Electromagnetic migration in the time domain

Time domain electromagnetic (EM) migration is based on downward extrapolation of the residual field in reverse time. In this section I will show that electromagnetic migration, as the solution of the boundary value problem for the adjoint Maxwell s equation, can be clearly associated with solution of the inverse problem in the time domain. In particular, I will demonstrate that the gradient of the residual field energy flow functional with respect to the perturbation of the model conductivity is equal to the vector cross-correlation function between the predicted field for the given 

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Zhdanov, M. S., and O. Portniaguine, 1997, Time domain electromagnetic migration in the solution of the inverse problems Geophysical Journal International, 131, 293-309. 

The definition of the electromagnetic migration field in time domain was introduced in the monograph by Zhdanov (1988). According to this definition, the migration field is the solution of the boundary value problem for the adjoint Maxwell s equations. For example, we can introduce the migration anomalous field E ", H " as the field, determined in reverse time t = —t, whose tangential components are equal to the anomalous field in reverse time at the surface of the earth S... 

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