Observational Errors and Limitations

Introduction and Statement of Problem

Like modern magnetometers, resistivity meters do not rely on an operator to read or interpolate a dial reading. Rather, the current strength is fixed and the voltage difference between to two potential electrodes is measured and displayed. In addition, on many modern instruments it is possible to enter the electrode configuration and spacing, and have the instrument directly display and store apparent resistivity.

The portable resistivity meters used for most near-surface investigations can deliver and measure currents in the range of a few milliamperes to a few hundreds of milliamperes. The voltage difference between the potential electrodes can be read to within a few tens of millivolts. What these parameters mean for the absolute accuracy of the measurement when converted to apparent resistivity depends on the resistivity underlying the survey and the spacing of the electrodes. The most significant limitation to these portable systems is that the small amount of current that can be delivered into the ground limits the distance at which electrodes can be placed. At large electrode spacings, the voltage difference between the two potential electrodes can become smaller than the electrical noise associated with the electrodes and to a lesser extent the resolution of the voltmeter incorporated in the instrument. In this discussion, note that "large" is relative to the resistivity of the underlying material. In high resistivity environments, it will be more difficult to acquire stable resistivity estimates at smaller current electrode spacings than in lower resistivity environments.

To gain a better understanding of the noise inherent to DC electrical soundings, four survey crews collected DC data over the same electrode configuration. The results of the four surveys is shown below. Notice that at the shorter electrode spacings the apparent resistivities determined by each group are almost equal. As electrode spacings increase, the apparent resistivities, as determined by each group, become increasingly different.

Repeated DC Resistivity Observations - Schlumberger Array

Procedure

To complete this portion of the exercise perform the following tasks.

• Download the resistivity data set to your machine. The first column in this data set is the half-spacing of the current electrodes, AB/2, in meters. The second through fifth columns represent the apparent resistivities determined by each group from a single voltage reading at the specified electrode spacing. A Schlumberger spread was used to collect these observations. Clicking on the highlighted area will create a file with the name resgrp.dat on your machine. *
• Import resgrp.dat into your favorite spreadsheet.
• Using the graphical features of your spreadsheet, plot the apparent resistivity versus electrode spacing for each group on a Log-Log plot. This is a plot that has as its axes the Log of the electrode spacing versus the Log of the apparent resistivity.
• For the listed electrode spacings, compute the average apparent resistivity and the standard deviation of the apparent resistivities observed by the four groups.
• On a Log-Log plot, plot the average resistivity versus electrode spacing, and on a Log-Linear plot, plot the standard deviation of the measured apparent resistivities versus electrode spacing.
• If the errors associated with each voltage reading are randomly distributed, we can reduce the standard deviation of the apparent resistivity observations by making repeated voltage readings at each electrode position and averaging the repeated observations. For noise that is randomly distributed, the standard deviation of the average observation is reduced by the square root of the number of readings made at each electrode position. How many repeated readings must be collected at each electrode spacing to reduce the standard deviation of the average at each spacing to 1 ohm.m? **
• Briefly discuss your results.

* From the notes, it appears that the precision of the voltage, current, and distance measurements is probably no more than 1%. Do you think these field crews are justified in quoting their resistivities to two decimal places?

** In fact the errors in apparent resistivity are also distributed logarithmically (think about the effect of a 1 mV error in the voltage for a small or a large apparent resistivity, for instance), so we should better think about reducing the relative error to 1%, say. With the resistivity values seen here the effect is slight, however.