# Enabling surface nuclear magnetic resonance at high-noise environments using a pre-polarization pulse

Enabling surface nuclear magnetic resonance at high-noise environments using a pre-polarization... Summary The technique of surface nuclear magnetic resonance (SNMR) has been widely used for hydrological investigations in recent years. Unfortunately, the detected SNMR signals are limited to tens of nanovolts and are thus susceptible to environmental noise. While pre-polarization pulses to enhance the detected signal amplitudes are common in laboratory applications, SNMR field testing has only utilized excitation pulses until now. In conducting measurements in China, we demonstrate that adding a pre-polarization field to the SNMR pulse sequence is feasible and allows for the reliable detection of SNMR signals in noisy scenarios that otherwise prohibit signal detection. We introduce a forward modelling for pre-polarization using SNMR and present a three-layer model obtained from inverse modelling that satisfies the observed data from the field experiment. We expect this development to open up new applications for SNMR technology, especially in high-noise level places, such as active mines. Hydrogeophysics, Electromagnetic theory, Geomagnetic induction, Remagnetization, Numerical modelling 1 INTRODUCTION Surface nuclear magnetic resonance (SNMR) is, thanks to its direct sensitivity to groundwater, a more and more frequently applied geophysical technique used for near-surface hydrological characterization. In recent years, fundamental progress has occurred, extending the method to allow for 2-D (Hertrich 2008; Hertrich et al.2009; Dlugosch et al.2014) and 3-D (Legchenko et al.2011; Jiang et al.2015a) subsurface imaging. Further, new measurement configurations (Davis et al.2014; Jiang et al.2015b), new measurement sequences (Grunewald & Walsh 2013), improved inversion techniques (Müller-Petke & Yaramanci 2010), and data processing schemes to enhance signal-to-noise ratios (SNRs) were develop. The methods for data processing are of considerable importance, as SNMR signals occur only in the nanovolt range and thus, SNMR is sensitive to natural and manmade electromagnetic (EM) noise. Two specific strategies are followed to improve the SNR by (i) suppressing noise and (ii) increasing the signal amplitude. In terms of noise suppression, previous research has focused on using reference loops to cancel correlated noise (Walsh 2008; Dalgaard et al.2012; Müller-Petke & Costabel 2014) and to process harmonic (Legchenko & Valla 2003; Larsen et al.2014) and impulse noise (Jiang et al.2011; Costabel & Müller-Petke 2014; Larsen 2016). To increase the signal amplitude, sophisticated transmitting pulses or pulse sequences are necessary. Grunewald et al. (2016) proposed the method of adiabatic pulses and Grombacher & Knight (2015) introduced composite and off-resonant pulses. Either method effectively increases the excitation volume, and thus the signal amplitude, as the amplitude of the measured signal depends on the number of protons that are excited. In line with these methods, here, a method is proposed that increases the detected signal amplitude. However, in contrast to the work of Grunewald et al. (2016) and Grombacher & Knight (2015), the magnetization of the hydrogen proton is increased by utilizing the pre-polarization (PP) technique. PP is a well-known approach in the laboratory applications of NMR, which was first proposed by Pachard & Varian (1954), and is now also routinely applied in earth-field NMR (e.g. Callaghan et al.1997). However, until now, SNMR has not used PP in practice but was used only in a modelling study without the results from actual measurement (de Pasquale & Mohnke 2014). In this letter, we introduce a new SNMR instrument that is capable of transmitting PP pulses and thus, taking advantage of a significantly enhanced SNR. We present a forward modelling of PP and compare it to traditional alternating current (AC) pulses. To verify the effectiveness of our approach and modelling, we conducted a field measurement of the surface of a frozen free water reservoir which was located in a high-noise area in Shaoguo, China, and estimate a three-layer inverse modelling of the observed data. Comparing the derived subsurface model obtained via our field measurements with ground-truth data obtained from the existing hydrological data and measurements, we can demonstrate the advantages of PP use in SNMR. 2 MATERIAL AND METHODS 2.1 PP surface-NMR measurement physics The signal amplitude detected by any NMR technique fundamentally depends on the macroscopic magnetization M0 of an ensemble of hydrogen protons and