Conjugate complex variables method for the computation of gravity anomalies

Using conjugate complex variables, a generalized method is presented to derive formulas to calculate first- and higher-order derivatives of the gravity potential due to selected mass models. Double integrals in the computation of gravity-gradient anomalies are transformed into complex contour integrals. Analytical expressions for higher-order derivatives of the gravitational potential in arbitrary directions due to two-dimensional (2-D) polygonal mass models are derived. The method is extended to 2-D polygonal bodies whose density contrasts vary with depth and horizontal distance and can be generalized to deal with 2-D bodies of any shape. The vertical gravity field and its first derivatives due to a homogeneous radially symmetric body are also computed using conjugate complex variables. Derivation of gravity and gravity gradient formulas generally is greatly simplified by the use of complex variables.