Ambiguity in Geophysics,Gravity,Magnetic,EM,MT Error reduction by Available applications Geosoft,Euler,Anaylitical,Equpotential,Spectral, Principal Components

1. DILEEP PVVSS ALLAVARAPU
Department of Geophysics-Andhra University.
Abstract:
Undoubtedly ambiguity or un-uniqueness is a in built problem in geophysical potential fields but above abstract title
is mind storming doubt in a graduate geophysicist, it is not a kind of criticism of great research minds and their
contributions to geophysics; it may be an ultra positive vision of a graduate geophysicist. Most of the geophysical
problems are non linear in nature ,while solving a graduate geophysicist transform it in to linear by set of assumptions
, finally obtained solution for transformed problem is a perturbed solution of real problem , it never be a solution for
real problem. Therefore perturbations introduced is a result of assumptions introduced. Nature of the geophysical
potential field is radial everywhere and not generated form a single ,simple ,regular geometry. While executing
most of the operations geophysical problem treated quite contradictory to its reality. Spectral and Variance analysis
assumes that field from numerous sources those follow regular geometry and confined to certain radial distance
bands , Homogeneity analysis assumes that field from numerous sources those follow regular geometry not confined
to certain radial distance bands dispersed everywhere , Continuation assumes that field from single irregular
geometry, …… likewise several assumptions lead to perturbed solutions of real problem.
A comprehensive treatment on obtained solution designed to de-assumption and discussed in this note.

2. Description of Depth solutions and Misfit index:
A typical model constructed to explain how a regular practice in description of sources varies in this note.
It varies from spectral analysis and variance or principal component analysis to continuation and moving window
deconvolution or euler analytical homogeneity analysis. Algorithm deals with canonical operations on vector-scalar
spaces to decompose correlated variables into standard form of un-correlated variables. By scaling the power
corresponding to wave number for un correlated distribution and orienting the axis for minimum variance such those
expressions must contain the terms of source depths and by gradients distribution with respect to observation and a
simplest model described below likely representing three main components corresponding to energy parameter ,
top depth ,bottom depth and figure informing the methodological base of the analysis .

3. An algorithm for refinement of Euler (or moving window deconvolution) default solutions also proposed as
follows later procedure for every level of continuation carried out.
If two or more potential field credentials used in same area of survey then the change in nature of components
(of depths) attributed to change in energy parameter of respective fields. Otherwise continuation is utilized to
replace it. Operational clarity and command on homogeneity analysis through existing continuation and euler
application in geosoft , enable to follow this.

4. Regarding the results of Continuation and Euler (or Moving Window Deconvolution ), If a particular source is
common in successive levels of continuation, it should have single set of final solutions rather than a two un-
matched sets of solutions after deconvolution; since Method of deconvolution is same. A kind of analysis is done
for misfit and gives two misfit index , Depth misfit and Uncertainty misfit.
If question rises “Why un-matched sets of solutions? “
Continuation mechanism is based on few assumptions that entire field is due to single source, the level of
continuation is not touching the source geometry and far from the influence of surroundings…..
In fact real situation is different from assumptions and reflect as miss fit.
If know how and in what manner these applications are wrong then it will be easy to find out what will be the
right solution. Characterstics of Fall (Misfit )in topology from original data set to rest of continued data sets
reveal the source topology information,
Fall (Misfit) nature/shape reveal location error, and
Fall (Misfit) magnitude reveal parameter error.
Iteration of technique will give a direct inversion of field for geometric-contributing parameters.
Here uncertainty in z-direction for each depth solution will play an important role in defining Mis-fit Index. It
gives the meaning that mis approximated depth during continuation at the rate of its uncertainties. Apart from
that depth solutions of original data set or mode taken as depth index.
Therefore Depth index, its Depth Misfit index and corresponding Uncertainty index are obtained in this stage.

5. Description of Energy parameter, Influence index:
Obtained depth solutions in the application are in un distinguishable way and by its expression always
refer to top depth of a source , therefore bottom depth of the same source refer by top depth of next
deep source. Therefore another tool of analysis is required, analytic signals of field and topography which
contain the information regarding change of energy parameter lies in a specific geometry of source and
inclusive effect of all such in un distinguishable way. In potential fields, equivalence and greens integral
application a great deal with the vertical component of the field to energy parameter contrast on the
surface to produce potential field equal to its contrast inside.
Iteration for energy parameter based on obtained depths is less ambiguous and if it combines with analytical
signal it may produce great agreement and it refer to Energy parameter index.
Therefore Energy parameter index, Field index and Topography index are obtained in this stage.

6. Index Algebra and Actuating solutions :
Index algebra involves the matlab programming of pseudo inversion; in relation to potential fields , obtained
depth solutions and its mis-fit index will not having an independent relationship withoout influence of energy
parameter change inside.
Therefore a consideration of both sets (Depth Solutions index, Depth Misfit index, Uncertainty index) and
(Energy parameter index, Field index, Topography index) is mandate. Finally their contributions estimated……..
Thereafter getting pseudo coefficients mode depth of original data set is replaced with real depth solutions of
original field or even same operation for certain continuation level avoid or enhance field from respective
depth bands .
If produced total field (by inputting credential in index algebra expression) have difference with respective
original field and that difference will be related to error in depth estimation. After getting error , depth
solution will be actuated.