recall that the proton precession magnetometer makes measurements of the total field, not the vector...

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. cos sin i H i Z F A A AT

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In this diagram F ET 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 F ET.

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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.

cossin iHiZF AAAT

Page 2: Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total

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

22GFF

LMf

fFE 4874.23

The proton precession magnetometer measures the scalar magnitude of the earth’s main field.

Page 3: Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total

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.

Page 4: Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total

Magnetic Elements for your location

F is known

http://www.ngdc.noaa.gov/cgi-bin/seg/gmag/fldsnth1.pl

Page 5: Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total

In most applications the anomalous field FA is much smaller than the main field FE.

Page 6: Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total

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.

quantity. vector anot quantityscalar a is T

. isanomaly magnetic The

EET FFT

Page 7: Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total

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.

Page 8: Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total

In the case where FA is large the projection FAT is significantly different from T.

Page 9: Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total

Let’s zoom in for a closer look at the tip of FE.

quantity. vector anot quantityscalar a is T

. isanomaly magnetic The

EET FFT

Page 10: Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total

Horizontal line parallel to earth’s surface

i is the inclination of the earth’s main magnetic field. is the angle of FA relative to the earth’s main field FE.

TFET

Page 11: Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total

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.

ET E ATT F F F

Page 12: Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total

The horizontal and vertical projections of FA

Consider the significance of the terms cos and sin in the previous expression.A AF F

Page 13: Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total

The horizontal and vertical projections of FA appear in the expansion of FAT = FAcos(-i).

Page 14: Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total

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.

sin cosAT A AF Z i H 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.

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