Applied Geophysics : Magnetics

Applet    ( in separate window )

ca. 640 x 670 Pixel ( 4 [Pix/mm] )    ca. 395 x 630 Pixel ( 3 [Pix/mm] )    ca. 325 x 510 Pixel ( 2 [Pix/mm] )   

The applet simulates a Schmidt Vertical Balance, for many years the standard instrument for field observations of variations of the vertical component of the magnetic field of the earth.

The dip angle of a permanent magnet ( "dip needle" ) rotating about a horizontal axis is calculated from a difference equation in constant time steps of 40 [msec] ( 25 steps per decond )
and displayed in a simplified vertical section of the instrument.

Comments

Details of Construction

Adjustment of Range and Sensitivity

Compensation of Temperature Variations

Taking a Reading

Math.-phys. Background ( in separate window )

HowTo

Dialogue Panel of the Applet

Graphic Display of the Applet

Example : Orientation Error

Field Observations

Start of a Field Observation

Taking a Station Reading

Display of Observations and Subsurface Model

Raw Observations

Anomaly, Model Curve + Model

Interpretation

Adjustment of the Model

Model "Correctly" Adjusted

Details of Construction :
( Scaling 3 [Pix/mm] )

In an insulated case with bubble levels

two permanent magnets ( N-Pole red, S-Pole green )

are connected by a cube made of aluminium or brass ( dark yellow ).

Two quatz knife edges fixed to the cube are supported by quartz base plates ( magenta )

forming a horizontal axis of revolution for the magnet assembly.

Both ends of the magnets move in the gap between copper vanes ( orange )

providing the damping of free oscilations of the magnet system.

The position of the magnet ( dip angle ) depends on the the equilibrum of the moments of force

of the local magnetic field acting on the magnet

and

of the gravitational acceleration acting on the center of gravity of the assembly,

and is observed in an eyepiece on top of the case.

A scale is reflected by the mirror ( light blue ) , mounted on top of the magnet assemly, and

the displacement of the image is proportional to the angular excursion of the magnet for "small" dip angles ( here : < approx. 2.4 [deg] ).

A "range" magnet, mounted at an adjustable distance on a rod ( brass ) below the instrument, allows

to shift the center of the measuring range  ( i.g. approx. ±200 ... ±500 [nT] ) without changing the sensitivity.

The instrument is locked for transport and installation

by lifting the magnet assembly and pressing it against leaf springs,

and freed

by "gently" lowerring the magnet to prevent damages to the knife edges / the base plates.

For field observations the instrument is mounted on a tripot ( not shown )

providing leveling screws and

allowing to rotate the instrument about a vertical axis between two stops 180 [deg] appart

to take two readings : N-pole of the magnet to E and to W.

Details of construction    Table of content    Top of page

Range and Sensitivity :

If the axis of revolution of the magnet assembly is horizontal and points to mag. North,

the horizontal component of the magnetic field is eliminated, and

the equilibrum postion of the magnet depends on the moments of force

due to the vertical component of the local field

and

the gravitational force acting on the center of gravity.

The center of gravity

lies below the axis of revolution,

and, for observations on the northern hemisphere,

is shifted to the south pole of the magnet assembly.

The horizontal distance of the center of gravity ( ≤ 1 [mm] ) is determined by the region of the field survey,

i.e. by the average value of the vertical component of the local magnetic field to be compensated by the gravitational moment of force ( reference value => magnets approx. horizontal ),

and can be adjusted

by positioning two small additional masses ( each approx. 4 [g], dark yellow ) on "horizontal" spindles.

The vertical distance of the center of gravity determines the sensitivity ( [nT/deg], scale : [nT/div.] ) of the instrument and is adjustable

by a screw below the axis of revolution  ( Not implemented in the applet ).

The sensitivity [nT/div] of the instrument can be determined / examined ( if necessary even during field work )

in the known magnetic field of a Helmholtz coil, but

the reference value of the vertical component ( Z_Ref -> equilibrum position = 0 [div] ) and its variations with time

are not known sufficiently exact.

! A magnetic balance is a so called relative instrument, suitable to observe differences of the vertical component with respect to observations at a base station !

