Differential probe

Differential probe. (Courtesy of Tetronix Inc. DuPont Application Note Reference H-67771.) 

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Separate driver and receiver and front balancing. The board can be programmed to use absolute probes, differential probes, additive and subtractive fluxes it can be operated in three modes receiver only, driver only, and driver-receiver. All of these configurations only depend on the way the probe is connected, and software configuration. Each board has connections for 2 drivers and 2 receivers. 

In order to maximize the excitation, precautions have to be taken to avoid cross-talk between excitation and signal. Therefore differential probes are commonly used with a SQUID system Nevertheless, for the discussed defects the SQUID system has a lower excitation field by a factor of about 100 compared with the commereial system This we must keep in mind, when we compare measured signal to noise ratios. There is a potential to improve for small defeets, when eross-talk is managed very well. 

The development of these systems first led to the u.sc of differential rcsp. multi-differential probes. These probes offer the highest possible sensitivity towards gradual influences, but... 

For all these reasons H. Doll suggested, in 1946, multi-coil differential probes and also developed an approach allowing us to determine parameters of these systems. 

Arbitrarily, a multi-coil induction probe can be presented as a sum of two-coil induction probes. Currently, there are known symmetrical and non-symmetrical multi-coil induction probes, and their characteristics will be considered in detail in the next sections. As a rule in induction logging using one frequency the electromotive force, caused by the current in the transmitter coil or coils, is significantly greater than that generated by induced currents in the medium. For this reason an additional compensating coil to increase the accuracy of measurement is installed. Due to this the electromotive force caused by the primary field is practically equal to zero. It is also appropriate to notice that some differential probes do not require a compensation coil. 

Let us remember that unknown parameters of the multi-coil differential probe are lengths of the two-coil probes and moments of coils. 

The analytical approach is also convenient to analyze radial responses of known differential probes, specially when the probe consists of only one transmitter coil, while others are receiver ones or vice versa. 

Choice of optimal parameters of a differential probe which provides a certain depth of investigation or a sensitivity to specific parts of a medium as well as a maximal signal from these parts of the medium. 

It is appropriate to notice that eq. 7.15 can be used for calculation of radial responses of differential probes in a medium which is not uniform with respect to magnetic permeability. 

Physical Principles of Multi-coil Differential Probes... 

For this reason we can say that a necessary condition for the application of differential probes is the absence of interaction between currents in those parts of a medium the influence of which should be significantly reduced. In other words, those parts of the medium have to correspond to Doll s area where the current density is defined by the primary magnetic flux and the conductivity at a given point. It is natural that in choosing parameters of probes in order to increase the depth of investigation in the radial direction, it is important to eliminate the influence of parts of the medium located relatively close to the source. As calculations show, this condition usually takes place even for sufficiently high frequencies. 

Analysis of physical principles of differential probes permits us to discuss one aspect related to obtaining radial responses of these probes. 

It is natural that the following question arises whether this characteristic allows us to obtain information on the focusing features of the probe in a medium when the resistivity changes in a radial direction. It is obvious that until the signal from cylindrical conductor does not depend on currents induced in the external medium, regardless of their resistivity, this function can be used for evaluating the efficiency of a differential probe in a uniform as well as in a nonuniform medium. 

This consideration shows that the application of direct radial responses obtained from either physical modeling or making use of the exact solution is hardly useful for the determination of parameters of differential probes. 

As is well known, coil induction probes used in induction logging have various arrangements of coils. It is appropriate to distinguish in every differential probe the basic (main) two-coil probe having a maximal product of transmitter (T) and receiver (R) coil moments. Other coils are considered to be focusing coils and, they form several additional coil probes which provide focusing features of the induction tool. 

For internal focusing additional coils are placed between basic ones for external focusing they are located outside the main probe, and finally for mixed focusing additional coils are placed inside as well as outside the basic probe. The configuration of symmetric differential probes is shown in Fig. 7.4. 

We will consider several differential probes and will start with a symmetrical four-coil probe with additional internal coils. This type of probe is defined by three parameters, namely the distance between basic coils, L, the ratio of the length of focusing probe RTr to that of the basic probe, which is denoted by p, and the ratio of moments of focusing coils to the moment of basic ones (parameter c). 

