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ambiguity in geophysical interpretation_dileep p allavarapu

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National Geophysical Research Institute- Gravity student Ideas about Ambiguity in Gravity, Magnetic or any Geophysical interpretation_dileep p …

National Geophysical Research Institute- Gravity student Ideas about Ambiguity in Gravity, Magnetic or any Geophysical interpretation_dileep p allavarapu

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  • 1. Ambiguity in Geophysical Interpretation:Dileep P Allavarapu(student of Dr.Bijendra Singh)(dpa.teaching@gmail.com)School of Gravity, Gravity Observatory-NGRIAmbiguity is an in built unsolvable problem in Geophysics? Or can be approximated?Ambiguity is an in built problem in Geophysics which is not solved or approximated since five decades.Because of unknown geometrical and parametrical constrains in each data set. Without solving thefundamental issue of constrains; the interpretation of processed data is not hundred percent useful tounderstand what exactly in underground.Why because basic consideration in processing and interpretation of data is mis-correlation of data withtopography is directly related to source parameters. It may or may not be true hundred percent Natureof parameter what measured in survey is very important in later stage. If it is having radial nature(cRn)and your approximations are linear (cR) with single source parameters will be quite wrong solutions.To overcome the problem radiality approximation is required which can be possible through wavenumber domain analysis of curvilinear transformation operations like continuation (shift of signal overthe space) along with derivative (decomposition of signal over the space) interpretation will give a misfit index. And the transformations are correlated with integral approximations of equivalent parametergeometries like surface slice to volume slice. Further design of algebra of non linear approximations tofind mis fit deconvolution(MFDcon) relationship will leads to success of solving or at least approximationof ambiguity in geophysics.A part of process ,data handling is given here that any (lp+q)s dimensional data (1<p<m,1<q<n,1<s<k) canbe split into (jp)s plus (iq)s data such that (jp)s as a signal in (iq)s space (one dimension may corresponds totime also) .In space , signal have harmonics of real and complex LAE functions, then at least onetransform will be represented asJ’p=LAET((jp)s ) = Integral/Sum[(jp)s )Log complex((iq)s ) Arthamatic complex((iq)s ) Exponential complex((iq)s )]Completeness of expression will be achieved through drastic-logarithmic, dynamic-arithmetic termsalong with complex static-exponential terms.Here J’p, (jp)s and ((iq)s obeys boundedness of group and ring with respect to arithmetic operations.(jp)s Sum (jp)s (iq)s D(iq)s =0For each static p, dynamic q operated to get relationship between nature of tilt (grad), (jp)s (iq)s andshift in dimension (radial), D(iq)s
  • 2. Interpretation of shift in dimension of a signal (jp)s over the space (iq)s and fit fall of defined shift, D(iq)srevels the orientation and strength of origin, phase of fit fall corresponds to orientation and amplitudecorresponds to strength.Its application in simplest form:In potential field data analysis, signal (jp)s of force or energy(p=1) over a space (iq)s of 3D geometry(q=1,2,3).
  • 3. By using continuation, movement of force (jp)s about vertical z(i3) will be possible for same horizontalcoordinates.Further derivative of force and convolution will allow to locate topology of the source ,fall in fit oftopology from original data set to rest of data sets revels the source topology information , fall naturerevels location error, fall magnitude revels parameter error.Iteration of technique gives a direct inversion of force for geometric contributing parameter.Analyzed (spectral) energy set (j2 )s for a force set (jp)s will be utilized to orient the source (some of (j2 )will be repeated such that 1<s<<k). At the same time inverted to topology sets revels that nature ofparameter (same topological nature can be observed for same parameter, if parameter changedtopology might get affected).