Migration versus Inversion in Electromagnetic Imaging Technique

Abstract

One of the most challenging problems in electromagnetic (EM) geophysical methods is developing fast and stable methods of imaging inhomogeneous underground structures using EM data. In our previous publications we developed a novel approach to this problem, using EM migration.In this paper we demonstrate that there is a very close connection between the method of EM migration and the solution of the conventional EM inverse problem. Actually, we show that migration is an approximate inversion. It realizes the first iteration in the inversion algorithm, based on the minimization of the residual field energy flow through the profile of observations. This new theoretical result opens a way for formulating a new imaging condition. We compare this new imaging condition with the traditional one, obtained for simplified geoelectrical models of the subsurface structures.This result also leads to the construction of a solution of the inverse EM problem, based on iterative EM migration in the frequency domain, and gradient (or conjugate gradient) search for the optimal geoelectrical model. However, the authors have found that in the framework of this method, even the first iteration, based on the migration of the residual field, generates a reasonable geoelectrical image of the subsurface structure. IntroductionOne of the most challenging problems in electromagnetic (EM) geophysical methods is developing fast and stable methods of imaging inhomogeneous underground structures using EM data. Solution of this problem is important for many practical applications ranging from mineral exploration to waste and building site characterization. In the papers (Zhdanov et al., 1995) and (Zhdanov et al., 1996) and the references therein we have developed a novel approach to EM imaging based on the notion of EM migration. The method includes downward continuation of the observed field or one of its components in reverse time and application of the corresponding imaging conditions. However, until recently the relationship between EM migration imaging and traditional EM inversion have remained unexplored. The conventional EM inversion means a method which predicts the geoelectrical model generating the theoretical data closed to observations. The EM migration introduced in our previous publications constructed an image of subsurface geoelectrical structures, and there was no guarantee this image, if included in a geoelectrical model, would give rise to theoretical EM fields that matched those observed. Meanwhile, Tarantola (1987) demonstrated that seismic wave migration, which was the prototype for EM migration, can be treated exactly as the first iteration in some general wave inversion scheme. In this paper we formulate an important new result: EM migration, as the solution of the boundary value problem for the adjoint Maxwell's equation in frequency domain, can be clearly associated with the inverse problem solution. In other words, we prove that a geoelectrical model constructed on the basis of migration images would actually generat...

Interpretation of the short period variations in geomagnetic anomalies of Shaanxi region

“…The obtained conductivity structures by our inversion agree with the results in the paper of Zhdanov and Traynin (1997), it indicates that the our program has same good result in the inversion of MV sounding data. The optimal value of ko can be calculated by that the residual field energy is the function ofko and the derivative of residual field energy to ko is equal to 0.…”

“…The method presented by Zhdanov and Traynin (1997) will be used in our investigation. It can be briefly described as following.…”

“…Supposing that the model of conductivity distribution Orb(X, Z) is given, the electro-magnetic fields corre- lWlJoG~ Ey H~ OG~,, b , According to the definition by Zhdanov and Traynin (1997), the migrated residual field E~ can be written as: Supposing that the model of conductivity distribution Orb(X, Z) is given, the electro-magnetic fields corre- lWlJoG~ Ey H~ OG~,, b , According to the definition by Zhdanov and Traynin (1997), the migrated residual field E~ can be written as: …”

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A temporary profile from Shiquan in the southern part of Shaanxi Province to Ningxian in Gansu Province for observation of geomagnetic short period variations was set up. The inversion method (Zhdanov, Traynin, 1997) which is based on the minimum of the total energy of the residual field between observational electro-magnetic field and the calculated theoretical field of conductivity model and the conception of migrated residual field is introduced into our inversion of the data of magneto-variation sounding. According to the theory of multi-scale analysis of wavelet transform, the components affected by regional origin in the region is extracted in this paper.

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Increasing the sensitivity of controlled-source electromagnetics with synthetic aperture

“…The streamer system has the potential of reducing acquisition cost and providing denser receiver spacing. The dense receiver spacing is crucial for many techniques such as CSEM migration (Zhdanov et al, 1995(Zhdanov et al, , 1996Zhdanov and Traynin, 1997), up-down decomposition, and CSEM interferometry (Wapenaar et al, 2008;Fan et al, 2009;Hunziker et al, 2009Hunziker et al, , 2010. One drawback, however, is the bigger loss of energy in the sea water because the source and receiver are near the sea surface.…”