETIZATION OF IGNEOUS ROCKS A27

be less reliable. On the other hand, assignment of a large number, 

say 5 or more, eliminates from the calculation the phase angle associated with the smallest intensity, and this weighting is undesirable 

where the three phase angles all have approximately the same reliability. However, for very weakly magnetized specimens where only 

two of the three pairs of measurements are above the backgroundnoise level, a large A^may be required to permit rejection of the meaningless weak measurement. On the basis of computer experiments 

with a wide variety of data, we have adopted a value of N=2; although 

no single value is adequate for all types of data, this value has proven 

satisfactory for almost all routine measurements made over a 2-year 

period.

CALCULATION PROCEDURE

Step 1. 4> re , ra <180.0° 0W , M : input 

yes 0re> m=4>n. m 

no 0»lBI=-(360.00 -<fc,, M)

2. (0,, a+0re , 6)<90.0°

yes 0re =i(0«, a 0«,») 

no (0ra , a -0re, 6)>0.0°

yes 0»=|(0B,«-0». 6)-180.00

no -^=K«».a-^, 6) + 180.00

3. Mn=?(Mn,a+Mni t) M,,,*: input

4. M=[|(M|+M,2 +Mf)] 1/2 M: output

5. J=M/V J: output

N: program parameter 

7. WZ >WX >WV or Wz >Wy>W 

yes g=0, r=0, s=l 

no Wx>Wg >Wy or Wx>Wy>W 

yes q=l, r=Q, s=0 

no <jr=0, r=l, s=0
A28 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

Step 8. W^

10. m^=cos

11. /=

12. l=

13. 0=

14. r=

yes proceed to step 35 

no proceed to step 15 

15. p=arc cos (ljk/g~) 0<p< 180.00

16.

yes 6\=p

no ^= p

17. 0<<05

yes X=l 

no X=0

18. fl?=^ flJ+X 360.00°
REMANENT MAGNETIZATION OF IGNEOUS ROCKS A29

Step 19. 0IiI <180..00° 

yes M= 

no ju=

20. 0Ii

?

21. 00P<0.07°

yes proceed to step 35 

no proceed to step 22

22. 0r=0?(l TO+Kl+MW 360.00

23. 07

? 

24. 0?> 180.00°

yes 0yr =:0y-360.000

no

25. 4=0

yes dj= (nk cos 0T1 )/! % cos 0P| 

no dj=nklk l\nk lk

26.

yes c^fc 

no d

sin 0J1 )/ ^ sin QVI

27.

28.

29.

n3 rrij

< -180.00°

yes ^ I

? 

no ^>180.00°

yes 0?=0} 360.00 

no 0.I=0
A30 EXPERIMENTAL AND THEORETICAL GEOPHYSICS 

?

Step 30. e\< 180.00°

yes 6^= 0^+360.00°

no e\> 180.00°

yes ^=^-360.00° 

no P*=6l 

31. A^

32. Transfer At to storage and accumulate for all cycles through 

reiterative part of program.

33. Transfer to step 10 and replace 

*« by 6^

h by 8%

34. Reiterate steps 10 through 33 until yes option in step 21 is 

reached, or until 10 reiterations have been completed. 

In latter procedure, stop calculation and print "NO." 

Omit steps 25 and 26 on each reiteration, retaining the 

values of dj and dk from the first cycle.

35. l=sljk+rmjk+qnjk

n=rljk+qmjk+snjl:

T

36. A= A: output

where T is the total number of reiterations through steps 

10-33.

37. M'z=M[l2+m2 ] 1/2 

M'x=M[m2+n2 ] 1/2 

My=M[n2+l2 ] lf2

38. MM= (1/2.449M)[ (M'f-Mt. a) 2+ (M'f-Mg, 6) 2+ (M'X -MX< a) 2

MM: output
REMANENT MAGNETIZATION OF IGNEOUS ROCKS A31

Step 39. 7=0 ?

yes 0=90.0°

yes x= 180.0° skip steps 40, 41 

no x= 0.0° skip steps 40, 41

no «<90.0° 

yes 5=1

no a<180.00° 

yes 5=2

no a<270.0° 

yes 5=3 

no 5=4

40. (5-7) = ! or (5-7) = 3 

yes e=0

no (5 7) = ! or (5 7) =3 

yes e=l 

no stop calculation, print out "QE"

41. X=90.0°-/3+e(2/3+180.0°)

42. l' = l cos X+TI sin X 

n' = l sin x-\-n cos X

43. 7=arc sin n', 90.0°</<90.0° /: output

44. X=m cos a-\-l' sin a 

F=m sin a-\-l' cos a

45. D'=arc cos [X/(X2 -\-Y2 ^]Q.O°<Df < 180.0°

46. Tr>0.0°

yes D=D' D: output 

no #=360.0°-£>'
A32 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

REFERENCES

Bruckshaw, J. M., and Robertson, E. I., 1948, The measurement of magnetic

properties of rocks: Jour. Sci. Instruments, v. 25, p. 444-446. 

Cox, Allan, 1961, Anomalous remanent magnetization of basalt: U.S. Geol.

Survey Bull. 1083-E, p. 131-160. 

Doell, R. R., and Cox, Allan, 1962, Determination of the magnetic polarity of rock

samples in the field: U.S. Geol. Survey Prof. Paper 450-D, Art. 151,

p. D105-D108. 

 1963, The accuracy of the paleomagnetic method as evaluated from

historic Hawaiian lava flows: Jour. Geophys. Research, v. 68, No. 7,

p. 1997-2009. 

Graham, J. W., 1949, The stability and significance of magnetism in sedimentary

rocks: Jour. Geophys. Research, v. 54, no. 2, p. 131-167. 

Graham, K. W. T., 1961, The re-magnetization of a surface outcrop by lightning

currents: Geophysics Jour., v. 6, no. 1, p. 85-102. 

Gray, T. S., ed., 1954, Applied electronics: 2d ed., New York, John Wiley & Sons,

881 p. 

Johnson, E. A., and McNish, A. G., 1938, An alternating-current apparatus

for measuring small magnetic moments: Terrestrial Magnetism and Atmospheric Electricity, v. 43, p. 393-399. 

Nagata, Takesi, 1961, Rock magnetism: revised ed., Tokyo, Maruzen Co.,

Ltd., 350 p.

U.S. GOVERNMENT PRINTING OFFICE: 1964 O 745-239