is given as (e.g. Levitt 2002)   $${M_0} = \frac{{N{\gamma _p}^2{\hbar ^2}\left| {{{\bf B}_0}} \right|}}{{4{k_{\rm{B}}}T}},$$ (1)at thermal equilibrium and for a unit volume of temperature T, the gyromagnetic ratio γp, Planck's constant ℏ, Boltzmann's constant kB, and the number of spins per unit volume N. Consequently, the macroscopic magnetization depends on the static magnetic field B0, and increasing B0 increases M0. In turn, the NMR detected signal is the induced voltage in the receiver coil caused by the time derivative of the macroscopic magnetization rotating at the Larmor frequency. Thus, the signal amplitude is a function of M0. SNMR utilized by the Earth's magnetic field and M0 is small. Nevertheless, the concept of PP is not to permanently change B0 but to temporarily apply an additional static magnetic field Bp by driving a coil with a constant direct current (DC) I for a certain period. The temporal diagram for PP SNMR is shown in Fig. 1(a). First, the resulting field B0 + Bp increases M0 to MBp  $${M_{\rm Bp}} = \frac{{N{\gamma _p}^2{\hbar ^2}\left| {{{\bf B}_0} + {{\bf B}_{\rm p}}} \right|}}{{4{k_{\rm{B}}}T}},$$ (2)while the increase follows an exponential function with T1 as the relaxation time. Further, MBp is orientated in the direction of B0 + Bp. One may set Bp immediately to zero (even though this is practically impossible) but this causes MBp to rotate about the direction of B0, which is unwanted. Thus, Bp declines in an adiabatic manner (Melton et al.1995; Melton & Pollak 2002) to keep MBp orientated along B0 without rotation. The shutdown waveform of the DC current is shown in Fig. 1(b). The DC shutdown needs to be fast enough to allow the magnetic field B0 + Bp to collapse much faster than the T1 relaxation but slow enough to satisfy adiabatic conditions. This leaves a short time of some milli-seconds to ensure that the energy is released. Detailed descriptions of the electronic circuit and spin-dynamics modelling for PP shut down adiabatically are beyond the scope of this letter, but they have been accomplished. One can find similar technologies described in Conradi et al. (2017) and Melton & Pollak (2002), respectively. Next, the common free-induction-decay (FID) experiment (e.g. Levitt 2002), which applies an excitation pulse Bac at the Larmor frequency, can be conducted under Earth-field conditions but takes advantage of the increased MBp magnitude. Figure 1. View largeDownload slide Schematic for pre-polarization used in SNMR. (a) Pulse sequence, DC transmitting for Bp and AC for Bac. (b) Shut down waveform for the pre-polarization field. For the case in this paper, a 2 m square coil with 10 turns and a 120 A DC for one turn is used; the current declines to zero for 1.5 ms, and another 3.5 ms is left to ensure the energy is completely released before AC is transmitted. The waveform will need to be redefined once the transmitting coil or the DC current are changed to satisfy the adiabatic condition. Figure 1. View largeDownload slide Schematic for pre-polarization used in SNMR. (a) Pulse sequence, DC transmitting for Bp and AC for Bac. (b) Shut down waveform for the pre-polarization field. For the case in this paper, a 2 m square coil with 10 turns and a 120 A DC for one turn is used; the current declines to zero for 1.5 ms, and another 3.5 ms is left to ensure the energy is completely released before AC is transmitted. The waveform will need to be redefined once the transmitting coil or the DC current are changed to satisfy the adiabatic condition. 2.2 Forward modelling To account for the PP pulse, the constant M0 in the commonly used forward modelling formulation for coincident loops (Weichman et al.2000) needs to be replaced by a non-uniform magnetization MBp(r) and reads as follows (de Pasquale & Mohnke 2014):   \begin{eqnarray} V(q,t) &=& - 2{\omega _L}\int\limits_{r}{{\int\limits_{{T_2^*}}{{{M_{\rm Bp}}({\bf r}){\rm sin}\left({\gamma _p}q\left| {{\bf B}_ \bot ^ + ({\bf r})} \right|\right)}}}}\nonumber\\ &&\times \left| {{\bf B}_ \bot ^ - ({\bf r})} \right| \cdot {e^{i2\xi ({\bf r})}} \cdot w({\bf r},T_2^*) \cdot {e^{ - t/T_2^*}}{\rm{d}}T_2^* \cdot {{\rm{d}}^3}r, \end{eqnarray} (3)MBp(r) is calculated according to eq. (2), with Bp(r) derived from the modelling of the DC in the polarization loops using the commercial finite-element software COMSOL (COMSOL 2012). In eq. (3), ωL is the Larmor frequency; $$| {{\bf B}_ \bot ^ + ({\bf r})} |$$ and $$| {{\bf B}_ \bot ^ - ({\bf r})} |$$ are the amplitudes of the circularly polarized co-rotating and counter-rotating components of B(r) perpendicular to B0 and are normalized to a unit current, respectively; ξ is the phase; and q = I0τp