7. Coordinates, Sign Conventions and Units: A Quick Guide¶
Here we provide a quick guide for the following:
Some codes may have internal coordinate systems. These details are not important here. This section is focused on the data that are read and output by each code.
7.1. Coordinates for Data Locations¶
Here, we define the coordinate systems for data points for each code. In general X is Easting, Y is Northing and Z is +ve up. The 1D codes are an exception; where ve Z locations refer to positions above ground and the coordinate system is lefthanded. Certain codes may use a different coordinate system internally. However, the majority of users will not need to worry about this. Certain codes may use unique data conventions. The users should worry about this.
Type 
Name 
Versions 
Easting 
Northing 
Z +ve 
Details 

GUI 
GIFtools 
All 
X 
Y 
up 

Gravity 
GRAV3D 
5.0, 5.1, 6.0 
X 
Y 
up 

Gravity 
GRAV PDE 
octree 
X 
Y 
up 

Magnetic 
MAG3D 
5.0, 5.1, 6.0 
X 
Y 
up 

Magnetic 
MAG PDE 
octree 
X 
Y 
up 

MVI 
MVI 
3.0 
X 
Y 
up 

DC/IP 
DCIP2D 
3.1, 5.0 
X 
N/A 
up 

DC/IP 
DCIP3D 
X 
Y 
up 

DC/IP 
DCIPoctree 
octree 
X 
Y 
up 

FDEM 
EM1DFM 
1.0 
X 
Y 
down 

FDEM 
EH3D 
X 
Y 
up 

FDEM 
E3D 
octree 
X 
Y 
up 

TDEM 
EM1DTM 
1.0 
X 
Y 
down 

TDEM 
H3DTD 
X 
Y 
up 

TDEM 
TDoctree 
octree 
X 
Y 
up 

MT/ZTEM 
MTZ3D 
X 
Y 
up 

MT/ZTEM 
E3DMT 
1 (2014,2015) 
X 
Y 
up 

MT/ZTEM 
E3DMT 
2 (2017) 
X 
Y 
up 
7.1.1. DCIP details¶
PENDING
7.1.2. EM1DFM and EM1DTM details¶
The EM1DFM and EM1DTM codes read and write data files where X is Easting, Y is Northing and Z is +ve downward. Thus Z = 5 m indicates the observation location is 5 m above the surface; even if the surface is not at an elevation equal to 0 m. When loaded into GIFtools (Z +ve upwards), the Z values are automatically transformed into the correct elevation values. If EM1DFM or EM1DTM data are modeled from the GIFtools GUI in a scenario where there is surface topography, the resulting Z (elevation) values in GIFtools will take surface topography into account.
7.2. GIF Data Sign Conventions and TimeDependency¶
Here, we define the sign conventions for various data types and the timedependence for frequency domain codes. If data are not formatted using the proper convention, it is unlikely that the inversion will be able to fit the data and return meaningful results.
Important
Make sure you scroll all the way to the right within the table to see all information pertaining to a particular code.
Type 
Name 
Versions 
Sign Convention 

Gravity 
GRAV3D 
5.0, 5.1, 6.0 
+ve data represents +ve gravity anomalies 
Gravity 
GRAV PDE 
octree 
+ve data represents +ve gravity anomalies 
Magnetic 
MAG3D 
5.0, 5.1, 6.0 
+ve data represents +ve magnetic anomalies (details) 
Magnetic 
MAG PDE 
octree 
+ve data represents +ve magnetic anomalies (details) 
MVI 
MVI 
3.0 
+ve data represents +ve magnetic anomalies (details) 
DC/IP 
2D DCIP 
\(\mathbf{E}=\nabla V\) and \(\Delta V = V_N  V_M\) (details) 

DC/IP 
3D DCIP 
\(\mathbf{E}=\nabla V\) and \(\Delta V = V_N  V_M\) (details) 

DC/IP 
DCIP octree 
octree 
\(\mathbf{E}=\nabla V\) and \(\Delta V = V_N  V_M\) (details) 
FDEM 
EM1DFM 
1.0 

