Transcript F AT is an approximation of T

Recall that the proton precession magnetometer
makes measurements of the total field, not the
vector components of the field.
Recall also that the total field can be derived from
other magnetic elements.
The formula below represents the anomalous total
field in terms of the horizontal and vertical
components of the anomalous field.
FAT  Z A sin i  H A cos i
Remember how the proton precession
magnetometer works. Protons precess about
the earth’s total field with a frequency directly
proportional to the earth’s field strength
M
GF
f 
F
2L
2
FE  23.4874 f
The proton
precession
magnetometer
measures the scalar
magnitude of the
earth’s main field.
In this diagram FET is is the vector sum of the earth’s main field
and the anomalous field associated with a buried dipole field. The
proton precession magnetometer measures the magnitude of FET.
Magnetic Elements for your location
F is known
In most applications the anomalous field FA
is much smaller than the main field FE.
In this case, the magnetic
anomaly is approximated as the
difference between the measured
field (FET) at some point and the
predicted value of the earth’s
main field (FE) at that point. This
anomaly is often referred to as T.
The magnetic anomaly is
T  FET  FE .
T is a scalar quantity
not a vector quantity.
53
FA
When FA (the anomalous field) is small, we consider the
difference T = FET - FE to be equivalent to the projection
of vector FA onto the direction of the main field.
In the case where FA is large the projection
FAT is significantly different from T.
Let’s zoom in for a closer look at the tip of FE. The magnetic anomaly is
T  FET  FE .
T is a scalar quantity
not a vector quantity.
Horizontal line
parallel to
earth’s surface
FET
T
i
is the inclination of the earth’s main magnetic field.
 is the angle of FA relative to the earth’s main field FE.
T  FET  FE  FAT
FAT is the projection of FA onto the direction of the main field FE, and
is considered equal to T, the scalar difference between FE and FET.
Consider the significance of the terms
FA cos  and FA sin  in the previous expression.
The horizontal and vertical projections of FA
The horizontal and vertical projections of FA
appear in the expansion of FAT = FAcos(-i).
In summary - FAT is an approximation of T,
the scalar difference obtained from
measurements of the total field (FET) made by
the proton precession magnetometer.
FAT  Z A sin i  H A cos i
For the purposes of modeling we work backwards.
Given a certain object, we compute the
horizontal (HA) and vertical (ZA) components of
the anomaly and combine them to obtain FAT - the
anomaly we obtain from the proton precession
magnetometer measurements.