Figure 7.4. Symmetrical differential probes (a) internal focusing (b) external focusing ...

The probe 6F1M has six coils with symmetrical internal and external differential probes (mixed focusing) based on the use of frequency 50 kHz. Probe 4F1 is a four-coil non-symmetrical system with an internal differential probe and frequency of the current is 70 kHz. Finally, probe 4F1.1 is a four-coil nonsymmetrical probe with internal focusing and frequency 1 MHz. Table 7.11 describes the position and parameters of coils of these probes. Let us notice that all considered probes are systems where the electromotive force caused by currents in the transmitter coils, i.e. the primary electromotive force is compensated. In other words, the moments of coils satisfy the condition ... 

Calibration curves for basic two-coil induction probes are also shown in Figs. 7.11-7.13. From comparison with calibration curves of corresponding differential probes it follows that a decrease of the signal with respect to that of the basic probe within the range of measured resistivities in average constitutes ... 

Now we will investigate vertical response of these differential probes. As has been shown differential probes allow us to reduce significantly the influence of the borehole and the invasion zone, that is areas of a medium, directly surrounding the probe. On the other... 

However, with help of external focusing when some coils are located outside the formation, we can improve the vertical response due to the fact that for such position a differential probe permits us to reduce the signal from the surrounding medium to a greater extent than from the formation. 

Curves of aajoi for various parameters of geoelectric section when differential probes 6F1M, 4F1 and 4F1.1 are located symmetrically against the formation are presented in Figs. 7.24-7.29. 

This behavior of the radial response of a three-coil differential probe is of great practical interest for solution of various problems, in particular for the determination of a relatively high resistive formation when the borehole is filled by a strongly mineralized solution (s = (T2/(Ji < 0.001). Inasmuch as for obtaining reliable measured signals created by currents in a slightly conductive medium it is necessary to apply relatively high frequencies, when the skin effect in the mineralized solution of the borehole can be noticeable, it is appropriate to use results of calculations by exact formulae. 

As was shown before, the better the focusing of a multi-coil induction probe the narrower the range of measured resistivities, and correspondingly the same effect is observed for other differential probes. We will characterize the range of measured resistivities by the... 

In conclusion, it is appropriate to notice that three-coil differential probes due to their simplicity can be used for lateral soundings. Examples of sounding curves, calculated for the range of small parameters, are given in Figs. 7.41-7.44. They demonstrate that such soundings can be performed with relatively short probes. 

Inasmuch as in all considered probes moments of coils and distances between them are chosen in such a manner than the electromotive force of the primary field is compensated, the right part of eq. 7.52 turns out to be zero. Therefore, if the differential probe does not contain relatively short two-coil probes we can expect that such a probe preserves focusing features even when it is shifted from the borehole axis within a wide range of parameter... 

With an increase of the probe length the value of the integral approaches its asymptote and, within certain limits, the influence of coil length is negligible. In known probes finite dimensions of coils do not practically influence the value of the probe coefficient. For example, if ai = 0.1 m, the four-coil differential probe l.L 1.2 has the following parameters a = 24, = 9.6, Q3 = 4.8, Smax = 1, P = 0.4 and c = 0.05. Taking into... 

Interpretation of induction logging data measured by such differential probes is mainly based on measuring the quadrature component of the electromotive force, shifted by 90° with respect to the primary electromotive force. 

As is well known with the help of multi-coil differential probes we can reduce significantly the influence of the borehole and, often, the invasion zone, if the conductivity and the radius of the latter are not large enough. In other words, the depth of investigation of such probes in the radial direction essentially depends on the geoelectric parameters of the medium. Also, in calculating coil moments and their position for these probes it is assumed that the resistivity of the medium is only a function of the distance from the borehole axis, i.e. it changes only in the radial direction. 

As is well known, an increase of the depth of investigation in induction logging is usually realized with the help of multi-coil differential probes that in many cases permit us to eliminate the influence of currents in the borehole and in the invasion zone. 

All these factors, which restrict to a certain degree the application of induction logging with differential probes, impel us to investigate the possibilities of the transient method, which is successfully applied in other areas of exploration geophysics. 

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