FDEM 
EH3D 


FDEM 
E3D 
octree 

TDEM 
EM1DTM 
1.0 

TDEM 
H3DTD 


TDEM 
TDoctree 
octree 

MT/ZTEM 
MTZ3D 


MT/ZTEM 
E3DMT 
octree ver. 1 

MT/ZTEM 
E3DMT 
octree ver. 2 

7.2.1. Timedependency (Fourier convention)¶
The relationship between a timedependent function \(f(t)\) and its corresponding frequency response \(F(i \omega\)) is given by the inverse Fourier transform:
where the choice in sign of \(\pm i\omega t\) defines the Fourier convention. The choice in Fourier convention ultimately affects the phase relationship between real and imaginary components of \(F(i \omega)\) and how Maxwell’s equations are represented in the frequency (Fourier) domain. To demonstrate this, let us first show Maxwell’s equations in the time domain:
Using \(\boldsymbol{+i \omega t}\) convention: If the inverse Fourier transform is defined using \(+ i\omega t\), then
and Maxwell’s equations in the frequency domain are:
where \(e^{+i\omega t}\) is suppressed.
Using \(\boldsymbol{i \omega t}\) convention: If inverse Fourier transform is defined using \( i\omega t\), then
and Maxwell’s equations in the frequency domain are:
where \(e^{i\omega t}\) is suppressed.
As we can see, the phase relationship between \(\mathbf{E}\) and \(\mathbf{B}\) in Faraday’s law is different for each convention; similarly for \(\mathbf{H}\) and \(\mathbf{D}\) in the AmpereMaxwell law. Thus it is important to know which convention is being used when examining the electric and magnetic fields for a particular FDEM code.
7.2.2. Magnetics¶
Total magnetic intensity data:
For total magnetic intensity (TMI) data, the sign of the data is more or less determined by whether the secondary magnetic field has components parallel or antiparallel to the Earth’s inducing field; where the Earth’s inducing field can be at a variety of orientations depending on latitude and regional variations. In this case, a positive data value generally indicates that the secondary magnetic field has vector components parallel to the Earth’s inducing field; i.e. it ‘adds to’ the inducing field. In contrast, a negative data value indicates that components of the secondary field are antiparallel, or ‘oppose’, the Earth’s inducing field.
Amplitude data:
For amplitude data, a positive value indicates that the magnitude of the total observed magnetic field (\(\mathbf{B_p + B_s}\)) is larger than the Earth’s inducing field (\(\mathbf{B_p}\)); i.e. \( \mathbf{B_p + B_s}  > \mathbf{B_p} \). The opposite is true for negative data values.
7.2.3. DCIP data¶
In the electrostatic case, the AmpereMaxwell equation shows that \(\nabla \times \mathbf{E} = 0\) and that \(\mathbf{E}\) can be written as the gradient of a scalar potential:
By taking the divergence of Faraday`s law and substituting the previous expression, the DC resistivity problem is ultimately defined by the following expression:
As we can see, our choice in the relationship between \(\mathbf{E}\) and \(V\) changes the sign convention for the voltage measurements. In the case of UBC GIF codes, we choose \(\mathbf{E} =  \nabla V\). By this convention, 1) secondary potentials are positive in the vicinity of positive electric charges and negative in the vicinity of negative electric charges, and 2) positive potentials are observed near current sources and negative potentials are observed near current sinks.
7.2.4. EM1DFM data¶
The EM1DFM code models data for a small loop transmitter with dipole moment in the X (Easting), Y (Northing) or Z (downward) direction, and receiver coils with dipole moments in the X (Easting), Y (Northing) or Z (downward) direction. Thus a Z oriented transmitter will have a primary field which points downwards. And positive Hz values indicate fields with vertical components pointing downward. In X and Y however, the primary field and observed field components are in the Easting and Northing directions, respectively. If working outside the GIFtools framework, it is important to realize that transmitters, receivers and data are defined in a lefthanded coordinate system with Z +ve downward.
In GIFtools, we define transmitters and receiver for the 1D codes in the X (Easting), Y (Northing) and Z (upward) directions. So long as the appropriate sign change is applied, the EM1DFM code can be used to model data for transmitters and receivers defined within GIFtools. Therefore, the appropriate sign change is automatically applied to EM1DFM data when loaded into/exported from GIFtools.
7.2.5. EM1DTM data¶
PENDING**
7.2.6. H3DTD and TDoctree data¶
For most of the data columns (Hx, Hy, Hz, dBx/dt, dBy/dt), the data represent the true anomalous field components in the coordinate system that defines the data locations; i,e, X (Easting). Y (Northing) and Z (upwards). However, these codes represent the timederivative of the vertical component as dBz/dt.
