IEEE Instrumentation and Measurement Technology Conference Ottawa, Canada, May 19-21,1997 Subsurface Resistivity Measurements Using Square Waveforms Manel Gasulla, Josep Jordana, Ramon Pallas-Areny and J.M. Torrents Divisio d'lnstrumentacio i Bioenginyeria. Departament d'enginyeria Electrbnica Universitat Politecnica de Catalunya Jordi Girona 1-3, Edifici C-4, 8034 Barcelona (SPAIN) Phone +34-3-401-6766, Fax +34-3-401-6756, E-mail: elerpa8eel.upc.es WWW:http:Npetrus.upc.es/-wwwdib/homepageuk.html Abstract- This work analizes the effect of inductive and capacitive coupling from the injecting circuit to the detecting circuit in resistive field surveys. Experimental results demonstrate that if a square waveform is injected into the soil and synchronous sampling is used to sample the flat zone of the detected voltage, then the interference is greatly reduced. Furthermore, square waveforms are easier to generate than sinusoidal waveforms, so that they offer a new approach to subsurface resistivity measurements. I. INTRODUCTION. The detection of buried structures from the surface without drilling the soil is of interest in archaeology and in other situations such as detection of water and contaminants from leaking underground pipes. There are several techniques that can be applied in these cases: Ground Penetrating Radar (GPR), Time Domain Reflectometry (TDR), etc. Our work is centered in geoelectrical prospecting methods, which consist on injecting current to the soil with a pair of electrodes and detecting the drop in voltage with another pair of electrodes. The parameter that provides the information of the buried structure (anomaly) is the apparent resistivity p, which is given by p, = kav /I [l], where AV is the detected potential, I is the injected current and k is a geometric factor, which depends on the configuration of the electrode array. It is important to recognize that any possible error in the measured voltage will affect p, and can hinder the detection of the anomaly. Some error sources are the position of the electrodes, telluric noise (which has its main influence in dc measurements) and the electromagnetic coupling between the injecting and detecting circuits in ac measurements. In all electrical surveys, electromagnetic induction between current and voltage cables must be avoided. This is easily achieved by using dipole-dipole arrays [2], but it is interesting to devise a method able to reduce this interference independently of the electrode configuration. II. PROBLEM STATEMENT In electrical impedance measurement we inject a current (frequency fs) and detect a drop in voltage whose amplitude is modulated by the impedance sensed. Modulation produces an upward translation of the message spectrum. Demodulation, therefore, implies a downward frequency translation in order to recover the message from the modulated wave. A common demodulation technique providing a good signal to noise ratio is homodyne detection. This method can be applied to impedance measurement as shown in Fig. 1. d(t)=vsig(t)+n(t) Fig.1. Homodyne detection 0-7803-3312-8/97/$5.0001997 IEEE 1252
If we assume that the signal detected is V,, (t) = &Vs cos(2nfst + (bs) and the reference signal is V,, (t) = avr cos 2nf,.t, then the demodulated signal, when f,=f,, is, v, (t) = v, v, cos qiy (1) In a resistive medium, Cp,y = 0, then V, (t) = V,V,. If there is an interfering signal n(t) = AVi cos(2nfi t + Oi ), having the same frequency than the carrier, typically capacitively or inductively coupled, then the demodulated signal in a resistive medium is If the phase angle Cpi of the interference is 90E then the message will be recovered without any error because homodyne detection is phase sensitive. But whenever Gi # 90" there will be a measurement error. In principle, the larger the frequency of the injected current, the larger will the interference be, because both inductive and capacitive interference increase with frequency. In extreme cases the detector can even saturate because of the interference. Impedance measurement by synchronous sampling (Fig. 2) is another phase-sensitive amplitude demodulation technique [3]. If d(t) is sampled at t= nt, n integer, T being the period of the sinusoidal waveform, (that is, if the signal is sampled at its maximal value), then the detected signal will be V,(t) = 2/2v,(1+-cos~i) Vi (3) VS It can be seen that