is the pulse moment. Other details used to calculate the 1-D kernel function follow the works of Weichman et al. (2000) or Hertrich (2008). To further improve the calculation accuracy, Hammer integrations (Yu 1984) for unstructured non-uniform tetrahedral meshes, which are also employed (Jiang et al.2015b). Comparing the kernel functions with and without PP in Fig. 2, the effectiveness of using PP in SNMR is shown for a 2 m diameter square loop with 10 turns used for transmitting (both DC and AC pulse) and 60 turns used for receiving. With PP pulses, a 120 A DC current is assumed to be applied for one turn, thus 1200 A of DC current is used for 10 turns. Both kernel functions show that sensitivity decreases with depth with increasing pulse moments. In comparison, the PP-kernel shows higher sensitivity at shallow depths, down to approximately 3.0 m, due to the increases in MBp. As we expected, the Bp field decreases with depth, and therefore, MBp decreases and both kernel functions become similar for larger depth. Consequently, the higher sensitivity of the PP-kernel at shallow depths implies that this experimental setup will be more focused on near-surface depths. Figure 2. View largeDownload slide The absolute values of the 1-D kernel as a function of depth and pulse moment using 2 m square coils for transmitting (10 turns for PP and AC) and receiving (60 turns); the DC for PP is 120 A for one turn. (a) SNMR with a PP kernel function and (b) SNMR without a PP kernel function. Figure 2. View largeDownload slide The absolute values of the 1-D kernel as a function of depth and pulse moment using 2 m square coils for transmitting (10 turns for PP and AC) and receiving (60 turns); the DC for PP is 120 A for one turn. (a) SNMR with a PP kernel function and (b) SNMR without a PP kernel function. 2.3 Study site description The study site of Taipingchi is a water reservoir located in Shaoguo, north-east China. The bed of this reservoir is mainly characterized by clay stone and sandstone. A thin silt layer with an approximately 0.2 m thickness separates the free water reservoir from the bedrock. The thickness of the water reservoir changes are typically between 3 and 4 m (based existing hydrological data and measurements). During the winter, the reservoir freezes in its shallow areas. Besides this ability to serve as a ground-truth site, this area was chosen to demonstrate the effectiveness of PP in high-noise areas. The site is located near a brickyard, which is 0.9 km from the site, that generates spike noises and harmonic noises that prohibit standard surface-NMR measurements. 2.4 Field experiments To demonstrate the principal applicability and use of PP, an experiment was conducted using the new SNMR instrument. The geomagnetic field was measured to as 54 720 nT, with an inclination of 62.2° and a declination of −9.8°. The AC pulse moments are distributed between 5 and 1000 A ms for 10 turns in a logarithmic manner. The experiment uses the same configuration as that for the forward modelling, that is, a 2 m square loop with 10 turns, 0.1 Ω in total are applied to the transmitting coil resistance with 60 turns, and 4.34 Ω in total are applied to the receiving coil resistance. The PP coil was powered by a 120 A DC current in one turn using batteries (12 V, 60 A h) to provide a steady current. The PP pulse duration was 8 s to account for the long T1 relaxation. The shutdown of the PP pulse takes approximately 5 ms, during which the current decreases for approximately 1.5 ms and the energy releases for approximately 3.5 ms (the same as Fig. 1b). The PP pulse was followed by the excitation pulse for a duration of 40 ms using the same transmitting coil as PP, and the FID is recorded after approximately 5 ms of dead-time. The collected data were stacked 32 times. We applied despiking (time domain) and adaptive notch filter (for the harmonic of 50 Hz) after stacking. The environmental noise was estimated to be approximately 100 nV after processing for a 1.5 kHz bandwidth. The same experiment was conducted without the PP pulse for comparison. The time and frequency domains of a pulse moment of 9.3 A ms are shown in Figs 3(a) and (b). While an NMR signal at 2330 Hz (the expected Larmor frequency) is clearly visible when using a PP pulse, no NMR signal can be distinguished from the overall noise level without PP, even after noise cancellation. Figure 3. View largeDownload slide SNMR experiment with and without applying a PP pulse to the surface of the ice layer of the Taipingchi water reservoir site in Shaoguo, China. (a) The complete records of the time domain for the pulse moment of 9.3 A ms (after noise cancellation); the