A weak approximation of stochastic time domain electromagnetic response of a conductive permeable sphere

Time domain electromagnetic (TDEM) response of a conductive permeable sphere is a main topic for good understanding and in developing past studies for detection and discrimination of buried metallic objects. Stochastic differential equation model is a valuable tool for stimulating real experience. In this paper, according to an Itô integral, we have obtained a weak approximation of stochastic TDEM response of permeable and nonpermeable sphere. We have used the deterministic solution of TDEM response of conductive permeable sphere by changing one of the variables that have been obtained from the boundary conditions of problem to random variable. By adding white noise to random variable and using stochastic integral, we have displayed stochastic time domain response of conductive permeable sphere. The Itô integral includes a factor that shows infirmity and intensity of noise which has been simply considered constant. Accordingly, we have showed the effect of noise for magnetic and nonmagnetic spheres. Numerical results from step and impulse response of TDEM have shown that the amount of this factor is different for the two types of spheres.