The sign convention for dBz/dt data can be explained as follows. For coincident loop airborne systems, the true dBz/dt response observed at the center of the receiver coil is typically negative and decaying during the offtime. However, the decay curves for this component have historically been plotted as positive and decaying. This is done for two reasons. 1) A positive decay curve is analogous to the strength of a decaying inductive response. 2) The raw voltage induced within the receiver coil is in fact positive and decaying. This is because the induced EMF is proportional to dB/dt. When people first plotted the raw voltages for this component, it was positive and decaying and the convention for plotting dBz/dt data was born.
7.2.7. MT data¶
Fourier Convention
The NSEM GIF codes are formulated to use a \(i\omega t\) convention for the timedependence. However, this may not match the convention used by data loaded into GIFtools from other sources. MT data loaded from EDI files generally uses the MT/EMAP data interchange standard , which is \(+i\omega t\). If the convention used for the data does not match that of the code, it is unlikely that the inversion will be able to fit the data and return meaningful results.
We can determine the convention used by the data by examining the data. If data are represented using the \(\boldsymbol{+i \omega t}\) convention and are in a righthanded coordinate system, then we expect:
at background locations: \(Z_{xy} \sim \dfrac{i \omega \mu}{k} \;\;\; \textrm{and} \;\;\; Z_{yx} \sim \frac{ i \omega \mu}{k} \;\;\; \textrm{where} \;\;\; k = \sqrt{i\omega \mu \sigma}\)
\(Re[Z_{xy}] > 0\), \(\; Im[Z_{xy}] > 0\) and \(\phi_{xy} \in [0^o, \; 90^o]\) (\(\sim 45^o\) for a halfspace)
\(Re[Z_{yx}] < 0\), \(\; Im[Z_{yx}] < 0\) and \(\phi_{yx} \in [90^o, \; 180^o]\) (\(\sim 135^o\) for a halfspace)
If data are represented using the \(\boldsymbol{i \omega t}\) convention (GIFtools) and are in a righthanded coordinate system (GIFtools), then for these data we expect:
at background locations: \(Z_{xy} \sim \dfrac{i \omega \mu}{k} \;\;\; \textrm{and} \;\;\; Z_{yx} \sim \frac{ i \omega \mu}{k} \;\;\; \textrm{where} \;\;\; k = \sqrt{i\omega \mu \sigma}\)
\(Re[Z_{xy}] > 0\), \(\; Im[Z_{xy}] < 0\) and \(\phi_{xy} \in [0^o, \; 90^o]\) (\(\sim 45^o\) for a halfspace)
\(Re[Z_{yx}] < 0\), \(\; Im[Z_{yx}] > 0\) and \(\phi_{yx} \in [90^o, \; 180^o]\) (\(\sim 135^o\) for a halfspace)
As we can see, to switch from one convention to another we must:
Multiply the imaginary components of all impedance tensor elements by 1
Multiply the phase values for all elements of the impedance tensor by 1
Data Convention
MT data represent the entries of the impedance tensor (\(\mathbf{Z}\)) where:
MT data for GIF codes uses a labeling convention where X = Northing, Y = Easting and Z = Down. Superscript (1) denotes fields resulting from plane waves with electric fields polarized along the X (Northing) direction, and (2) denotes fields resulting from plane waves with with electric fields polarized along the Y (Easting) direction. The labeling of the impedance tensor elements is given by:
\(Z_{xx}\) is ZNorthingNorthing
\(Z_{xy}\) is ZNorthingEasting
\(Z_{yx}\) is ZEastingNorthing
\(Z_{yy}\) is ZEastingEasting
For more on this, see the E3DMT manual
7.2.8. ZTEM data¶
Data Convention
ZTEM data represent transfer functions \(\mathbf{T_{zx}}\) and \(\mathbf{T_{zy}}\) where:
ZTEM data for GIF codes uses a labeling convention where X = Northing, Y = Easting and Z = Down. Superscript (1) denotes fields resulting from plane waves with electric fields polarized along the X (Northing) direction, and (2) denotes fields resulting from plane waves with with electric fields polarized along the Y (Easting) direction. The labeling of field elements is such that:
\(H_{x}\) is the component of the magnetic field along the Northing direction
\(H_{y}\) is the component of the magnetic field along the Easting direction
\(H_{z}\) is the component of the magnetic field in the down direction
For more on this, see the E3DMT manual
7.3. Units¶
Here, we define the physical property and data units used by each code.
Physical Property Definitions:
\(\boldsymbol{\rho :}\) density
\(\boldsymbol{\kappa :}\) susceptibility or effective susceptibility
\(\boldsymbol{\sigma :}\) conductivity
\(\boldsymbol{\eta :}\) Intrinsic chargeability. If linear approximation is chosen, any convention of intrinsic or integrated chargeability is acceptable. However, it will change the units of the corresponding data.
Fields and Data Types:
\(\mathbf{E}:\) Electric field
\(\mathbf{J}:\) Current density
\(\mathbf{H}:\) Magnetic field intensity (auxiliary field)
\(\mathbf{B}:\) Magnetic flux density
\(\partial \mathbf{B}/\partial t:\) Timederivative of the magnetic flux density
\(Z_{ij}:\) The ijth element of the impedance tensor
\(T_i:\) The x or y component of the ZTEM transfer function
Units Definitions:
\(mGal:\) milliGal
\(T:\) Teslas
\(S:\) Siemens
\(V:\) Volts
\(A:\) Amperes
\(ppm:\) parts per million
Important
Make sure you scroll all the way to the right within the table to see all information pertaining to a particular code.
Type 
Name 
Versions 
Property Units 
Data Units 

