Electromagnetic field expressions in the wavenumber domain from both the horizontal and vertical electric dipoles

In this paper, we present wavenumber domain (WD) electromagnetic field expressions at any depth in a layered conductivity earth due to both the horizontal and vertical electric dipoles, which can be buried anywhere within the layered earth. In modeling controlled-source electromagnetic (CSEM) responses for a 2D conductivity structure with a 3D source, it is very common to separate electromagnetic fields into a primary field and a secondary field to avoid the source singularity. This secondary field scheme requires WD background fields at any depth for a layered conductivity structure. To obtain primary electromagnetic fields in the WD, one can calculate quasi-analytical primary fields in the space domain (SD) and then transform them into the WD. However, this SD method is not a very efficient method of calculation. With the use of Schelkunoff potentials, we derive the quasi-analytic expressions for the electromagnetic fields in the WD, i.e. the WD method. Numerical tests indicate that the WD method can give results with the same accuracy as the SD method, and furthermore, the WD method is much faster than the SD method. (paper)