We present a new versatile datalogger that can be used for a wide range of
possible applications in geosciences. It is adjustable in signal strength
and sampling frequency, battery saving and can remotely be controlled over
a Global System for Mobile Communication (GSM) connection so that it saves
running costs, particularly in monitoring experiments. The internet connection
allows for checking functionality, controlling schedules and optimizing
pre-amplification. We mainly use it for large-scale electrical resistivity
tomography (ERT), where it independently registers voltage time series on
three channels, while a square-wave current is injected. For the analysis of
this time series we present a new approach that is based on the lock-in (LI)
method, mainly known from electronic circuits. The method searches the
working point (phase) using three different functions based on a mask
signal, and determines the amplitude using a direct current (DC) correlation
function. We use synthetic data with different types of noise to compare the
new method with existing approaches, i.e. selective stacking and a modified
fast Fourier transformation (FFT)-based approach that assumes a
In geosciences there is a high demand of data from observations of different sorts. Particularly, understanding processes requires monitoring various variables with a high temporal resolution. Typical fields are hydrology, geochemistry and geophysics. Consequently, there is a variety of solutions, mostly for very specific purposes. Dataloggers are often installed in regions without a power supply and must therefore have low battery consumption. Furthermore, communication with dataloggers is beneficial when checking their functionality or even to adjusting settings such as pre-amplification, sampling time or wake-up times.
Autarkic dataloggers are very beneficial in large-scale DC resistivity surveys. ERT (electrical resistivity tomography) is a standard exploration and monitoring technology for environmental and engineering problems owing to its high resolution and low cost. The target parameter electrical resistivity and its inverse electrical conductivity exhibit high sensitivity to important variables such as groundwater salinity or clay content. So-called multi-electrode instruments are popular where a multiple-wired cable connects a number of electrodes. Two electrodes are used to inject a current and two others to measure a voltage. By varying these combinations, hundreds or thousands of measurements are easily conducted per hour. However, the use of these multi-electrode systems is limited to rather small layouts, typically in the order of about 100 electrodes with maximum electrode distances of about 10–20 m. This restricts the depth of penetration to a few hundreds of metres.
In order to achieve deeper signal penetration, one can use dipole–dipole experiments, in which both current injection and voltage measurement are realized by dipoles that are small compared to the total layout (Alfano 1974). Usually, square-wave signals are injected, because the signal can easily be recognized. Alfano (1980) imaged geological structures in dipole–dipole experiments. The longest measured profiles measure up to 22 km length: Storz et al. (2000) imaged fault zones at the German continental deep-drilling site KTB (Kontinentale Tiefbohrung) and Schütze and Flechsig (2002) conducted such a profile across the flanks of the long valley caldera by using a large-scale dipole–dipole experiment to image fluid flow (Pribnow et al., 2003). Friedel (2000) used measurements along the flanks of the Merapi volcano to derive 2-D subsurface images to locate the magma chamber. Günther et al. (2011) described how a fault zone can be imaged with large-scale ERT and structural information from seismics along a 2.5 km long profile.
However, one can easily extend the technique to three dimensions. Brunner et
al. (1999) investigated a Tertiary maar using a layout of each 24 dipoles in
three rings. Schünemann et al. (2007) used a star layout to derive
apparent resistivity tensors over a buried valley. Similarly, Agricola et
al. (2016) used this layout to map the volcanic structure of the
Vogelsberg. Flechsig et al. (2010) demonstrated a feasibility dipole–dipole
test in a 20
In all these experiments, long time series are recorded and need to be
analysed in order to determine the current and voltage strengths. Friedel (2000) compared different approaches and presented a method based on signal
stacking using a programme called DC trap that was applied in some cases (e.g.