Details of construction    Table of content    Top of page

Compensation of temperature variations :

The effect of temperature changes to the dipole momentum of the magnet assembly, reduced by a rise of temperature and vice versa,

is compensated using different materials for the two spindles supprting the additional masses.

For obsevations on the northern hemisphere, the spindle pointing to the N-pole of the magnet

is made of aluminium ( rel. high temperature coefficient, light gray ), and

the spindle pointing to the S-pole

is made of Invar, an alloy with a very small temperature coefficient :

The center of gravity is moved horizontally

towards the axis of revolution for rising temperatures

( = decreasing dipole momentum )

and

away from the axis for falling temperatures

( = increasing dipole momentum ).

The positions of both additional masses can be calculated from the temperature coefficients of the dipole momentum and of both spindles

for a given horizontal distance of the center of gravity,

i.e. for a given reference value of the vertical component of the magnetic field.

A correct adjustment of these positions only ensures the invariance of the equilibrum postion of the magnets for the reference value of the field, whereas

the sensitivity to field variations ( observed anomalies ) remains temperature dependent

due to changes of the dipole momentum and of the vertical distance of the center of gravity.

A thermometer ( not implemented in the applet ) inside the insulated case allows to calculate approx. corrections.

! A relatively important and inevitable temperature effect is induced by the "range shift" described above, since

the range magnet and the supporting rod are exposed directly to the surrounding temperature, and

changes of the dipole momentum of the magnet and of the distance to the instrument affect the additional field in the same direction !

Details of construction    Table of content    Top of page

Taking a Reading :

After a coarse levelling of the tripod ( without instrument )

a sensitive compass ( length of the needle approx. 10 [cm] ) is mounted, and

the head of the tripod is adjusted

to ensure an exact orientation E-W of the magnet assembly at both stops ( see above )

after mounting and levelling carefully the instrument case.

At each profile station the mean value of two readings is saved :

N-pole of the magnet assembly pointing to east

and

N-pole pointing to west.

Thus reading errors due to levelling errors E-W

are eliminated,

the influence of the horizontal component of the field due to orientation errors

( magnet assembly not exactly E-W )

are strongly reduced.

! A levelling error N-S ( axis of revolution not exactly horizontal ) leads to a reading error of the same amount in both readings :

N-S levelling should be performed very careful !

Details of construction    Table of content    Top of page

Applet :
( Screenshot :  4 [Pix/mm],  magnet locked )

The figure shows the state of the applet after start :

magnet assembly locked,

N-pole ( red ) to east,

reference value of the vertical component ( REF_Z ) 45000 [nT],

local value ( survey area, LOC_Z ) 45000 [nT].

Dialogue panel :

MAGN. BALANCE  displays in a separate, scalable window

a simplified vertikal and horizontal section of the instrument.

Positioning the mouse pointer on a notation marks the respective component of the instrument by a blue frame.

RUN

starts calculation and graphic display,

HALT

"freezes" the actual state, and

STEP

calculates a single time step ( 40 [ms] ).

LOCK

lifts and locks the magnet assambly, and

FREE

"gently" lowers and frees the magnet.

ROT

rotates the locked instrument by 180 [deg]

( N-pole to east / west ).

( RUN / HALT / STEP and LOCK / FREE / ROT are coupled :

RUN / STEP -> FREE,  FREE -> RUN,  LOCK -> HALT. , and ROT  -> FREE + RUN )

NO ADJ ERROR ...  allows to observe the influence of adjustment errors and temperature variations.

NO ADJ ERROR :

levelling and orientation correct,

temperature as during adjustment of the additional masses,

HOR EW 1 [min]  ( levelling error EW ) :

instrument tilted to west by 1 minute of arc,

HOR NS 1 [min]  ( levelling error NS ) :

instrument tilted to south by 1 minute of arc,

MAG N 1 [deg]  ( orientation error to mag. N ) :

instrument rotated to east by 1 [deg],

TEMP +10 / -10 [Deg C] :

temperature increased / decreased.

INFO  and  HELP  ( in HALT mode ) display

informations ( INFO ) and

hints to possible mouse actions ( HELP )

concerning the actual cursor position ( graphics panel of the applet ).

