MAGNETIC DISTURBANCE 1373 
THEORETICAL CONSIDERATIONS 
The magnitude and direction of the resultant magnetic field near 
the casing head of a vertical string of pipe depends on the physical com- 
position and proportions of the metal, the mechanical and thermal stresses 
involved, the perpendicularity of its vertical axis, the intensity and di- 
‘rection of the earth’s magnetizing field, and the physical and magnetic 
characteristics of the subsurface media. 
Referring to Figure 1, let us consider the vertical string of casing gh, 
having its major axis lying in YY’. It is evident that by induction the 
terrestrial magnetic field will establish a negative pole near the, upper 
end of the casing and a positive pole near its lower end. Assuming the 
surrounding media to have unit permeability, and denoting the positive 
and negative pole strengths by +m and —m c. g. s. units respectively, 
we have 
Se pe * (a — d?) kZ 
= AkZ (1) 
where d, is the external diameter of the casing in centimeters; 
d; is the internal diameter of the casing in centimeters; 
A is the cross-sectional area of the casing in square centimeters; 
k is the susceptibility of the casing material; 
Z isthe vertical component of the earth’s magnetic field in gauss. 
For our purposes we may regard the casing as a bar magnet having 
the length LZ centimeters and distance between poles / centimeters. The 
magnetic moment in c. g. s. units will be given by 
M =m (2) 
Let us consider the strength and direction of the anomalous field 
at the point P, lying in OX, caused by the vertical string of magnetized 
casing gh. The resultant force Ps at the point P will be determined in 
magnitude and direction by the vectors Pr and Pn, the former repre- 
senting the attractive reaction on a unit positive pole placed at P, caused 
by —m, and the latter representing the repulsive reaction of the pole, 
+m. The solution of the problem is simplified by solving for the vertical 
and horizontal components dZ and dH, after which the resultant force 
dR and the angle of inclination df may be readily determined. 
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