Schütze and Flechsig, 2002; Flechsig et al., 2010; Bergmann et al.,
2012). Other approaches (e.g. Günther et al., 2011; Agricola et al.,
2017) use the energy of the signals in the Fourier spectrum to retrieve
signal strength. Schünemann et al. (2007) used an inverse method to
determine the correlation coefficient between the current and voltage. This
approach is already related to the lock-in approach, which is also used in
some multi-electrode resistivity instruments (e.g. 4point light 10 W of LGM
electronics,
Lock-in detectors working with the principle of phase-sensitive detection are widely used to retrieve small signals from a huge noise floor (Meade, 1982, 1983; Blair and Sydenham, 1975). The signal to be measured is modulated by a reference frequency. The receiver “locks in” to this frequency thus reducing the effect of ambient noise (Scofield, 1994). This results in detection at very low signal-to-noise ratios. In the beginning only analogue lock-in amplifiers were implemented with tubes (Baker, 1954, Dereppe, 1961), operational amplifiers (De Marcellis et al., 2012) and application-specific integrated circuits (ASIC) (Ferri et al., 2001). Nowadays digital lock-in detectors implemented by discrete circuits (Saam and Conradi, 1998), digital signal processors (DSP) (Sonnaillon and Bonetto, 2005; Proksch, 2006), field programmable gate arrays (FPGA) (Wilson et al., 2015), microcontrollers (Bengtsson, 2012) or software (Andersson et al., 2007) are more common. Digital lock-in detection is more robust compared to analogue solutions. In particular, performances at low frequencies are significantly better. The field of applications which require the detection of very low signals in noisy surroundings where the use of lock-in detectors from optics is widespread (Andersson et al., 2007; Masciotti et al., 2008; Holzman et al., 2005), impedance spectroscopy (Albertini and Kleemann, 1997), wireless networks (Gabal et al., 2010), biologic applications (Ferri et al., 2001; Johnson et al., 2002), electron spin resonance (ESR) (Vistnes et al., 1984; Murányi et al., 2004) to nuclear magnetic resonance (NMR) (Saam and Conradi, 1998; Caracappa and Thorn, 2003).
In the following, we describe layout and usage of the datalogger before presenting a new approach for processing the retrieved time series along with established routines. We use synthetic noisy data to compare the performance of the methods and show the application to field data from a large-scale ERT survey before drawing some conclusions.
Block diagram of datalogger consisting of a GigaLog-S data acquisition module, a combined GSM/GPS modem and three preamplifiers.
The core of the datalogger (Fig. 1) is a GigaLog-S (Controlord, France)
data acquisition module. It contains a 16-channel 24 bit delta–sigma A/D
converter connected to an Atmel microprocessor. Only three of the channels are
used by three DC-coupled high-impedance differential preamplifiers, with four
programmable gain stages (factors 2, 10, 20 and 100) that are controlled by
the microprocessor. It is vital for good ERT data to optimize the input
gain, as ERT signals cover a wide range of magnitudes due to different
geometries (source-receiver distance). We designed the datalogger using
three channels to record data in all spatial directions generally. For the
particular case of 2-D set-ups, where adjacent dipoles in the same direction
are measured, it is also a good trade-off between minimizing the length of
wires to the electrodes and the number of dataloggers to be installed in the
survey area. The sample interval can be between 1 ms and 1 s in steps of 1 ms
and is therefore significantly higher than
existing MT (Roßberg, 2007) or ERT (Balasco et al., 2008) dataloggers.
The sampled data will be stored in a text file on a micro SD card. The
memory consumption is about 100 MB h
Datalogger system with datalogger, GSM/GPS antenna and 12 V accumulator. A laptop with GSM modem and antenna for remote control.
The software GUI is written in LabView. In the single-channel mode it is possible to connect to one logger and control the different functions, such as starting or stopping the data acquisition or setting the filename, gain or sampling interval. It is possible to read the directory of the SD card, monitor the accumulator voltage, the temperature of the logger or the free memory of the SD card. Entire data files can be downloaded, but this is only advisable with a USB connection due to the slow transfer rate of the GPRS connection. Another major feature of the remote controllability is that the signals of the acquired data can be monitored in realtime. To control many loggers simultaneously we provide a tabular control (Fig. 3). For a survey setting you can choose the loggers by filename, gain and sample interval in the first four columns. By executing this sequence the online status of every logger will be checked and the parameters will be set and read back. It also checks whether the data acquisition is running and if the logger temperature, accumulator voltage and SD memory are within predefined values. A small amount of data are downloaded and it is checked that the input signals of the three channels are in the proper range of amplitude and offset voltage. The datalogger time is checked for recent synchronization with GPS time. GPS coordinates are displayed and a Google map image is created to show the datalogger positions. It is also important to set the shut-down and wake-up times for the sleep mode.
Software GUI in multi-channel mode.
Exemplary voltage time series
Figure 4 shows a sample signal containing the response of an injected 0.2 Hz ERT square-wave current as visible in the GUI monitoring software. A fast Fourier transform (FFT) algorithm calculates the corresponding frequency spectrum. On top of the underlying broadband noise one can see the 50 Hz signal of the power lines, the 16.7 Hz from the railway lines, and the 0.2 Hz ERT signal with their odd harmonics. Colella at al. (2004) also shows a frequency spectrum of a time series.
The most common approach to retrieve the amplitude of an ERT square-wave
signal from the recorded time series is a stacking algorithm, as used by
some multi-electrode instruments (e.g. RESECS by
For the processing we use the frequency spectrum of the recorded time
series. This power spectrum is created by a fast Fourier transformation (FFT)
using a Gaussian window. If the duty cycle of the square-wave signal is
50 %, the frequency power spectrum is
FFT-based fitting of a noise function (
There are many different ways to stack a signal (Naess and Bruland, 1985).
