水平多层大地上垂直磁偶极频率测深的全波视电阻率

本文根据视电阻率定义的原则,以及用不同的场量定义的视电阻率效果不同这一事实,提出一种新的全波视电阻率定义.在全区同时用均匀大地上电磁场的三个分量来分区定义祝电阻率.在远区视电阻率由磁场的水平分量求出,在近区由磁场的垂直分量或其实分量定义,而在过渡区则由电场的水平分量确定.用这种方法定义的视电阻率为电磁响应的单值函数,它随频率变化的曲线显著改善,能直观地反映地层电阻率随深度的变化,数值比较接近地层的真电阻率值,假极值效应明显压低.在计算中用切比雪夫多项式分段拟合均匀大地电磁响应的反函数,并给出一套系数,由此算出的视电阻率误差小于1％.

FULL-WAVE APPARENT RESISTIVITY FROM VERTICAL MAGNETIC DIPOLE FREQUENCY SOUNDINGS ON A LAYERED EARTH

The apparent resistivity in frequency electromagnetic soundings is defined as the resistivity of a homogeneous half-space which gives the same response as the measured one. However, the values of the apparent resistivity would be different when defining it by means of different electromagnetic field components. On the principle of apparent resistivity, i.e., it should approach the true resistivity of each layer rapidly, a new full-wave apparent resistivity is proposed in this paper. It is defined by means of the amplitude of the horizontal magnetic field component in the far-field zone, that or real part of the vertical magnetic field component in the near-field zone and the amplitude of the horizontal electrical field component in the transition zone. The modified apparent resistivity is a single valued function of the electromagnetic responses. The curves of the apparent resistivity are improved significantly in the following respects: the apparent resistivity gives closer value to the true resistivity of each layer, the fluctuation of the curves becomes larger and the superfluous extremes are largely suppressed. The apparent resistivity is calculated by fitting the theoretical response using Chebyshev polynomials in a least squares sense. It was found necessary to perform the fitting separately in two or three intervals for each field component. A set of Chebyshev polynomial coefficients for calculating the full wave resistivity is given. The maximum relative error in the polynomial fitting is less than one percent in the apparent resistivity.