 # Interpretation of Aeromagnetic Maps

## Excerpt

BY V. VACQUIER

I. COMPUTATION OF ANOMALIES DUE TO VARIABLE POLARIZATION OF A FLAT BASEMENT

Magnetic anomalies of geologic origin are usually due to extended bodies that cannot be represented by isolated poles or linear arrays of poles and dipoles. In this book, the idealized bodies for which anomalous total magnetic intensity is computed are prisms of infinite length with vertical sides. The upper surface of the prism is horizontal, and the total magnetic intensity is computed on a horizontal plane above it. The polarization of the prism is uniform and is directed along the earth's magnetic field. Because the polarization is constant with depth, one can express the anomalous magnetic intensity as a surface integral of the product of two functions of position, the polarization I (α, β) which is assigned, and an irrational algebraic function U (α, β, δ) (Tables 11-26). The total magnetic intensity due to the prism can be written:

ΔT = ∫∫ I (α,β) U (α,β,δ) dα dβ, (1)

where α and β are respectively the north and east co-ordinates on a plane containing the upper surface of the prism, and 5 the complement of the dip angle which is assumed constant over the area of any one map. The magnetic intensity Δ T is computed at a height h = 1 immediately above the origin α = β = 0. The co-ordinates α and β are measured in terms of the depth of burial h which is taken as unity.

The integral can be evaluated approximately as a finite sum by dividing the α, β, plane into small squares, estimating the average values of the functions I and U for each square and summing up the individual products:

ΔT ≅ ∑ ∑ Ī(α,β)Ū(α,β,δ). (2)

On Figure 6, the function U (α, β, δ) is contoured on a square grid. The contours are shown dashed, and the grid is shown light. Average values of the U function for each square are inserted. The grid so constructed can be traced on a transparent template and placed on a plot of the polarization function I (α, β) shown in heavy contours. The map of the polarization is divided into squares of the same size as the squares on the template. They are drawn heavy in Figure 6. An average value for the polarization can be assigned each square. To compute the total magnetic intensity on a plane a unit distance above the surface of the polarization map, the template is oriented so that the a axis points north on the polarization map; then, having matched the squares, the products of Ī and Ū for each square are computed and added. To compute the magnetic intensity at the next grid corner the template is moved and the procedure repeated.

To compute the magnetic intensity for a prism of finite length, the computation can be carried out for two prisms of infinite length and same cross section buried at . . .

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