the measurement erroir also depends on the phase angle $i of the interference. But here this drawback can be avoided by injecting a square waveform to the soil instead of a sinusclidal waveform [4]. In this case the detected signal is sampled at a zero-slope point, thus avoiding the stray current coupling from the injecting circuit to the measuring circuit ("transformer effect"). Therefore, this allows us to measure at a frequency high enough in order for electrode impedance to be relatively low. Fig.2. Impedance measurement by synchronous sampling. This interference is particularly troublesome in subsurface resistivity measurements because of the physical dimensions and arrangement of the circuits. These measurements derive from geoelectrical prospection techniques and can help in detecting shallow anomalies buried into the soil. Fig. 3 shows the principle of this technique. A current of strength I is injected by electrodes A and B. The potential difference between points M and N is The apparent resistivity pa is obtained by solving (4) for P ' 2nAV Pu =I P -' whera P is the geometric factor. pa provides information about the presence of an anomaly. In the frequency domain, AV can be affected by the electromagnetic coupling from the injecting circuit to the detecting circuit, which will alter the value of pu A M N B Fig.3. Linear array of current and potential electrodes. 1253
~ There are two main coupling mechanisms: capacitive coupling and inductive coupling [5]. Capacitive coupling results in a voltage change due to electrical leakage or 4 displacement currents that causes errors in AV. It arises from displacement currents between injection and detection wires. 4 6 4m 14m 6,9 m 5 9m 1 1 Inductive coupling appears when the injecting circuit and the detecting circuit behave like the primary and secondary windings of an ordinary electrical transformer. The primary circuit induces a current in the secondary circuit, which alters the desired detected signal. Stray coupling is shown in Fig. 4. Fig. 5. Field survey: Electrode array and wire arrangement. Fig. 4. Inductive and capacitive coupling between injecting and detecting circuits. If dc currents are used, then there is not capacitive nor inductive coupling. But another important problem arises: the polarization potentials generated at the contact between a metallic conductor (the electrode) and an electrolytic conductor (the moist ground). These polarization potentials are dc voltages that affect the measured voltage difference. Ill. MATERIALS AND METHODS In order to quantify the interference in a field survey, we have made some measurements in a typical soil of our Campus. The electrode array was arranged as shown in Fig. 5. The injecting and detecting cables were arranged in a triangular geometry parallel to the ground surface. The transmitter and the receiver were placed in a vertex (TD) of this triangle, in front of the electrode array. The generator was an HP3245A and the detector was a fully differential synchronous demodulator, based on synchronous sampling [6]. The four electrodes were made from stainless steel, 20 cm in length and 1 cm in diameter. They were inserted several centimeters into the ground to ensure a good electrical contact. Connecting wires were 1 mm in diameter and had plastic insulation, which avoided any posible leakage current to the ground. The HP3245 generates the sinusoidal/square input of 20 V, and the signal reference for the sampler. The sampling frequency was the same that the input signal (f,=f,) and its values were 100 Hz, 1 khz and 10 khz. The duty cycle for the sampling signal was 10%. The sampling instant was at nt/4. The injected current was monitored by the drop in voltage across a 10 resistor in series with an injecting wire, by means of a portable oscilloscope (Tektronix THS-71 OE). IV. EXPERIMENTAL RESULTS In order to analyze the effect of capacitive and inductive interference, the measurements described in tables 1, 2 and 3, were performed. Capacitive interference increases in value if coupled to a high-impedance circuit. In order to demonstrate this effect, a variable resistor was connected to the end of two twisted cables. The potential detected was proportional to that resistor values. At 10 khz and by sampling at nt/4 of the injected signal, 141 mv were detected for a sinusoidal waveform and only 14 mv for a square waveform. Capacitive coupling increased with frequency and with cable length. Inductive interference was minimal because the detecting wires were twisted. If the area of the detecting circuit is increased and its terminals shortcircuited, capacitive interference is negligible (zero dependence) and inductive coupling predominates. This interference can be reduced by decreasing the signal frequency or by using square waveforms and sampling at the interval [T/4-T/2], because in this interval interference has disminished. Table 1 shows the effect of inductive interference. It can 1254