The magnetic field seen by the instrument is selected / modified in a subpanel ( light blue ) of the dialogue :

REF Z  and  LOC Z  ( instrument locked ) opens a separate window, where

REF_Z selects

the reference value and the local magnetic field of the survey area ( vertical component rounded to 1000 [nT] ), and

determines the position of the additional masses, calculated automatically,

LOC_Z selects

the local magnetic field only, wehre

the vertical component ( rounded to 10 [nT] ) is the base value of an anomaly to be observed on a profile, and

the horizontal component stabilizes / labilizes the angular excursion of the magnet assembly in case of an orientation error.

0 [nT], 200 [nT] ... selects

known values of an additional ( vertical ) field generated in a Helmholtz coil for test and calibration of the instrument.

( Switching on / off -> FREE + RUN )

Z_HLP > 0 / < 0 installs a "range" magnet at an adjustable distance below the instrument, generating an additional ( vertical ) field

positive  for Z_HLP > 0  ( N-pole downward ),

negative for Z_HLP < 0  ( N-pole upward ).

Field observations on a profile over a subsuface dipole are contolled by a subpanel ( light green ) at the lower edge of the applet dialogue ( see Field Observations ).

HowTo    Table of content    Top of page

Applet :
( Screenshot :  4 [Pix/mm],  magnet free )

The figure shows the working state of the instrument :

magnet free,

N-pole ( rot ) to east,

Z_ref = 45000 [nT],    Z_Loc = 45150 [nT],    test field = 0 [nT],

=> Del_Z = 45150 + 0 - 45000 = +150 [nT],

range shift = -200 [nT] => Z_eff = 150 - 200 = -50 [nT].

Graphics panel :

The scale, to be observed in the eyepiece, is displayed enlarged above the instrument, and differs slightly from the origial :

the divisions of the fixed reference scale are numbered,

and

its moving image is symbolized as a moving pointer.

The actual dip of the magnet assembly is indicated by

a vertical line ( blue ) moving across the scale,

and

changing its colour to magenta after the system has come to rest at the actual equilibrum position ( approx. 10 - 15 [sec]  after RUM / FREE ).

Postioning the mouse cursor in HALT mode on the pointer ( magenta ) :

INFO displays informations to the actual equilibrum position

( rectangle left, yellow ),

the field acting on the magnet

( blue, here : TEST, Del_Z = +150 [nT] + Z_Hlp = -50 [nT] ),

and

the position [div] of the pointer and the reading [nT] ( magenta ).

CAL  = as calculated in the simulation and ploted ( "hi res" ),

OBS = as observed by a user ( rounded to 1/2 [div] = approx. 5 [nT] ).

HELP displays hints to actally possible mouse interactions

( rectangle right, foreground red ) :

left mouse button lists parameters and readings of the actual equilibrum position screen / JAVA-console,

and

right button marks the actual reading position for use together with the following reading ( see below ).

Below the instrument the "range" magnet is shown :
( here : N-pole upward = Z_HLP < 0 in dialogue )

Right to its center the distance to the center of the instruments magnet assembly is displayed and is adjustable in the field -- ... ++ ( orange ),

 -   /  +   =>  0.1 [mm] ( left mouse button ), 1.0 [mm] ( right button ),

- - / + + =>  10 [mm] ( left button ), 100 [mm] ( right button ).

INFO displays

the value of the additional field, calculated from the distance and dipol moment of the "range" magnet,

( not or approx. only known for the original instrument )

and

for a temperature change ( TEMP ±10 [Deg C] in dialogue )

the resulting values of distanve and additional field

( background yellow, foreground red ).

HowTo    Table of content    Top of page

Example orientation error :
( Screenshots :  2 [Pix/mm],  MAG N  1 [deg] )

Parameters for both figures :

magnet assembly freed ( FREE ),

test field +500 [nT]  +  range field 0 [nT],

INFO on,   HELP off.

Figure left. :

A first reading was taken for N-pole -> E and correct adjustment of the instrument ( NO ADJ ERROR ), and

the position of the reading pointer was marked blue

( right mouse button on ponter ).

Next MAG N  1 [deg] was selected to demonstrate

the effect of the orientation error to the reading.