To keep this comparison simple, we used only one stacking method, the
alpha-trimmed-mean stack (Friedel, 2000). The first step is a drift correction
(Friedel, 2000). The drift-corrected function
Sorted amplitude distribution for the alpha-trimmed-mean stacking.
In the lock-in processing, also known as phase-sensitive rectifying, the negative part of the acquired square wave is rectified, accomplished by a reference signal at the slopes of the square wave. Harmonic noise annihilates itself and disharmonic noise is thus reduced. The DC value of this convoluted signal is the desired amplitude. Usually lock-in amplifiers retrieve the hard-wired reference signal from the transmitter in order to have the correct phase information at the receiver. In a survey area of a few square kilometres it is not practical to connect all dataloggers with trigger cables to the current source and so destroy the advantage of the autonomous remote-controlled datalogger. However, we show that it is also possible to solve this problem numerically.
Determination of effective stacking window for calculating the mean value at the plateaus for a synthetic signal containing a 250 ms overshoot.
First step is a drift correction (see Sect. 3.2). With a sample interval
of
Drift-corrected signal
The main criteria used to obtain the real phase is the maximum of the DC function
within a specific DC search area (THdc threshold of DC function, usually
25 %). At an ideal square-wave signal the DC value of the convoluted
signal is the desired amplitude. As this can lead to the wrong results for
signal contributions like overshoots, we additionally see whether there is also
a minimum of the Vpp function within a Vpp search area (THvpp threshold of
Vpp function, usually 20 %). The LabView function for the Vpp amplitude
calculates the positive and negative peak values from a histogram
statistics that can cause the minimum of the Vpp function to be wide. To
find the real phase within a wide Vpp minimum, the minimum of the rms
function below the rms search area (THrms threshold of rms function, usually
10 %) is used because the rms value is very sensitive. This procedure is
shown in the flow diagram in Fig. 10a and on the example in
Fig. 10b: the minimum of the quadratic sum eval(
Evaluated functions of direct current (DC) value, peak-to-peak voltage Vpp and effective root mean square (rms) of the mask-convoluted signal.
To compare the results of the lock-in-, stacking- and FFT-processing we
created two artificial data sets. Both data sets exhibit a square-wave signal
with a frequency of 0.2 Hz using a 50 % duty cycle and an amplitude of
10 mVp. The first data set has a 10 mV overshoot (5 % duty cycle wide) at
the leading and trailing edges of the added signal. The second data set is
without overshoot. To create realistic noise conditions, we added 75 mV of
railway noise at 16.7 Hz and 100 mV of power noise at 50 Hz. The variable noise
source was a pink noise with increasing effective noise amplitude from 0 to
249 mVrms added to both signals. The pink noise is created from white noise
filtered through a
Detected amplitude and mean square error MSE of an artificial signal with 10 mV overshoot and 29 mVrms pink noise over length of 0 state, showing the plateau between 16 and 35 %. Up to 16 % 0 state is the effect of the overshoot; above 70 % is the reduced noise rejection.
Quality criteria over noise level of test data set without overshoot.
Each processing has different kind of quality criteria to judge whether a result
is valid or not. At the lock-in it is the mean square error of the slope of
the DC function. At the stacking it is the ratio of the positive and the
negative plateau amplitudes and at the FFT it is the spectral
signal-to-noise ratio at the base frequency. For the comparison we adjusted
the threshold values of the different quality criteria so that an equal
number (30 %) of invalid results were rejected. This leads of course to an
overestimation towards higher noise values of all three methods, because at
low amplitudes the tendency to be rejected by the
quality criteria is higher. Figure 12 shows the three different quality criteria over
noise amplitude in a normalized graph. The criteria for FFT, lock-in and
stacking show an exponential increase. Figure 13 shows the results of the
comparison of the three processing algorithms for the two data sets without
(a) and with (b) overshoot. For low-noise amplitudes all methods yield
similar results except the FFT at the data set with overshoots, because at
the frequency spectrum we cannot separate between the fractions from the ERT
signal and the overshoot. Lock-in and stacking cut off overshoots at the
signal slopes and are therefore not sensitive to transient effects if the
0 state has been chosen appropriately (typically 20 %). At higher
noise amplitudes stacking overestimates the signal more than lock-in and
FFT. Stacking bases the amplitude decision on a wider-frequency spectrum,
while lock-in and FFT just look at a narrow-frequency band. Lock-in
and FFT are therefore less affected by broadband noise. Note that the
performance of FFT might be overestimated as we applied a noise model that
perfectly matches the
The quality criteria MSE of lock-in data of the synthetic data over noise
can be used to validate the quality of the processed data. If we assume the
function of MSE over noise (Fig. 12) valid for realistic signal amplitudes
we can normalize the signal-to-noise ratio with the signal amplitude of
10 mV:
We apply the developed datalogger and analysis methods to a large-scale ERT
field case measured near the town of Schleiz in Thuringia, Germany. We focus
on the second part of the field campaign and on the part of the profile and