blue curve represents the NMR signal with PP and the red curve represents the signal without PP. (b) The spectrum of the signals with the Larmor frequency of 2330 Hz. Figure 3. View largeDownload slide SNMR experiment with and without applying a PP pulse to the surface of the ice layer of the Taipingchi water reservoir site in Shaoguo, China. (a) The complete records of the time domain for the pulse moment of 9.3 A ms (after noise cancellation); the blue curve represents the NMR signal with PP and the red curve represents the signal without PP. (b) The spectrum of the signals with the Larmor frequency of 2330 Hz. Fig. 4(a) shows the whole observed dataset after signal processing. In addition, we applied a logarithmic data resampling (Behroozmand et al. 2012; Dalgaard et al. 2016) using 30 gates. As expected for a shallow water reservoir, the signal amplitude quickly decreases with increasing pulse moments. Further, the data shows long decays, indicating free water. We do not show the full dataset without PP except for the pulse moment of 9.3 A ms, which has been shown in Fig. 3, as NMR signals were submerged in the environmental noise, and the signals can hardly be distinguished with the high-noise levels. Figure 4. View largeDownload slide Results of the SNMR field experiment at the Taipingchi water reservoir site using PP fields. (a) displays the observed data, (b) shows the simulated data for the estimated model, given as black line in (d, e), and the deviation shown in (c) is between (a) and (b). (d) and (e) show the relaxation times and water contents of 10 block models obtained from independent inversion runs. All models fit the observed data equally well. (f) provides the ground-truth of the water reservoir from the literature. Figure 4. View largeDownload slide Results of the SNMR field experiment at the Taipingchi water reservoir site using PP fields. (a) displays the observed data, (b) shows the simulated data for the estimated model, given as black line in (d, e), and the deviation shown in (c) is between (a) and (b). (d) and (e) show the relaxation times and water contents of 10 block models obtained from independent inversion runs. All models fit the observed data equally well. (f) provides the ground-truth of the water reservoir from the literature. 2.5 Inverse modelling To verify our forward modelling kernel for PP, we carried out an inverse modelling to evaluate whether the estimated model matches the available ground-truth. We used MRSmatlab (Müller-Petke et al. 2016) to estimate a three-layer model (Figs 4d and e) of the mono-exponential relaxation time of each layer and water content. The bounds of the relaxation time and water content are 50–2000 ms and 0.05–2 m3 m−3 (i.e. 5–200 per cent), respectively. The block inversion implemented in MRSmatlab is based on a genetic algorithm (Akca et al. 2014). The data misfit (Fig. 4c) shows no remaining structure and the error weighted data fit with χ2 = 1.14 indicates that the data is well explained by the estimated model (Figs 4d and e). To display the model uncertainty, ten independent inversion runs are conducted and are plotted as grey lines. Each of the models fit the data equally well. The obtained relaxation times and water content models are in good agreement with the ground truth (Fig. 4f). The first layer represents the ice layer. As short decays cannot be detected with SNMR (Müller–Petke et al.2011), this layer is given a low water content. Note, even though the water content uncertainty is low, the uncertainty of the relaxation time can be high as no water and, therefore, no signals are detected. Next, the bottom of the ice layer and the top of the water reservoir are very well estimated to be at approximately 0.6 m below surface. The water content of the free water reservoir is well estimated at 100 per cent with an approximately 10 per cent uncertainty. Furthermore, the relaxation time of approximately 650 ms is well within what can be expected for free water. The lower boundary of the water reservoir is represented with high uncertainty. Considering an SNR of approximately 6 and a loop size of 2 m, this is not surprising. 