Detectability of an intermediate layer by magnetotelluric sounding

Abstract The recent publication by Verma and Mallick (1979) on the detectability of an intermediate layer by time domain EM sounding provides some informative answers to a problem of practical interest. That is, an attempt has been made to probe the usefulness of the sounding system with regard to its ability to detect a subsurface layer. It is worthwhile to attempt to analyze the same problem of detectability in a three-layer sequence by magnetotelluric (MT) sounding which is finding increasing use in recent years in exploration for minerals (Strangway and Koziar, 1979) and in prospecting for geothermal resources (Hoover and Long, 1975), particularly in the audio-frequency range. We present results of an analysis of the problem of detectability of an intermediate layer in a three-layerFIG. 1. Isoline maps of h (super *) 2 derived from AMT resistivity sounding data of three-layer models. horizontal sequence with several possible combinations of the layer resistivities of practical interest covering all the four types H, K, A and Q, by the AMT sounding system. The computational approach used by Verma and Mallick (1979) has been adopted in our study.The definition of detectability in an explicit form, at least qualitatively, was first given by Roy (1970) who observed that detectability is the resolution of, or the separation between, the theoretical master curves as controlled by the geometrical and physical parameters of the target. Following this definition, Verma and Mallick (1979) noted that, in the case of a three-layer sequence, the problem of detectability of the intermediate layer can be studied by examining how thin the intermediate layer can be so that the response of the three-layer earth is still significantly different from that of the two-layer sequence without the target layer. Consequently, the separation between the response curves with and without the target layer is the resolution or detectability. They further attempted to quantify the definition of detectability by examining the relative rms difference between the two response curves. If RES''' 1 , RES''' 2 , RES''' 3 , ..., are the values of the response (resistivity or phase) of a three-layer sequence at frequencies f 1 , f 2 , f 3 , ..., and RES' 1 , RES' 2 , RES' 3 , ..., are the values of response of a two-layer sequence (the one obtained by removing the target layer from the three-layer sequence) at the same frequencies f 1 , f 2 , f 3 , ..., then the relative rms difference over n frequency points is defined as (Verma and Mallick, 1979)EquationAssuming measurement errors in MT field data to be 4 percent, an rms difference of three times this error (12 percent) can safely be taken as detectability level. In the present study, a target is considered to be detectable if the relative rms difference between the two response curves is 12 percent or more.We consider three-layer sequences with the resistivity of the first layer (rho 1 ) fixed at 100 Omega -m and its thickness (h 1 ) fixed at 100 m. The resistivity of the second layer (rho 2 ) and its thickness (h 2 ) and the resistivity of the lower half-space (rho 3 ) are the variable parameters. Evidently the relative rms difference between the two responses at frequency f depends upon the four variables rho 2 /rho 1 , rho 2 /rho 3 , h 2 /h 1 , and f h 21 /rho 1 . If frequency f covers the range defined byFIG. 2. Isoline maps of h (super *) 2 derived from AMT phase data of three-layer models. Equationcorresponding to almost complete penetration (skin depth > h 1 ) to negligible penetration (skin depth < h 1 ) of the first layer (obviously a reasonable range for our problem), then the relative rms difference is essentially a function of the three variables rho 2 /rho 1 , rho 2 /rho 3 , and h 2 /h 1 . Accordingly, in the present models with h 1 fixed at 100 m and rho 1 at 100 Omega -m and taking mu 0 equal to 4pi X 10 (super -7) , the frequency should cover a range from f 1 < 2.5 kHz to f 2 > 2.5 kHz. The frequency range 0.1 Hz to 20 kHz considered in the present study satisfies this criterion. The computations also showed that the rms difference becomes negligibly small at both ends of our frequency range.The following values of rho 2 /rho 1 and rho 2 /rho 3 are considered for the three-layer sequence in the computation of AMT response curves for various values of h 2 /h 1 in the frequency range of .1 Hz to 20 kHz, with 10 equally spaced frequency points in each decade. For H type sequence,rho 2 /rho 1 = 0.01, 0.02, 0.05, 0.1, 0.2, 0.4, 0.6, and 0.8.rho 2 /rho 3 = 0.01, 0.02, 0.05, 0.1, 0.2, 0.4, 0.6, and 0.8.For Q type sequence,rho 2 /rho 1 = 0.01, 0.02, 0.05, 0.1, 0.2, 0.4, 0.6, and 0.8.rho 2 /rho 3 = 2, 4, 6, 8, 10, 20, 50, and 100.For K type sequence,rho 2 /rho 1 = 2, 4, 6, 8, 10, 20, 50, and 100.rho 2 /rho 3 = 2, 4, 6, 8, 10, 20, 50, and 100.For A type sequence,rho 2 /rho 1 = 2, 4, 6, 8, 10, 20, 50, and 100.rho 2 /rho 3 = 0.01, 0.02, 0.05, 0.1, 0.2, 0.4, and 0.6.Next, for each three-layer sequence that value of h 2 is determined, which makes the relative rms difference between the response of the three-layer sequence and the corresponding response of two-layer sequence 12 percent. Let this value of h 2 be called h (super *) 2 . For each pair (rho 2 /rho 1 ) and (rho 2 /rho 3 ), the ratio h (super *) 2 /h 1 exactly satisfying our detectability criterion has been obtained. These ratios h (super *) 2 /h 1 are displayed in (rho 2 /rho 1 ) versus (rho 2 /rho 3 ) plots as isolines (Figures 1 and 2). It may be noted, however, that the isolines cannot be extrapolated to either of the axes with rho 2 /rho 1 = 1 and rho 2 /rho 3 = 1, since it is obvious that the intermediate layer becomes indetectable for these values. Results of the analysis that utilized amplitude of the apparent resistivity response are shown in Figure 1 and those that utilized phase response data in Figure 2.These diagrams are self-explanatory and provide valuable information regarding the minimum value for target layer thickness that can be detected, if resistivities of different layers and thickness of the first layer are known. It is easily seen that a thin conducting intermediate layer has a better chance of detection than a thin resistive intermediate layer. For H and A type sequences, an increase occurs in the value of h (super *) 2 with an increase in the ratios of either (rho 2 /rho 1 ) or (rho 2 /rho 3 ), while for Q and K type sequences, one observes an increase in h (super *) 2 with an increase in the ratio (rho 2 /rho 1 ) and a fall in the value of h (super *) 2 with an increase in (rho 2 /rho 3 ). On utilizing the phase response data alone, the target layer becomes detectable with relatively higher values of h (super *) 2 . The difference in h (super *) 2 values as obtained from utilizing resistivity data and phase data is minimum for A type sequence and maximum for Q type sequence.;Although the present analysis was done for AMT sounding curves, the law of EM similitude extends these results to other frequencies as well. It may also be added that in studying the detectability problem, besides rms criteria, one can also examine distribution of residuals (RES''' i - RES' i ) versus frequency. For example, presence of large residuals over a narrow frequency band would be expected to correspond to higher resolution. ACKNOWLEDGMENTThe authors are grateful to the Director, National Geophysical Research Institute, Hyderabad, for his kind permission to publish the results of these in