remove data from two other dataloggers. The slightly reduced profile thus
consists of 31 electrodes with spacings of 125 m. We used a high-current
generator to maximize the magnitude of the measured voltages. Into each
dipole we injected the maximum current, ranging from 3 to 25 A, depending on
coupling conditions. As for close dipoles, the measured voltage exceeded the
input range, we additionally injected a small current of about 2–3 A. Here
we only used these data for reasons of homogeneity and the greater
A complete dipole–dipole survey was carried out. The principle of reciprocity states that interchanges current and dipole does not change the measured impedance (Friedel, 2000). As a consequence, reciprocal measurements can be used for error estimation. For single data this is a checks how the two independent measurements (a forward and a backward dipole–dipole) are combined before going into the inversion routine. For multi-electrode data it has become common practice to use reciprocal data in a statistical sense to derive error models for weighting data in inversion routines (Udphuay et al., 2011). An error model consists of a constant relative error and a voltage error to take the magnitude of the data into account. It is achieved by distributing the data into bins of similar voltage and fitting a curve to the standard deviation of the reciprocal error. As another quality check we injected two different current strengths. The proportion of the recorded dipole voltages should be identical to the proportion of the injected currents. The small current does not saturate dataloggers in the vicinity of the current source, and the high current provides enough amplitude for the biggest source–receiver distances.
To estimate the error level we use Eq. (11) to calculate the
Signal-to-noise values of field data.
Calculated apparent resistivity
All three processing approaches were applied to the time series. The
resulting voltages were divided by the driving current and multiplied by the
analytically known geometric factor resulting in the apparent
resistivity which represents the resistivity of an equivalent homogeneous
half-space. Additionally, we computed the normal reciprocity from each available pair of forward
and backward measured array, i.e. the percentage
difference divided by the mean value. Figure 15 shows the pseudo-sections of
the apparent resistivity (mean values of forward and backward measured) and
reciprocity for the three approaches. The upper images are hardly
distinguishable – only a few points show distinct deviations due to the wide
range of values between 1 and 1000
Remote dataloggers can provide valuable information on the subsurface in multi-source or monitoring experiments. The presented datalogger, powered by ordinary batteries, can register long time series with sampling rates of up to 1 kHz. It can be accessed and controlled remotely using GSM connection and can therefore save time for a lot of different geoscientific experiments, e.g. in the fields of environmental and groundwater monitoring, or in applied geophysics.
One example is large-scale ERT surveys for geological investigations that cannot be measured with conventional instruments. The registered voltage time series have to be processed to obtain single voltages and their measuring uncertainties. For the ERT experiments that typically use square waves with periods below 1 s and 50 % duty cycle, there have been two approaches for data analysis, i.e. stacking and FFT methods. In addition, we present a lock-in-based approach, a technique that had been used as hardware solution but can also be applied numerically. To make it robust against different kinds of transient effects and noise, several functions are computed from the convolution with a mask signal. The combination of them is used to determine the working point (phase lag), the voltage amplitude and a measure of uncertainty based on a mean square error. The software lock-in processing represents a robust method for determining signal the strength using a reference signal and is thus well suited for ERT.
Synthetic data are used to compare the new method (LI) with an alpha-trimmed
stacking and an improved FFT-based method that includes a
There is space for future development of both the dataloggers and the
processing schemes. One could analyse the decay of the voltage curves to
retrieve induced polarization properties. However, this range is often
dominated by overshoots; hence IP analysis would require exact knowledge of
the source signals. Beyond direct-current (frequencies of 1 Hz or below) one
could use the instrument for controlled-source electromagnetic (CSEM)
surveys that use frequencies from several Hz to several kHz. However, the
limited sampling rate of 1 kHz restricts the frequency range and would
require a new logging concept. The lock-in approach (and similarly stacking)
is expected to work until a sufficient amount of samples are required.
Therefore we expect a better performance of FFT for higher frequency;
however this is very sensitive to the
Codes and data for this publication are available at
FO developed the datalogger including the control software, worked on the processing methods and prepared the manuscript with contributions from the co-author. TG analysed the field data and put the manuscript into the context of ERT.
The authors declare that they have no conflict of interest.
We like to thank Raphael Rochlitz, Robert Meyer, Dieter Epping and Vitali Kipke for help in producing the field data as part of the DESMEX project funded by the German Ministry of Education and Research (BMBF) under grant number 033R139D.Edited by: Jean Dumoulin Reviewed by: two anonymous referees