Resistivity imaging by time domain electromagnetic migration (TDEMM)

Journal ArticleOne of the most challenging problems of electrical geophysical methods is the interpretation of time domain electromagnetic (TDEM) sounding data in the areas with the horizontally inhomogeneous geoelectrical structures. This problem is of utmost importance in mining exploration and environmental study, in particular, in the case of sounding conducted in the transmitter offset or slingram mode. The conventional 10 EM inversion technique cannot solve this problem, because the observed data are strongly distorted by horizontal conductivity inhomogeneities. The multidimensional EM inversion techniques existing today can handle only simple models, require repetitive forward modeling solutions, and therefore are very time consuming. We developed a new approach to the interpretation of TDEM data over inhomogeneous structures based on downward extrapolation of the observed electromagnetic field in reverse time (the time domain electromagnetic migration). Numerical solution of this problem is provided by an electromagnetic analog of the Rayleigh integral. TDEM migration transforms EM data, observed on the surface of the Earth, into immediate geoelectrical images of geological cross sections. This transformation is very fast (requiring only a few seconds of CPU time on PC) and stable to the random noise in the data. The numerical results of rapid inversion based on the time domain electromagnetic migration illustrate the property of migration described above. This method has also been applied to waste site characterisation. We have analysed the data obtained as a result of high density TDEM profiling survey with the Geonics EM47 along the set of profiles, intersecting Cold Test Pit waste site within the Radioactive Waste Management Complex (RWMC) at the Idaho National Engineering Laboratory (INEL). Time domain electromagnetic migration and resistivity imaging made it possible to outline the conductive sections of the pit filled with the waste

On separable Fokker-Planck equations with a constant diagonal diffusion matrix

We classify (1+3)-dimensional Fokker-Planck equations with a constant diagonal diffusion matrix that are solvable by the method of separation of variables. As a result, we get possible forms of the drift coefficients $B_1(\vec x),B_2(\vec x),B_3(\vec x)$ providing separability of the corresponding Fokker-Planck equations and carry out variable separation in the latter. It is established, in particular, that the necessary condition for the Fokker-Planck equation to be separable is that the drift coefficients $\vec B(\vec x)$ must be linear. We also find the necessary condition for R-separability of the Fokker-Planck equation. Furthermore, exact solutions of the Fokker-Planck equation with separated variables are constructedComment: 20 pages, LaTe

On separable Schr\"odinger equations

We classify (1+3)-dimensional Schr\"odinger equations for a particle interacting with the electromagnetic field that are solvable by the method of separation of variables. As a result, we get eleven classes of the electromagnetic vector potentials of the electromagnetic field $A(t, \vec x)=(A_0(t, \vec x)$, $\vec A(t, \vec x))$ providing separability of the corresponding Schr\"odinger equations. It is established, in particular, that the necessary condition for the Schr\"odinger equation to be separable is that the magnetic field must be independent of the spatial variables. Next, we prove that any Schr\"odinger equation admitting variable separation into second-order ordinary differential equations can be reduced to one of the eleven separable Schr\"odinger equations mentioned above and carry out variable separation in the latter. Furthermore, we apply the results obtained for separating variables in the Hamilton-Jacobi equation.Comment: 30 pages, LaTe

To The Issue Of Termination Of Proceedings On Administrative Case

The article focuses on disputable issues of law enforcement concerning legislation which regulates release from administrative liability

Strong field lensing by Damour-Solodukhin wormhole

We investigate the strong field lensing observables for the Damour-Solodukhin wormhole and examine how small the values of the deviation parameter $\lambda$ need be for reproducing the observables for the Schwarzschild black hole. While the extremely tiny values of $\lambda$ indicated by the matter accretion or Hawking evaporation are not disputed, it turns out that $\lambda$ could actually assume values considerably higher than those tiny values and still reproduce black hole lensing signatures. The lensing observations thus provide a surprising counterexample to the intuitive expectation that all experiments ought to lead to the mimicking of black holes for the same range of values of $\lambda$.Comment: 6 page