|Geophysics Department TU Clausthal|
A Magnetic Profile across a 2D-Model
Students exercise at Geophysics Department TU Clausthal
Applet ( in separate Window )
DEMO version : No local I/O, Example data or Fieldobservations in HTML-File ( Applet Parameter ) only.
FULL version : Local I/O ( own observed data ) included
( Works with the Appletviewer of a JDK_1.1.x, provided the path to the local files is set with acl.read= and acl.write= in .hotjava/properties. )
The "sand box" restrictions of Applets, especially in browsers
as Netscape, Explorer etc., do not apply to Applications running in a
Java Runtime Environmet ( JRE ).
The Applet simulates a magnetic survey along an arbitrary orientated profile across a two-dimensional subsurface model of arbitrary strike direction and composed of the surface of a halfspace and up to six 2-d structures of arbitrary shapes in a vertical cross section.
Model calculations are based on Talwani's calculus for two dimensional bodies of homogenious magnetization.
The 2-d simplification approximates numrous practical cases, where the
extension of geological structures along their horizontal strike direction is
much greater than in a vertical cross section.
The asumption of homogenious magnetization strictly holds for elliptical cross sections only, but implies tolerable errors at least for "weakly" magnetized structures, where the magnitude of a body's internal field is far below the magnitude of the local magnetic field of the earth.
In addition to the 2-d bodies infinite lines of dipoles may be included,
- to represent 2-d stuctures of dimensions in a cross section much less than the shortest distance to the profile,
- to facilitate the understanding of the magnetic field surrounding a subsurface structure, the decomposition of the field vector into components of location dependent directions and the superposition of the local field of the earth.
Topographic effects along a profile are simulated by modelling the surface of the halfspace.
Students exercise :
Observation of vertical and horizontal component using a fluxgate magnetometer on a NS-profile, length 38 [m], across the center of a subsurface structure, srike EW and length ca. 10 [m] ( a row of radiators, cast iron, upper edge ca. 0.7 [m] below surface ).
Applet / Dialogue Window
Dialogue DATA I/O
Dialogue MODEL I/O
Model calculation :
For an obsevation point the contributions of all infinitesimal volume
elements of a body have to be summed up ( integrated ).
For a homogenious magnetization ( constant in magnitude and orientaion all over the body ) and for a point outside the body this procedure is greatly simplified by approximating the body's surface by plane triangles, and by transforming the volume integral over the structure into an integal over its surface, and further into line integrals along the sides of the triangles.
This, for three dimensional structures, still very time consuming calculation is further accelerated for 2-d bodies, reducing the integration path to the border lines in a vertical cross section ( a set of staight lines forming a closed polygon ).
As a result of the implicit integration along the ( infinite )
strike extension of a model, contibutions of magnetization components
parallel to this axis cancel out and the surrounding field parallel to this
axis vanishes: the field vector lies in the plane of the vertical cross
Consequently only the projection of the magnetization of a body / magnetic moment of a line of dipoles into this plane has to be taken into account.
For the simplified model of a homogenious line of dipoles the term "remanent" ( REM ) is used to indicate a magnetic moment of arbirary magnitude and direction, the term "induced" ( IND ) to indicate a magnetic moment parallel to the local magnetic field of the earth and proportional to its magnitude.
Within the dimensions of a survey area the magnetic field of the earth is assumed to be constant, neglecting changes of magnitude with height, ranging from -15 [nT/km] at the magnetic equator to -30&nbs;[nT/km] at the magnetic poles, and with latitude of up to about +4.5 [nT/km] at about 45 [deg] of magnetic latitude.To Table of Content
Components of the magnetic field :
This corresponds to a vertical component
Z = T * sin(INC), positive downward,
and a horizontal component
H = T * cos(INC), pointing to magnetic north.
The horizontal component may be split up into ( geographic ) north and a east components
N = H * cos(DEC) and E = H * sin(DEC),
for practical use affording a fairly precize absolute orientation of the magnetic sensors ( H = 20000 [nT] affords a precission of about 10 seconds of arc to keep errors in E component below 1 [nT] ).
Within the dimensions of a survey area the magnetic field of the earth is assumed to be constant, neglecting changes of magnitude with height, ranging from -15 [nT/km] at the magnetic equator to -30&nbs;[nT/km] at the magnetic poles, and with latitude of up to about +4.5 [nT/km] at about 45 [deg] of magnetic latitude.
In most field surveys the magnitude T is observed ( ! without any information about the orintation of the field ! ) and / or the change in vertical component DEL_Z ( affording a relatively simple and fast sensor orientation via bubble levels ).
To observe changes DEL_H of the horizontal component of the magnetic field, the sensors mostly are orientated towards magnetic north, thus neglecting small local variations of this direction due to the superimposed field of magnetized subsurface structures.
The gradients of vertical component Z or horizontal component H, selectable from the menue panel, are for information only without great importance for practical cases because of the difficulties in sensor orientaton.
