Discrete forms of 3-D gravity and magnetic forward modeling operators

7-4-1 Discrete forms of 3-D gravity and magnetic forward modeling operators 

We return now to the full 3-D gravity inverse problem. We divide the domain D, filled with the masses of a density p (r), into Nm small rectangular cells, Dk, D — and assume that the density is constant within each cell, p (r) = Pk-, v Dk - 

Assume that we use small rectangular cells Dk- We denote the coordinates of the cell center as Tk= xk, yk,Zk), k = 1,. ..Nm, and the cell sides as dx, dy, dz. Also, we have a discrete number of observation points = (x ,y, 0), n = 1,. ..Nd. Using discrete model parameters and discrete data, wc can present the forward modeling operator for the gravity field, (7.68), as 

Wc apply formula (6.5) and again divide the domain D into small rectangular cells, Dk, D = assuming that magnetic susceptibility is constant 

Using Poisson s theorem, we rewrite the last formula in the equivalent form  

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