INFO, ( mouse pointer in scale,  HALT mode ) displays the information panel DELTA ACT-MRK

revealing a reading error for N-pole -> E of approx. +12 [nT] ( CAL ) / +10 [nT] ( OBS ).

Figure right :

A first reading was taken for N-pole -> E and MAG N  1 [deg], and

the position of the reading pointer was marked blue.

Before taking the second reading the intrument was rotated ( LOCK + ROT ) by 180 [deg] without changing any other parameter.

The INFO panel SUM N-POL E/W displays the mean value of both readings and shows

a decrease of the reading error to approx. 0.1 [nT] ( CAL ) / 0.4 [nT] ( OBS ).

HowTo    Table of content    Top of page

Start of a field obsevation :
( Screenshot :  applet dialogue,  4 [Pix/mm] )

PROFILE ( istrument locked )

starts a field observation along a profile abobe a dipole in the subsurface,

and

opens a scalable separate window for the graphic display of readings taken at the field stations, of a model curve calulated for adjustable model parameters and a vertical section of the subsurface model. ( see below Example : Anomaly, ... ).

On the profile

12 field stations ( instrument height 1.2 [m] ) are aligned

in the vertical plane of the model dipole.

The base station

lies outside the radius of the anomaly ( => 0 [nT] ) and is used as a reference for the readings taken on the profile.

Parameters set before start :

Z_Ref = 45000 [nT],    Z_Loc = 45150 [nT],    ( test field N/A ),

=> Del_Z = 45150 + Z_nn - 45000 = Z_nn + 150 [nT],

Z_nn = anomaly at station nn, ( base = 0 [nT] )

Range shift = -200 [nT] => Z_eff = 150 + Z_nn - 200 = Z_nn - 50 [nT].

Field observations    Table of content    Top of page

Taking a station reading :
( Screenshots :  2 [Pix/mm] )

NEXT, PREV and BAS  "move" the instrument ( locked )

to the next, previous profile station or to the base station.

The actual station ( here base )

is diplayed in a text field of the dialogue panel, and

is marked by a circle ( red ) in the readings diplay ( see below ).

After FREE or RUN

the reading pointer moves to the equilibrum position determined by the effective vertical component ( Z_eff, see above ), and

the number of the reading, the actual orientation of the instrument and the value [nT] read are displayed ( fig. left,  OBS 1 : NP>E ..., magenta ).

Next the actual postion of the reading pointer

is marked using the righthand mouse button ( => blue mark ), and

the instrument is rotated by 180 [deg]  ( LOCK, followed by ROT ) to take a second reading.

The mean value of both readings

is displayed ( fig. right,  OBS 1 ..., red ), and

can be saved clicking SAVE ( red ) for display / interpretation.

LOCK enables NEXT, PREV and BAS buttons to "move" to the next station.

Up to 4 sets of data can be stored for every profile station ( 8 for the base stn. ), containing

the reading saved ( RAW [nT] ),

orientation and distance of the "range" magnet ( HLP / [mm] ),

the difference of the station reading to the base reading ( ANOM [nT] )

and

a weighting factor ( WGT, 0 or 1 ),

contolling the use of the reading for the interpretaion

( i.e. calculation of a RMS-error with respect to a model curve ).

Whenever necessary the range shift may be readjusted during field work,

provided a reading at the base station is taken for the new range shift value.

Field observations    Table of content    Top of page

Example : raw readings
( Screenshot :  1 reading/station,  Z_HLP < 0  793.7 [mm] => -200 [nT] )

The profile stations are symbolized by

numbered blue triangles above the upper profile axis,

the base station ( magenta )

right to the dispay area.

Dialogue panel ( background yellow ) :

DISP : RAW READINGS ... controls the display of readings and model curve,

RAW READINGS => readings saved ( rounded to 1/2 [div] = approx. 4 [nT] ), green sqares,

ANOMALY => differences to readings at the base station, blue crosses,

RAW + ANOM => both versions of observations,

CALC + RAW => model curve + raw readings and

CALC + ANOM => model curve + anomaly.

