Sondowania magnetotelluryczne w ośrodkach anizotropowych
Abstract
MAGNETOTELLURIC SOUNDINGS IN ANISETROPIC MEDIA
Summary
Magnetotelluric soundings calculated in two mutually perpendicular directions are often different. One of the reasons of this behaviour is anisotropy of the medium.
In the paper the layered anisotropic half-space is considered. In each layer two main axes of conductivity anisotropy make an arbitrary angle with the measuring system. Electromagnetic field is given by four independent amplitudes of electric field related, to propagation along vertical axis and along two conductivity axes. For N layers there are (4N-2) unknowns and (4N-4) equations resulting from boundary conditions. Two missing equations are obtained with the assumption that magnetic field Hx(O) and Hy(O) has specified polarization on the Earth's surface (z = 0). Solving the appropriate set of equations we obtain the analytical expressions for apparent impedance and, hence, for amplitude and phase of magnetotelluric soundings curves.
They depend not only on frequency of field variations and electric parameters of the medium but also on azymuth of the measuring system and magnetic field polarization.
In general case the dependance is complex and may be analysed qualitatively only by means of numerical computations. From analysis of the models whose conductivity anisotropy axes in each layer make the same angle with the measuring system axes it follows that for the angle equal to 0° or 90°, the obtained sounding curves correspond to the case of istoropic layered half-space.
Summary
Magnetotelluric soundings calculated in two mutually perpendicular directions are often different. One of the reasons of this behaviour is anisotropy of the medium.
In the paper the layered anisotropic half-space is considered. In each layer two main axes of conductivity anisotropy make an arbitrary angle with the measuring system. Electromagnetic field is given by four independent amplitudes of electric field related, to propagation along vertical axis and along two conductivity axes. For N layers there are (4N-2) unknowns and (4N-4) equations resulting from boundary conditions. Two missing equations are obtained with the assumption that magnetic field Hx(O) and Hy(O) has specified polarization on the Earth's surface (z = 0). Solving the appropriate set of equations we obtain the analytical expressions for apparent impedance and, hence, for amplitude and phase of magnetotelluric soundings curves.
They depend not only on frequency of field variations and electric parameters of the medium but also on azymuth of the measuring system and magnetic field polarization.
In general case the dependance is complex and may be analysed qualitatively only by means of numerical computations. From analysis of the models whose conductivity anisotropy axes in each layer make the same angle with the measuring system axes it follows that for the angle equal to 0° or 90°, the obtained sounding curves correspond to the case of istoropic layered half-space.