3 DISCUSSION As the measurements presented in this paper were conducted under high environmental noise conditions, the SNMR signals taken with PP are clearly detected while, without PP, no SNMR signals are visible. According to our measurements the maximum measured SNMR amplitude of an SNR of 6 is achieved (for a pulse moment 9.3 A ms, calculated by divided the maximum signal amplitude with the noise estimate). In contrast, without PP the SNR is at least below 1, as no SNMR signals were reliably detected. Consequently, by using a small transmitter loop of 2 m, 10 turns and 120 A, an obvious signal boost at shallow depths is gained by using PP in SNMR measurements. The maximum signal boost was achieved by using a small 2 m square loop with 10 turns and a 120 A DC. The increase in SNR is controlled by the DC. Increasing the DC will result in further increasing the magnetization MBp and, consequently, the SNMR signal amplitude will be increased. There is a linear relationship between the current and signal amplitudes. The focus of the presented study and the developed device is near-surface investigations and underground tunnel applications. Thus, the demanded penetration depth is low and the loop sizes are generally limited by the tunnel diameter. Nevertheless, one could consider the performance of PP for deeper penetrations and with the use of larger loops. Even though detailed analyses of these questions are beyond the scope of this paper, PP will be a valuable technique only for shallow depths, probably down to approximately 10 m. According the law of Biot-Savart, the magnetic field in the centre of a circular loop reads as follows:   $$B(z) = \frac{{{\mu _0}I{r^2}}}{{2{z^3}}},$$ (4)with I as the DC, r as the loop radius and z as the quadratic sum of depth and loop radius. Thus, a 120 A DC with 10 turns and a 2 m loop size at a depth of 1 m achieves a magnetic field of 0.27 mT, while Bp/B0 is approximately 5(B0 = 54 720 nT) and MBp/M0 is the same as that of the implemented configuration. To build up a similar polarization field to a 10 m depth, a 20 m diameter 100 turn loop needs to be energized by a 120 A DC, while at a 30 m depth, a 60 m diameter 300 turn loop needs to be energized by a 120 A DC. The latter appears unrealistic because as the size of the loop increases, the resistance also increase, causing large voltages and increased power. In detail, the transmitter is now a 2 m square loop with 10 turns, with 0.1 Ω in total. For the same material used for 60 m square loops, the resistance would be 90 Ω with 300 turns. Therefore, the voltage and power are 10800 V and 1296 kW for a 120 A DC. To satisfy the power supply, a parameter of ‘10800 V’ is necessary, which will require a large number of the batteries. It is unfeasible to integrate such a large number of batteries into the PP system, even without considering the tremendous resistive heating and other issues. 4 CONCLUSIONS In this letter, we presented the detection of SNMR signals after PP using 2 m coils and provided evidence that PP helps to improve the SNR and, thus, the detectability of SNMR signals. We provide the theoretical considerations for forward modelling of PP signals and show the increases of sensitivity in shallow regions by comparing a 1-D kernel function to traditional AC pulses. Conducting field measurements at a water reservoir site under high-noise conditions, we evaluated our forward and inverse modelling algorithms and found the estimated model to agree well with the available ground-truth data. In the future, we expect considerable interest in the use of SNMR with PP as a method of obtaining information about the properties of subsurface aquifers in tunnels and mines, where noise is a critical issue. ACKNOWLEDGEMENTS This work was supported by the National Foundation of China (Grant Nos 41722405, 2011YQ03113, 20140204022GX and 41374075) and the German Research Council (DFG) (Grant MU 3318/4–1). The authors thank PhDs Yang Zhang and Kun Zhou for their help in instrument system development. REFERENCES Akca İ., Günther M., Müller-Petke M., Baokur A.T., Yaramanci U., 2014. Joint parameter estimation from magnetic resonance and vertical electric soundings using a multi-objective genetic algorithm, Geophys. Prospect. , 62, 364– 376. Google Scholar CrossRef Search ADS   Behroozmand A.A., Auken E., Fiandaca G., Christiansen A.V., Christensen N.B., 2012. Efficient full decay inversion of MRS data with a stretched-exponential approximation of the distribution, Geophys. J. Int. , 190( 2), 900– 912. https://doi.org/10.1111/j.1365-246X.2012.05558.x Google Scholar CrossRef Search ADS   Callaghan P.T., Eccles C.D., Seymour J.D., 1997. 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Published by Oxford University Press on behalf of The Royal Astronomical Society. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geophysical Journal International Oxford University Press

# Enabling surface nuclear magnetic resonance at high-noise environments using a pre-polarization pulse

, Volume 212 (2) – Feb 1, 2018
5 pages

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Publisher
The Royal Astronomical Society
ISSN
0956-540X
eISSN
1365-246X
D.O.I.