Evtl. from horizontally narrow spaced field observations, corrected for diurnal variations, the horizontal gradient can be calculated from the processed observations.To Table of Content
Applet / Dialogue window ( screenshot ) :
The button DATA I/O opens / closes a window to load and to list geometry information of a profile and a set of data observed along the profile,
NO INP / CMP 1 ... selects one of up to three components of the data set for display and comparison to values calculated for a subsurface model.
The text fields to the right describe the data source ( file name / example xx / Applet param. ) and the component selected ( name, sensor height etc. ).
The button MODEL I/O opens / closes a window to load and to list geometry information and magnetic properties of a model of the earth's surface and of up to six subsurface structures ( 2-d bodies / dipole lines ).
The buttons SAVE ACT / REST SVD MOD allow to save the actual state of a model and to restore a previously saved state.
From two button arrays ( SENSOR / GRADIENT COMPONENT ) up to three components of the calculated magnetic field may be selected for display in the window PRO ( see below ).
The row SCALING provides three independent scaling factors for the coordinates of the profile, the dimensions of the model and for the height of the magnetic sensors above surface.
STOP ( Applet ) closes all windows,
EXIT ( Application ) exits the program.To Table of Content
Panel H_SENSOR / Menue SENSOR/GRADIENT COMPONENT :
The components DEL_Z and DEL_H directly represent the respective components
of the additional field of the subsurface structure, whereas DEL_T is the
difference in magnitude of the "disturbed" and the
"undisturbed" magnetic field ( total intensity, T ).
The total values for all three components may be estimated by adding the corresponding values for the undisturbed local field, listed in the window SRV.
! Loading observed data and selecting one of the observed components ( see DATA I/O and CMP 1 ... ) disables the panel H_SENSOR, the button arrays SENSOR / GRADIENT COMPONENT and the scaling buttons PROFILE and H_SENS, since the respective parameters are given in the dataset loaded !To Table of Content
Window DATA I/O :
Window MODEL I/O :
Window SRV :
The local magnetic field, based on the geographic coordinates of
the survey area and on the date of the field observations, is
approximated by a series of spherical harmonics, trucated at 10th degree /
The coefficients used here are distributed by the National Geophysical Data Center, USA, for the International Geomagnetic Reference Field ( IGRF ) model of the International Association of Geomagnetism and Aeronomy ( IAGA ).
In the lower part of the window magnitude and direction of the local field are listed and displayed in a local horizontal plane ( lower left ) and a local vertical plane ( lower right ).To Table of Content
Window MAP :
! The map is intended to show the horizontal extend and orientation of the profile and the subsuface model, i.e. the depth of structures overlapping in the projection is not taken into account, and the fact of hiding one structure by another only reflects their position in a structure table processed in ascendig order !
The reference line of the model ( magenta ) represents the projection of the "center of gravity" of the model and an arrow ( +X, magenta ) points to the pos. x-direction of the model cross section ( Window MOD ).
The origin of the coordinate system ( = 0 [m] E, 0 [m] N ) corresponds to geographic longitude ( LON ) and latitude ( LAT ) of the survey, that are listed in a headline, together with the declination angle of the local field.
Positioning the pointer over the letters DEC, the left button shows and the right button hides a red arrow pointing to magnetic north ( mag. N = direction of the horizontal component of the "undisturbed" local field ).
Positioning the mouse pointer over the intersction point of profile and model reference line, displays the coordinates of the intersection point ( E / N_REF [m] and S_MOD [m] ).
Menue field ( above the graphic display ) :
- MODEL, PROFILE and ROT BOTH
- enable various mouse interactions :
- model and/or profile can be rotated,
- the length of the profile can be adjusted at both end points ( left mouse button ),
- the profile can be moved as a whole ( right button ).
- toggle switch to undo / reapply last change.
! If observed data are loaded and one of the observed components is selected ( see DATA I/O and CMP 1 ... ), the profile geomerty is taken from the dataset loaded, and modification of the profile is disabled !
Window MOD :
- ALLOW ZOOM ONLY
- any changes of model parameters are inhibited.
- MOVE MOD / STR
- move the model or a selected structure by dragging the respective crosshair line.
- ROTATE / SHEAR
- rotate ( left mouse button ),
- shear horizontally or vertically ( right button )
- the model or a selected 2-d body by dragging the appropriate crosshair line
( Fixpoint = resp. "center of gravity" ).
- Horizontal and vertical shear is included to meet geological problems like dipping structures with a relatively well known horizontal top border or a vertical contact to some neighbouring sructure but unknown dip angle, that may be varied preserving the volume of a body ( here : area of a shape ) and its horizontal / vertical boundaries.
- MODIFY POINT
- move a vertice of a selected polygon ( 2-d body ),
- delete it by positioning it over one of its neighbours ( min = 3 vertices/shape ),
- insert a new vertice on a border line of the polygon ( max = 32 vertices/shape ).
- adjust the magnitude of induced or remanent magnetization / moment
- the inclination of remanent magnetization / moment.
