Abstract

The theoretical basis for applying the upward-continuation integral,  
T(x,y,z)=z2πT(α,β)dαdβ[(xα)2+(yβ)2+z2]3/2,z0,
to total magnetic intensity data T(α, β) measured on the plane z=0 has been recently reviewed by Henderson (1970). To perform upward continuation in the spatial domain, weights or coefficients obtained by numerical evaluation of equation (1) (Peters, 1949; Henderson, 1960; Fuller, 1967) may be convolved with the total intensity anomaly T(α, β) to produce T(x, y, z) at heights z<0 (for z positive downward). The accuracy of upward continuation is, therefore, dependent on the validity of the numerical coefficients and of the assumptions required to show that T(α, β) satisfies the conditions of the Dirichlet problem for a plane. These assumptions are that the quantity sensed by a total-intensity magnetometer is in the direction of the earth's normal field and that this direction is invariant over the area of interest.
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