10.1093/gji/ggx490
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### Abstract

Summary The technique of surface nuclear magnetic resonance (SNMR) has been widely used for hydrological investigations in recent years. Unfortunately, the detected SNMR signals are limited to tens of nanovolts and are thus susceptible to environmental noise. While pre-polarization pulses to enhance the detected signal amplitudes are common in laboratory applications, SNMR field testing has only utilized excitation pulses until now. In conducting measurements in China, we demonstrate that adding a pre-polarization field to the SNMR pulse sequence is feasible and allows for the reliable detection of SNMR signals in noisy scenarios that otherwise prohibit signal detection. We introduce a forward modelling for pre-polarization using SNMR and present a three-layer model obtained from inverse modelling that satisfies the observed data from the field experiment. We expect this development to open up new applications for SNMR technology, especially in high-noise level places, such as active mines. Hydrogeophysics, Electromagnetic theory, Geomagnetic induction, Remagnetization, Numerical modelling 1 INTRODUCTION Surface nuclear magnetic resonance (SNMR) is, thanks to its direct sensitivity to groundwater, a more and more frequently applied geophysical technique used for near-surface hydrological characterization. In recent years, fundamental progress has occurred, extending the method to allow for 2-D (Hertrich 2008; Hertrich et al.2009; Dlugosch et al.2014) and 3-D (Legchenko et al.2011; Jiang et al.2015a) subsurface imaging. Further, new measurement configurations (Davis et al.2014; Jiang et al.2015b), new measurement sequences (Grunewald & Walsh 2013), improved inversion techniques (Müller-Petke & Yaramanci 2010), and data processing schemes to enhance signal-to-noise ratios (SNRs) were develop. The methods for data processing are of considerable importance, as SNMR signals occur only in the nanovolt range and thus, SNMR is sensitive to natural and manmade electromagnetic (EM) noise. Two specific strategies are followed to improve the SNR by (i) suppressing noise and (ii) increasing the signal amplitude. In terms of noise suppression, previous research has focused on using reference loops to cancel correlated noise (Walsh 2008; Dalgaard et al.2012; Müller-Petke & Costabel 2014) and to process harmonic (Legchenko & Valla 2003; Larsen et al.2014) and impulse noise (Jiang et al.2011; Costabel & Müller-Petke 2014; Larsen 2016). To increase the signal amplitude, sophisticated transmitting pulses or pulse sequences are necessary. Grunewald et al. (2016) proposed the method of adiabatic pulses and Grombacher & Knight (2015) introduced composite and off-resonant pulses. Either method effectively increases the excitation volume, and thus the signal amplitude, as the amplitude of the measured signal depends on the number of protons that are excited. In line with these methods, here, a method is proposed that increases the detected signal amplitude. However, in contrast to the work of Grunewald et al. (2016) and Grombacher & Knight (2015), the magnetization of the hydrogen proton is increased by utilizing the pre-polarization (PP) technique. PP is a well-known approach in the laboratory applications of NMR, which was first proposed by Pachard & Varian (1954), and is now also routinely applied in earth-field NMR (e.g. Callaghan et al.1997). However, until now, SNMR has not used PP in practice but was used only in a modelling study without the results from actual measurement (de Pasquale & Mohnke 2014). In this letter, we introduce a new SNMR instrument that is capable of transmitting PP pulses and thus, taking advantage of a significantly enhanced SNR. We present a forward modelling of PP and compare it to traditional alternating current (AC) pulses. To verify the effectiveness of our approach and modelling, we conducted a field measurement of the surface of a frozen free water reservoir which was located in a high-noise area in Shaoguo, China, and estimate a three-layer inverse modelling of the observed data. Comparing the derived subsurface model obtained via our field measurements with ground-truth data obtained from the existing hydrological data and measurements, we can demonstrate the advantages of PP use in SNMR. 2 MATERIAL AND METHODS 2.1 PP surface-NMR measurement physics The signal amplitude detected by any NMR technique fundamentally depends on the macroscopic magnetization M0 of an ensemble of hydrogen protons and is given as (e.g. Levitt 2002)   $${M_0} = \frac{{N{\gamma _p}^2{\hbar ^2}\left| {{{\bf B}_0}} \right|}}{{4{k_{\rm{B}}}T}},$$ (1)at thermal equilibrium and for a unit volume of temperature T, the gyromagnetic ratio γp, Planck's constant ℏ, Boltzmann's constant kB, and