- The result is applied to the structure selected or to all structures of identical type ( 2-d body / dipol line ).
- EXCLUDE / INCLUDE STRUCT
- all structures or a selected 2-d body / dipole line are excluded from / included in field calculation,
- to facilitate the understanding of the contribution of individual bodies / dipole lines to the resulting superposition of the fields of all structures.
( A structure selected via STRUCTURE 1 ... is automatically included in the field calculation, SURFACE has to be included explictly by INCLUDE. )
- COPY STRUCT
- copies a selected 2-d body / dipole line right to the existing model.
- ADD NEW BODY / DIPOLE
- adds a 2-d body / dipole line with default parameter values right to the existing model.
- REMOVE STRUCTURE
- removes a selected 2-d body / dipole line from the model's structure table.
Positioning the mouse pointer over the "center of gravity" of the model or of one of the structures, displays coordinates ( Z / X_REF in cross section plane, S_PRO = intersection of reference line and profile ) and magnetic properties ( MAG / MOM and INC = magnitude and inclination of the projection onto the crossection plane of total magnetization / magnetic moment ).To Table of Content
Window PRO :
The window displays observed data and / or data calculated for the actual survey, profile and model parameters.
If no observed component is selected for display, ( see DATA I/O ), up to three field components selected from the SENSOR / GRADIENT COMPONENT menue are displayed.
Menue panel above graphic display :
- ADJ MOD
- enables the adjustment of the model position with respect to the profile,
- enables the menue items AUTO and APPLY, if only one structure contributes to the field calculation ( see STRUCT 1 ... / SURFACE and EXCLUDE / INCLUDE STRUCT in the MOD window ) :
- AUTO fits the calculated component to the field obsevations of the profile range displayed ( see Zoom ) by adjusting the magnitude of magnetization / moment,
- APPLY applies the result to the structure
( scaling ind. and rem. magnetization / moment ).
- toggle switch to undo / reapply last change.
If observed data are loaded and one of an observed components is selected, a second menue panel is shown below the graphic display :
- Selectable by OBS / CALC DATA / OBS + CALC
- blue squares represent the field observations,
- a red curve shows the corresponding calculated component.
- REG FIELD POLYNOME NONE / DEG 0 ...
- selects the dgree ( max 6 ) of a polynome approximating a regional field resulting from deeper structures and superimposing the observed data.
- Observations estimated to represent the background field are selected as input to a least square fit by dragging a rectangle using the left mouse button, and marked by filled squares,
observations to be excluded from calculations are selected using the right button.
- SHOW FCT / SHOW REG / FCT - REG selects the display mode for the background polynome :
- SHOW FCT = hide polynome, data unchanged as read in / calculated,
- SHOW REG = show polynome, used as bias for the calculated data,
- FCT - REG = subtract polynome from observed data.
Class files are available
for the DEMO version ( Applet )
as zip file and as .tar.gz file,
for the FULL version ( Applet + Application )
incl. example files for model parameters and field observations
as zip file and as .tar.gz file.
The Java Runtime Environment ( JRE ) needed to run the Application is available for several platforms at Sun Microsystems, Inc..
Both versions include a HTML-file containing
To Table of Content
Example : Profile survey as Applet Parameter<PARAM name="MES" value="
To Table of Content
Most of the Header lines starting with "#XXX> contain informations for the user and are ignored by the program,except :
The "#DAT>" line contains the date of observation, tranferred to SRV for local field calculation,
- the "#SOD>" line describes the format of the field observations starting immediatly below :
=> coordinate S_Pro ( along the profile ) in column 1, azimuth A_S2n = 0 [deg] ( S pos. -> N ),
=> observed components in columns 2 to 3,
=> col. 2 = Delta_Z, sensor height H_Mes = 1.20 [m],
=> col. 3 = Delta_H direction mag. N, sensor height H_Mes = 1.20 [m],
- ( alternative "C=2,3" ... , and for Delta_H :
"DEL_H" = "DEL_M" => magn. N,
"DEL_G" => geogr. N,
"DEL_Q" => across the profile ),
=> coordinates of the survey area ( longitude, latitude and altitude above NN, here Clausthal, see window SRV ),
- ( alternative :
"L=CLZ" => coordinates and lokal field for Clausthal,
"N=48700.=0.=67.0" => total intensity, declination and inclination in the survey area, here Clausthal ),
=> 3 culumns/line in data record.
To Table of Content
Example : Model as Applet Parameter<PARAM name="MOD" value="
To Table of Content
Only lines starting with "#XXX>" are interpreted,
the character "!" marks comment lines, containing user informations to facilitate generating / editing of a model.
Model calculation :
D_X = X(N_Ref,E_Ref,A_X2n) + X_Off(SRF/BDY) + X_Pnt - X(S_Pro,Q_Pro,A_S2n)
D_Z = Z_Ref + Z_Off(SRF/BDY) + Z_Pnt + H_Mes
To Table of Content
Additional Applets : Keller-clz.de
( ned gschempfd isch globd gnueg )
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