Forward Modeling of Frequency_Domain Response of the Vertical Magnetic Component of Electromagnetic Field from Horizontal Magnetic Dipole Source over Layered Earth Models

Summary Geo-electromagnetic (EM) forward modeling is a scientific accepted tool for understanding complex behavior of EM wave in the earth, and can be used for the purpose of inverse modeling, and also, for evaluation of geological interpretations based on EM field measurements. There are different EM forward modeling programs, which are capable of computing responses of electric and magnetic components of the EM field, generated from different dipole sources with variable source-receiver configurations. In this paper, an available forward modeling algorithm, coded in Fortran 77 and called “EMDPLER”, is used for computing frequency domain response of the vertical magnetic component of the EM field, generated from a horizontal magnetic dipole source over different one-dimensional (1-D) layered Earth models. Thus, by conducting the forward modeling code on different 2- and 3-layer earth models with different resistivity and thickness values, real and imaginary parts of vertical component of the secondary magnetic field (Hz), its phase variations, and normalized amplitude of the ratio of secondary to primary component of the vertical magnetic field (Hz/Hz0) in case of considering/ignoring the displacement currents, are calculated and plotted as a function of frequency.
Introduction Considering EM primary source, EM methods are divided into two groups: 1. EM methods with natural sources that incorporate natural electric and magnetic fields of the earth, and 2. EM methods that incorporate man-made sources. The man-made EM sources, which transmit either transient currents or continuous sinusoidal waves, have variable physical, electronic and geometric specifications. In EM-geophysics, continuous sinusoidal wave transmitters are known as frequency domain EM (FDEM) sources. Based on geometry and shape, FDEM sources are categorized into four common types: 1. vertical magnetic dipole (VMD), 2. horizontal magnetic dipole (HMD), 3. vertical electric dipole (VED) and 4. horizontal electric dipole (HED). A horizontal transmitting loop or a small vertical transmitting loop of wire that carries alternating current, if distance to observation point is five times greater than length of the loop radius, can be treated as HMD or VMD source, respectively. A source, consisting of a short wire and carrying an alternating current, can be treated as an electric dipole, if the distance to the observation point is at least five times greater than the cable length. For a FDEM source that generates EM field only in transverse magnetic (TM) mode, e.g. a vertical electric dipole, the tangential magnetic field at the earth surface is double the primary field, while the tangential electric field is zero and the earth appears to be a perfect conductor; hence, in practical geophysics only dipole sources that generate primary EM field in transverse electric (TE) and/or TE and TM modes simultaneously, are used as transmitter. In recent years, electronic and software developments in designing EM instruments have resulted in gathering more reliable field datasets, but despite to many successful progresses in the area of forward modeling and inversion of the EM geophysics, it is still a challenging and interesting area of work for the geophysicists. At present, there are different EM forward modeling programs, e.g. EMDPLER which is capable of computing response of electric and magnetic components of the EM field, generated from the most common dipole sources with variable source-receiver configurations.
Methodology and Approaches In this paper, by considering a Cartesian system (x,y,z) with vertically downward directed z-axis and an x-directed HMD carrying an alternating current (I) and the dipole moment m, frequency response of magnetic components of EM field from an isotropic non-magnetic layered earth in observation point is thoroughly formulated in SI units. Moreover,an FDEM forward modeling algorithm, coded in Fortran 77 and called “EMDPLER”, is used for computing frequency domain response of the Hz components of the EM field from different 1-D layered earth models. Computations of this program are performed by assuming variable transmitter-receiver configurations and considering displacement currents in the frequency range (50 KHzResults and Conclusions In this paper, by referring to scientific references, frequency response of the magnetic components of EM field, generated from an HMD source, from an isotropic non-magnetic layered earth in observation point is concisely formulated. Moreover, by conducting the EMDPLER forward modeling code on different 2- and 3-layer earth models with different resistivity and thickness values, real and imaginary parts of vertical component of the secondary magnetic field (Hz), its phase variations, and normalized amplitude of the ratio of secondary to primary component of the vertical magnetic field (Hz/Hz0) in case of considering/ignoring the displacement currents, are calculated and plotted as a function of frequency. This paper can provide geophysicists with the idea of computing other magnetic components of the secondary EM field in the case of layered earth models, and also, 1-D inversion of these components. Moreover, the results of the present paper would guide geoscientists for better geological interpretation of the models based on the EM field measurements.