Question

Relation between apparent angle of dip and real angle of dip

Answer 1

Angle of Dip δ is the angle in the vertical plane aligned with magnetic north (the magnetic meridian) between the local magnetic field and the horizontal.

Angle of Declination θ is the angle between the magnetic and geographic meridians, or the angle in the horizontal plane between magnetic north and true north.

In the magnetic meridian the vertical and horizontal components of the magnetic field are Bv=Bsinδ and Bh=Bcosδ. The projection of the horizontal component Bh onto the geographic meridian is Bg=Bhcosθ.

The plane perpendicular to the geographic meridian makes angle 180∘−(90∘+θ)=90∘−θ with the magnetic meridian. The projection of Bh onto this plane is Bp=Bhcos(90∘−θ)=Bhsinθ.

The apparent angles of dip in the geographic meridian and the plane perpendicular to it are given by

tanδ1=BvBg

tanδ2=BhBp

Therefore

tanδ1tanδ2=BpBg=BhsinθBhcosθ=tanθ

θ=tan−1(tanδ1tanδ2)