soboleva o.  

The resistivity logging in multyscale medium with lognormal conductivity

The effective coefficients of a conductivity field for estimating an average value of the current density and its variance for the problem of resistivity logging in a multi-scale isotropic porous medium are considered. The problem is solved by the method of subgrid modeling. We use a second-order term in perturbation expansion in scale of measurement. The results are verified by the $3D$ numerical modeling and compared with another methods

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