大地电磁法的理论探测深度

Depth of investigation in magnetotelluric method

文中先从二层介质波阻抗公式出发,从理论上证明了:第一层相同的二层介质的视电阻率曲线会在几个点相交;从低频到高频,第2个交点处的频点穿过第一层介质时振幅恰好衰减到地面处幅值的e-3π/4.然后,分析二层介质视电阻率曲线,认为自第2个交点处至更高频的结果几乎不受第二层介质影响,从而提出用振幅衰减到地面处幅值的e-3π/4时的深度作为均匀半空间的探测深度,即3π/4倍趋肤深度,并与趋肤深度及Brain(1989)提出的1.5倍趋肤深度进行了对比;然后,分别采用具有相同导电效应、等效衰减作用的替代层,得到了多层介质下的2种计算探测深度的方法;最后用多层介质及二维模型进行验证.结果表明本文的2种计算探测深度的方法均能较准确地反映探测深度,同时证明了趋肤深度及1.5倍趋肤深度作为探测深度的局限性.

Attenuation factor is defined asα= （ωμ/（2ρ）h）1/2,which means the amplitude of the electromagnetic wave attenuated to the ground＇s e-α.Then based on the impedance＇s formula of two-layer earth models,two conclusions were proved theoretically that：a.to the two-layer earth models with the same first layer earth,the apparent resistivity curves would cross at a few points whereα=π/4＋（n-1）π/2,n=1,2,…;b.from low to high frequency,the electromagnetic wave＇s amplitude of the second point＇s frequency would attenuate to the ground＇s e-3π/4 when penetrated the first layer earth.The results were independent with the second layer since the second intersection to higher frequency by analyzing the apparent resistivity curves.Thus,a reasonable estimate for the depth of investigation for MT is taken to be approximately equal to 3π/4skin depths namelyα=3π/4,and compared respectively with skin depth and 1.5skin depths.The results indicate that the second layer＇s biggest effect to apparent resistivity and phase are both more than 28%sinceα=1which corresponding to skin depth to higher frequency,the effect to apparent resistivity is more than 20%and the effect to phase is more than 5%sinceα=1.5 which corresponding to 1.5 skin depths to higher frequency,the effect to apparent resistivity and phase are both less than 1% sinceα=3π/4which corresponding to 3π/4skin depths to higher frequency.Then,extended respectively to multilayered earth with the same effective conductivity and the same effective attenuation.Lastly,tested by multilayered earth models and two-dimensional earth models,the results indicate that the two methods presented in this paper are able to reflect the investigation depth accurately,and the skin depth or 1.5skin depths is not very exact.