Analytical Solution Research Of Long Linear Wire Source In Whole Space And Horizontal Uniform Half Space

With the development of geophysical electromagnetic exploration,it is positively significant for the theory of electromagnetic exploration and the development of detection technology to obtain exact solution of the long-term source of harmonic currents in the entire field and advance observation points in the frequency domain electromagnetic method from far zone to near zone.First of all,the dissertation which starts from the whole space proves that the vector magnetic position of the uniformly-distributed current linear wire source has no closed form solution with using the third Liouville theorem.By reflecting the sinusoidal representation of the harmonic current distribution closer to the actual situation,a closed-form exact solution of the long linear wire source is obtained.The accuracy of the exact formula has been verified by neglecting source point vector of the exact field and comparing with the original dipole expression under the whole field area.The comparison of exact function and dipole approximation function.The errors of the electric dipole approximation in free space and geological environment in the wet soil are analyzed.Then,by confirming the third kind of boundary region condition,adding convergence conditions and radiation conditions,Helmholtz equation boundary value problem and uniqueness theorem of solution are supplemented and the complete theorem which removes the restriction of positive coefficients has been strictly verified.Finally,the grounding long linear wire source on horizontal uniform ground is treated as the connecting condition of the ground-air interface,and the non-homogeneous Helmholtz equations are transformed to homogeneous equations.According to the distribution of the source,the properties of the Bessel function,the directivity of the reference dipole approximation and the closed-form solution of whole space long wire,the form of excitation Hankel transformation and the solution of longitudinal component of the electromagnetic field are determined.According to the uniqueness theorem,the correctness and uniqueness of the exact solutions in half-space are verified by using convergence conditions.These following conclusions are drawn.The near-field error of free space dipole approximation can not be ignored.The near-zone formula derived from dipole approximation for the near-field limit is not consistent with the definition of dipole approximation and cannot be applied in the near-field.The conductivity of the geological environment causes the wavelength of the source current to shrink,resulting the impossibility of dipole approximation in the far area.When the conditions are appropriate,the longitudinal component method commonly used to solve the passive space can also solve the problem with the source space.The longitudinal component method that directly solves the electric and magnetic fields has a simpler convergence condition than bit function on the media interface.It creates a convenient condition for solving the exact solution of the long linear wire source in the horizontal layered uniform half space in the future.