On The Validity Of The Use Of The Upward Continuation Integral For Total Magnetic Intensity Data

Abstract

Abstract The integral solving the Dirichlet problem for a plane, known as the “upward continuation integral” to exploration geophysicists working with magnetic and gravity fields, is sometimes misunderstood. Recently, some geophysicists have commented that its use in continuing ΔT, the component of the total intensity anomaly in the direction of the earth's normal field, is suspect, the thought being that only components normal to the surface can be so continued. The integral in question is (1)ΔT(x,y,z)=−z2π⋅∫−∞∞∫−∞∞ΔT(α,β)dαdβ[(x−α)2+(y−β)2+z2]3/2, where ΔT(α, β) represents measured total intensity values on the plane of observations z=0, in a right handed rectangular coordinate system in which the z axis is positive vertically downward.