Gravity 
GRAV3D 
5.0, 5.1, 6.0 
\(\rho = g/cm^3\) 
mGal 
Gravity 
GRAV PDE 
octree 
\(\rho = g/cm^3\) 
mGal 
Magnetic 
MAG3D 
5.0, 5.1, 6.0 
\(\kappa = SI\) 
nT 
Magnetic 
MAG PDE 
octree 
\(\kappa = SI\) 
nT 
MVI 
MVI 
3.0 
\(\kappa = SI\) 
nT 
DC/IP 
2D DCIP 


DC/IP 
3D DCIP 


DC/IP 
DCIP octree 
octree 


FDEM 
EM1DFM 
1.0 


FDEM 
EH3D 



FDEM 
E3D 
octree 


TDEM 
EM1DTM 
1.0 
\(\sigma = S/m\) 

TDEM 
H3DTD 



TDEM 
TDoctree 
octree 


MT/ZTEM 
MTZ3D 


MT/ZTEM 
E3DMT 
octree ver. 1 


MT/ZTEM 
E3DMT 
octree ver. 2 

7.3.1. DC data units¶
DC data are represented by the measured voltage (\(\Delta V\)) normalized by the transmitter current (\(I\)). Thus the units for DC data are V/A.
7.3.2. IP data units¶
Generally, IP data are represented by the measured offtime voltage (\(\Delta V (t)\)) normalized by the transmitter current (\(I\)); which would be in units for V/A. In this case, the user is forward modeling with and inverting for the intrinsic chargeability (\(\eta \in [0,1]\)). If the user wishes to implement the linear model approximation, then other definitions of intrinsic chargeability (mV/V) or integrated chargeability (ms) can be used to define the chargeability. However, the units for the resulting IP data would no longer be V/A in this case.
7.3.3. EM1DTM data units¶
The EM1DTM code represents components of the dB/dt response as the induced voltage within an arbitrarily oriented receiver coil. Where \(\mathbf{m}\) is the dipole moment for the receiver coil, \(V = \mathbf{m} \cdot d\mathbf{B}/dt \,\) (no minus sign) because the coordinate system is lefthanded! Thus a +ve voltage corresponds to a +ve dB/dt response in the direction defining the dipole moment of the receiver coil (which is also defined in a lefthanded coordinate system).
7.3.4. Impedance tensor (MT) data units¶
MT data represent the entries of the impedance tensor (\(\mathbf{Z}\)) where:
where 1 denotes fields resulting from plane waves with an electric field polarized along the x direction, and 2 denotes fields resulting from planes with with an electric field polarized along the y direction. For a 3D Earth, \(Z_{xy} = E_{x1}/H_{x2}\). Where the electric field units V/m and the magnetic field has units A/m, the units for elements of the impedence tensor is V/A.
Important
MT data generally use a labeling convention wherein X = Northing, Y = Easting and Z = Down.
7.3.5. Transfer functions (ZTEM) data units¶
ZTEM data represent the entries of a transfer function (\(\mathbf{T}\)) where:
where 1 denotes fields resulting from plane waves with an electric field polarized along the x direction, and 2 denotes fields resulting from planes with with an electric field polarized along the y direction. Thus by dimensional analysis, the units of the transfer function elements \(T_x\) and \(T_y\) are unitless.