Download e-book for iPad: Analysis of Geophysical Potential Fields: A Digital Signal by P. S. Naidu

By P. S. Naidu

Whilst a few necessary info is hidden at the back of a mass of undesirable details we regularly inn to details processing utilized in its large feel or particularly to sign processing whilst the invaluable details is a waveform. In geophysical surveys, particularly in aeromagnetic and gravity surveys, from the measured box it is usually tricky to claim a lot approximately anybody particular objective until it truly is as regards to the outside and good remoted from the remaining. The electronic sign processing procedure may let us to carry out the underlying version of the resource, that's, the geological constitution. the various instruments of dsp reminiscent of electronic filtering, spectrum estimation, inversion, etc., have stumbled on vast functions in aeromagnetic and gravity map research. There are different rising purposes of dsp within the sector of inverse filtering, 3 dimensional visualization, etc.The goal of this e-book is to convey a number of instruments of dsp to the geophysical neighborhood, particularly, to those that are coming into the geophysical career. additionally the practising geophysicists, concerned with the aeromagnetic and gravity facts research, utilizing the commercially on hand software program applications, will locate this e-book priceless in answering their questions about "why and how?". it's was hoping that this type of historical past could let the training geophysicists to understand the customers and boundaries of the dsp in extracting beneficial info from the aptitude box maps. the subjects coated are: capability box signs and types, electronic filtering in dimensions, spectrum estimation and alertness, parameter estimation with errors bounds"

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Such fictitious line sources are presumed to have a frequency dependent radiation strength equal to +j(Gp/uZ)sgn(u). The position of the line source is naturally a point of singularity of the potential field. In the same manner the singularities for a fault may be found by examining the expression (Eq. 34). They are located at (0, h), (0, h + H), (0, h + Ah), and (0, h + Ah + H). The fictitious line sources at the points of singularity possess strength equal to +j(Gp/u2)sgn(u). The concept of singularity of a potential field has been widely discussed by several Russian scientists [11-14].

We replace mx, my and m~ with their respective Fourier integral representation (see Eq. 2b)). 24) The Fourier transforms M up(u, v, w), ... and MJ~ v, w ) , . , are defined as in Eq. 21). When the upper half space is filled with air of negligible density the second term in Eqs. 23) vanishes. 3. 1. Line source Consider a line source (horizontal) with density p and cross-section dx0dz0. The line source is located at (x0, z0). 2). 25) Note that the potential field due to a line source has a singularity at ( x - x0, Z -- Zo).

52) and using the result in Eq. 43), we can now write down the Fourier transform of the gravity field at the observation plane: 47 3D source models m m l 84 Fz(u, v, h) = Gpo e x p ( - s h ) exp(-j(udci_l + v~i_, )) 1 jv ~o o sin c(wc) s -jw • dw The last integral in the above equation is evaluated as in Eq. 48). 54a) This is valid when v 4: 0. Similarly we can derive an expression valid for u 4 : 0 and when u = v - 0. This we will leave as an exercise for the reader. The aeromagnetic field (total field) of the polygonal prism, in particular, its Fourier transform may be obtained from Eq.

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