the number of spins per unit volume N. Consequently, the macroscopic magnetization depends on the static magnetic field B0, and increasing B0 increases M0. In turn, the NMR detected signal is the induced voltage in the receiver coil caused by the time derivative of the macroscopic magnetization rotating at the Larmor frequency. Thus, the signal amplitude is a function of M0. SNMR utilized by the Earth's magnetic field and M0 is small. Nevertheless, the concept of PP is not to permanently change B0 but to temporarily apply an additional static magnetic field Bp by driving a coil with a constant direct current (DC) I for a certain period. The temporal diagram for PP SNMR is shown in Fig. 1(a). First, the resulting field B0 + Bp increases M0 to MBp  $${M_{\rm Bp}} = \frac{{N{\gamma _p}^2{\hbar ^2}\left| {{{\bf B}_0} + {{\bf B}_{\rm p}}} \right|}}{{4{k_{\rm{B}}}T}},$$ (2)while the increase follows an exponential function with T1 as the relaxation time. Further, MBp is orientated in the direction of B0 + Bp. One may set Bp immediately to zero (even though this is practically impossible) but this causes MBp to rotate about the direction of B0, which is unwanted. Thus, Bp declines in an adiabatic manner (Melton et al.1995; Melton & Pollak 2002) to keep MBp orientated along B0 without rotation. The shutdown waveform of the DC current is shown in Fig. 1(b). The DC shutdown needs to be fast enough to allow the magnetic field B0 + Bp to collapse much faster than the T1 relaxation but slow enough to satisfy adiabatic conditions. This leaves a short time of some milli-seconds to ensure that the energy is released. Detailed descriptions of the electronic circuit and spin-dynamics modelling for PP shut down adiabatically are beyond the scope of this letter, but they have been accomplished. One can find similar technologies described in Conradi et al. (2017) and Melton & Pollak (2002), respectively. Next, the common free-induction-decay (FID) experiment (e.g. Levitt 2002), which applies an excitation pulse Bac at the Larmor frequency, can be conducted under Earth-field conditions but takes advantage of the increased MBp magnitude. Figure 1. View largeDownload slide Schematic for pre-polarization used in SNMR. (a) Pulse sequence, DC transmitting for Bp and AC for Bac. (b) Shut down waveform for the pre-polarization field. For the case in this paper, a 2 m square coil with 10 turns and a 120 A DC for one turn is used; the current declines to zero for 1.5 ms, and another 3.5 ms is left to ensure the energy is completely released before AC is transmitted. The waveform will need to be redefined once the transmitting coil or the DC current are changed to satisfy the adiabatic condition. Figure 1. View largeDownload slide Schematic for pre-polarization used in SNMR. (a) Pulse sequence, DC transmitting for Bp and AC for Bac. (b) Shut down waveform for the pre-polarization field. For the case in this paper, a 2 m square coil with 10 turns and a 120 A DC for one turn is used; the current declines to zero for 1.5 ms, and another 3.5 ms is left to ensure the energy is completely released before AC is transmitted. The waveform will need to be redefined once the transmitting coil or the DC current are changed to satisfy the adiabatic condition. 2.2 Forward modelling To account for the PP pulse, the constant M0 in the commonly used forward modelling formulation for coincident loops (Weichman et al.2000) needs to be replaced by a non-uniform magnetization MBp(r) and reads as follows (de Pasquale & Mohnke 2014):   \begin{eqnarray} V(q,t) &=& - 2{\omega _L}\int\limits_{r}{{\int\limits_{{T_2^*}}{{{M_{\rm Bp}}({\bf r}){\rm sin}\left({\gamma _p}q\left| {{\bf B}_ \bot ^ + ({\bf r})} \right|\right)}}}}\nonumber\\ &&\times \left| {{\bf B}_ \bot ^ - ({\bf r})} \right| \cdot {e^{i2\xi ({\bf r})}} \cdot w({\bf r},T_2^*) \cdot {e^{ - t/T_2^*}}{\rm{d}}T_2^* \cdot {{\rm{d}}^3}r, \end{eqnarray} (3)MBp(r) is calculated according to eq. (2), with Bp(r) derived from the modelling of the DC in the polarization loops using the commercial finite-element software COMSOL (COMSOL 2012). In eq. (3), ωL is the Larmor frequency; $$| {{\bf B}_ \bot ^ + ({\bf r})} |$$ and $$| {{\bf B}_ \bot ^ - ({\bf r})} |$$ are the amplitudes of the circularly polarized co-rotating and counter-rotating components of B(r) perpendicular to B0 and are normalized to a unit current, respectively; ξ is the phase; and q = I0τp is the pulse moment. Other details used to calculate the 1-D kernel function follow the works of Weichman et al. (2000) or Hertrich (2008). To further improve the calculation accuracy, Hammer integrations (Yu 1984) for unstructured non-uniform tetrahedral meshes, which are also employed (Jiang et al.2015b). Comparing the kernel functions with and without PP in Fig. 2, the effectiveness of using PP in SNMR is shown