be seen how the interference increases with frequency and that for a square waveform it is small even at high frequency. The injected current increases with the frequency because electrode impedance decreases. Injected waveform Sinusoidal Sampling instant= T/3 Square Sampling instant= T/3 Sinusoidal Sampling instant=t/4 Square Sampling instant=t/4 100 Hz Table 1. Interference when detecting wires are shortcircuited. Interference by capacitive and inductive coupling results only when there is a change in the voltage or current in the injecting circuit. For a sinusoidal signal, this means the entire waveform except at maxima and minima. For a square signal, however, interference will result only during transistion times. Hence, by sampling at nt/4 or a bit later the effect of the interference will disappear (Fig. 6). Injected wave Sinusoidal 1 khz I V0=337 mv 10 khz I V-=644 mv I= 20.6 ma 1=21 ma Table 2. Detected voltage when interference coupling is maximum. If the detecting cables were twisted, interference reduced because the distance between detecting wires and injecting wires increases and the area of the detecting circuit is much smaller. The results are shown in Table 3. 10 khz I= 20.8 ma b21.2 ma Table 3. Detected voltage when detecting cables are twisted. V. CONCLUSIONS This work shows that capacitive and inductive interference in subsurface resistivity measurements result in gross errors when using sinusoidal signals. Fig. 6. Synchronous sampling with square waveforms. From T/4 to T/2 the interference is minimal. Table 2 shows the dc demodulated voltage V, and the injected current with sinusoidal and squarre waveforms at frequencies 1 khz and 10 khz when the detector was connected to electrodes M and N. In this case there was both capacitive and inductive interference and they increased with frequency. However, when using square waveforms the detected voltage was similar, which confirms our predictions that sampling in the flat zone of the square waveforms, minimizes thle effect of interference. When using sinusoidal waveforms, the voltage detected changed by 91 %. In order to minimize capacitive coupling, the receiver wires and the transmitter electrodes and wires should be placed well apart, particularly in a wet (conductive) environment. Inductive coupling can be avoided by reducing the area of the detecting circuit by twisting the detecting cables. However, interference can be reduced regardless of cable and electrode position by using square waveforms and synchronous sampling rather than sinusoidal waveforms and homodyne detection. This is because synchronous sampling allows to take samples in the interval [T/4-T/2], when the effect of interference has disappeared. 1255
ACKNOWLEDGMENT This work has been funded by the Spanish DGICYT, Project PB93-0961. REFERENCES [I] W.M. Telford, L.P. Geldart and RE. Sheriff, "Applied Geophysics," 2nd. ed., Cambridge: Cambridge University Press,l990. [2]. J.Milsom, "Field Geophysics", New-York: Open University Press and Halsted Press, 1988. [3]. R. Pallas-Areny, 0. Casas, "A Novel Synchronous Demodulator for AC Signals", IEEE Trans. Instrum. Meas., Vol45, No 2, April 1996, pp. 41 3-41 6. [4]. R. Pallas-Areny, J.A. Brescoli, "Electrical Impedance Measurements by synchronous sampling applied to square waveforms", Colloquium on "Innovations in instrumentation for electrical tomography", The Institution of Electrical Engineers, Digest No: 19951099. [5]. 0. Koefoed, "Geosounding Principles,l- Resistivity Sounding Measurements-Amsterdam, Elsevier Science Publishers BV. 1988. [6] M. Gasulla, J. Jordana, R. Pallas-Areny, J.M. Torrents. "A Fully Differential Synchronous Demodulator". Proceedings of the XI Design of Integrated Circuits and Systems Conference. Sitges (Spain). November 1996, pp. 41-46. 1256