By Prabhakar S. Naidu and M.P. Mathew (Eds.)
While a few worthy info is hidden in the back of a mass of undesirable details we regularly inn to details processing utilized in its large experience or in particular to sign processing whilst the precious details is a waveform. In geophysical surveys, specifically in aeromagnetic and gravity surveys, from the measured box it's always tough to assert a lot approximately anybody particular objective except it really is with regards to the outside and good remoted from the remaining.
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Extra info for Analysis of Geophysical Potential Fields
W) = I,K(u. ~. w) Mz(U. ~. w) = IzK(.. ~. w) where K(u,v,w) is the Fourier transform of the susceptibility variation. Hence, [l'uMx + j v M y - sMz] -- K(u, v, w)(l'UI x + j v l y - slz) -- K(u, v, w)I. 45) 3D source models 41 Using Eq. 45) in Eq. 46) As a consequence of non-uniqueness in potential field interpretation or principle of annihilation , an interesting interpretation of Eq. 41) follows. 41) may be looked upon as a Laplace transform, Fz(u , v, h -- O) - 27rG f o ~ P(u, ~, zo) ~p(-,z0) az0 Consider the possibility that P(u, V, Zo) = P0(u, v)cos(pz0)exp(sz0) then the above integral is simply a delta function leading to Fz(u,v,h = 0) = 0 or fz(x,y,h = 0) = 0 for any p 4= 0, independent of the actual density distribution.
It is easy to extend the concept of singularity to any two-dimensional model with polygonal cross-section. In fact this approach was taken in Ref. [ 15] for the estimation of the comers of a polygon. We return to this topic in Chapter 5 where we deal with parameter estimation. 5. A layer of rocks is faulted along ff. The infinite layer is now reduced to two semiinfinite layers. We consider the gravity effect of the left half and right half semi-infinite layers. 4. 1. Potential field in frequency domain We describe two-dimensional signals generated by idealized models of excess mass or magnetization in the frequency domain.
19) may be rewritten as follows: O(x,y,z -- O) -- Olo(X,Y,Z -- O) + O u p ( X , y , z -- O) where q51o(x, y, z -- O) -- G dxo dyo dzo oo . 20) Let us now replace the density function in Eq. 20) with its Fourier integral representation (Eq. 2b). 2. Magnetic potential We now derive the magnetic potential inside a source filled space. 22) where mx, my and m~ are functions of x0, Y0, and z0. As in the case of gravity potential, we divide the entire space into two halves and express the potential as a sum of the contributions from two semi-infinite half spaces.