MODEL displays

a vertical section of the subsurface model and

enables the dialogue panel ( light blue ) controlling the modification of model parameters to fit the model curve to the anomaly values ( see below ).

FIELD draws the field surrounding the subsueface dipole.

Possible mouse interactions :
( in HALT mode of the applet only )

Zoom  ( mouse button left => Set    right => Reset ) :

left to the vertical axis [nT] => range of function values,

below the horizontal axis S [m] => profile range,

or

rectangle within the plot area.

( details : INFO / HELP in applet menue )

INFO displays informations

to the actual state of the profile

( mouse pointer on STN NR, upper left, blue ),

to a specific station

( mouse pointer on a station symbol, blue triangle ).

( In both infos :

nn RAW    = number of readings

nn ANOM = number of anomaly values ( RAW-BAS )

nn USE     = number of anomaly values, WGT = 1.0 )

Lefthand mouse button lists informations to the profile / a station on the screen or the JAVA console.

A mouse click on a symbol representing a reading ( RAW or ANOM ) modifies the corresponding weighting factor :

left    => WGT = 1.0  ( symbol green / blue ),

right => WGT = 0.0  ( symbol light gray ),

Dispay of observations    Table of content    Top of page

Example : Anomaly, model curve + model
( Screenshot :  readings and Z_HLP  as above )

Dialogue panel :

CALC + ANOM. => upper part =

model curve ( red ) and anomaly ( RAW-BAS, blue )

+ RMS error of fitting the curve to the anomaly readings

( E_Rms [nT],  upper right corner ).

MODEL => lower part =

subsurface model ( dipole ),

FIELD =>

dipole field ( light gray ) in model display.

The vertical extend of both parts of the graphic dispay is adjustable

between 70 / 30 and 30 / 70 using the mouse

( left edge& of the window,  here : approx. 50 / 50 ).

Model display :

The position of the dipole is marked

by a small circle in the center of a crosshair ( cyan ),

the height of the instrument ( fixed, here : 1.2 [m] )

by a horizontal Line ( H_I, blue ).

The dipole moment is displayed as

a red pointer, scaled to fit the plot area.

Possible mouse interactions :
( in HALT mode of the applet only )

Zoom  ( see also above ) :

The depth axis i( Z [m] ) is scaled according to the profile scaling,

the depth range can be shifted ( preserving the scaling ) using the mouse left to the depth axis.

INFO ( in applet dialogue ) displays informations

to the position of the dipole positioning the mouse pointer on the crosshair,

to the dipole moment positioning the mouse on the end or on the extension ( gray line ) of the pointer representing the moment.

( The righthand mouse button lists the actual parameters of the model to the screen / the JAVA console. )

Dispay of observations    Table of content    Top of page

Adjustment of the model
( Screenshot :  readings / anomaly as above,  model :  S = 12 [m] -> ca. 13.5 [m] + AUTO )

ADJUST DIPOLE enables the adjustment of model parameters using the mouse.

At the crosshair ( cyan )

the position of the dipole is moved horizontally and/or vertically,

at end of the moment pointer ( red )

the magnitude of the dipole moment is adjusted, and

at the extension of the pointer ( gray )

the moment is rotated.

Modifications of the model are displayed in dark yellow

in the model display and

as resulting model curve in the anomaly display ( incl. RMS error ),

and can be

applied to the actual model by APPLY or

dismissed mit by CLR NEW.

The last modification applied can be removed by UNDO.

Activating AUTO ( -> foreground red ),

inhibits manual adjustments of to the magnitude of the dipole moment,

and instead

calculates a "best" value by fitting the model curve to the anomaly readings.

( For CALC + ANOM only )

Interpretation    Table of content    Top of page

Example : Model adjusted "correctly"
( Screenshot :  readings as above,  model :  S approx. 15 [m],  Z approx. 3.6 [m],
dipole moment :  INC approx. 120 [deg],  magnitude AUTO, )

The position adjustment has been prformed in a zoomed model display ( resolution approx. 1 [mm/Pix] ),
the remaining RMS error is due to rounding the readings to approx. 5 [nT].

Interpretation    Table of content    Top of page

Class and html files for a local installation of the applet are available as a zip file and as a tar.gz file.

More applets at : the author's Homepage

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