Mathematics

Analysis of Geophysical Potential Fields: A Digital Signal by P. S. Naidu

By P. S. Naidu

While a few priceless info is hidden in the back of a mass of undesirable info we regularly hotel to details processing utilized in its wide feel or particularly to sign processing whilst the beneficial details is a waveform. In geophysical surveys, particularly in aeromagnetic and gravity surveys, from the measured box it's always tough to claim a lot approximately anyone particular goal until it truly is as regards to the skin and good remoted from the remaining. The electronic sign processing strategy could let us to deliver out the underlying version of the resource, that's, the geological constitution. the various instruments of dsp resembling electronic filtering, spectrum estimation, inversion, etc., have came upon large functions in aeromagnetic and gravity map research. There are different rising functions of dsp within the sector of inverse filtering, 3 dimensional visualization, etc.The goal of this e-book is to convey various instruments of dsp to the geophysical neighborhood, specifically, to those that are getting into the geophysical career. additionally the training geophysicists, desirous about the aeromagnetic and gravity facts research, utilizing the commercially to be had software program applications, will locate this e-book invaluable in answering their questions about "why and how?". it's was hoping that this kind of history might let the practicing geophysicists to understand the clients and obstacles of the dsp in extracting important details from the capability box maps. the themes lined are: capability box signs and versions, electronic filtering in dimensions, spectrum estimation and alertness, parameter estimation with mistakes bounds"

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Additional resources for Analysis of Geophysical Potential Fields: A Digital Signal Processing Approach

Sample text

Y0. ob. (x0. y0. z0) The Fourier transform of Punobs(XO,Yo,Zo) is a separable function of the type, P1 (u, v)f(z0) exp(sz0) wheref(z0) is any periodic function with integer number of periods within the vertical extent of the source layer. The implication of this observation is that in any 3D modelling, any amount of unobservable component may be appended to the model without affecting the observed field. 8. The prism is just below the surface. The observation plane is h units above the surface into free space.

As a note of caution it may be mentioned that unless the size of the signal matrix is large (several times the depth expressed in units of sampling interval) there may be serious truncation and aliasing errors [17]. In the above computations we have used different matrix sizes and compared the results with those obtained directly from the formula given in Ref. [19]. The frequency domain approach for the potential field signal has been applied to more complex 3D source models such as a polyhedron with triangular facets [20].

2. We give the final result, a(" exp( - j j. Yi-I)]. Substituting Eq. 53)into Eq. 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.

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