for a 2 m diameter square loop with 10 turns used for transmitting (both DC and AC pulse) and 60 turns used for receiving. With PP pulses, a 120 A DC current is assumed to be applied for one turn, thus 1200 A of DC current is used for 10 turns. Both kernel functions show that sensitivity decreases with depth with increasing pulse moments. In comparison, the PP-kernel shows higher sensitivity at shallow depths, down to approximately 3.0 m, due to the increases in MBp. As we expected, the Bp field decreases with depth, and therefore, MBp decreases and both kernel functions become similar for larger depth. Consequently, the higher sensitivity of the PP-kernel at shallow depths implies that this experimental setup will be more focused on near-surface depths. Figure 2. View largeDownload slide The absolute values of the 1-D kernel as a function of depth and pulse moment using 2 m square coils for transmitting (10 turns for PP and AC) and receiving (60 turns); the DC for PP is 120 A for one turn. (a) SNMR with a PP kernel function and (b) SNMR without a PP kernel function. Figure 2. View largeDownload slide The absolute values of the 1-D kernel as a function of depth and pulse moment using 2 m square coils for transmitting (10 turns for PP and AC) and receiving (60 turns); the DC for PP is 120 A for one turn. (a) SNMR with a PP kernel function and (b) SNMR without a PP kernel function. 2.3 Study site description The study site of Taipingchi is a water reservoir located in Shaoguo, north-east China. The bed of this reservoir is mainly characterized by clay stone and sandstone. A thin silt layer with an approximately 0.2 m thickness separates the free water reservoir from the bedrock. The thickness of the water reservoir changes are typically between 3 and 4 m (based existing hydrological data and measurements). During the winter, the reservoir freezes in its shallow areas. Besides this ability to serve as a ground-truth site, this area was chosen to demonstrate the effectiveness of PP in high-noise areas. The site is located near a brickyard, which is 0.9 km from the site, that generates spike noises and harmonic noises that prohibit standard surface-NMR measurements. 2.4 Field experiments To demonstrate the principal applicability and use of PP, an experiment was conducted using the new SNMR instrument. The geomagnetic field was measured to as 54 720 nT, with an inclination of 62.2° and a declination of −9.8°. The AC pulse moments are distributed between 5 and 1000 A ms for 10 turns in a logarithmic manner. The experiment uses the same configuration as that for the forward modelling, that is, a 2 m square loop with 10 turns, 0.1 Ω in total are applied to the transmitting coil resistance with 60 turns, and 4.34 Ω in total are applied to the receiving coil resistance. The PP coil was powered by a 120 A DC current in one turn using batteries (12 V, 60 A h) to provide a steady current. The PP pulse duration was 8 s to account for the long T1 relaxation. The shutdown of the PP pulse takes approximately 5 ms, during which the current decreases for approximately 1.5 ms and the energy releases for approximately 3.5 ms (the same as Fig. 1b). The PP pulse was followed by the excitation pulse for a duration of 40 ms using the same transmitting coil as PP, and the FID is recorded after approximately 5 ms of dead-time. The collected data were stacked 32 times. We applied despiking (time domain) and adaptive notch filter (for the harmonic of 50 Hz) after stacking. The environmental noise was estimated to be approximately 100 nV after processing for a 1.5 kHz bandwidth. The same experiment was conducted without the PP pulse for comparison. The time and frequency domains of a pulse moment of 9.3 A ms are shown in Figs 3(a) and (b). While an NMR signal at 2330 Hz (the expected Larmor frequency) is clearly visible when using a PP pulse, no NMR signal can be distinguished from the overall noise level without PP, even after noise cancellation. Figure 3. View largeDownload slide SNMR experiment with and without applying a PP pulse to the surface of the ice layer of the Taipingchi water reservoir site in Shaoguo, China. (a) The complete records of the time domain for the pulse moment of 9.3 A ms (after noise cancellation); the blue curve represents the NMR signal with PP and the red curve represents the signal without PP. (b) The spectrum of the signals with the Larmor frequency of 2330 Hz. Figure 3. View largeDownload slide SNMR experiment with and without applying a PP pulse to the surface of the ice layer of the Taipingchi water reservoir site in Shaoguo, China. (a) The complete records of the time domain for the pulse moment of 9.3 A ms (after noise cancellation); the blue curve represents the NMR signal with PP and the red curve represents the signal without PP. (b) The spectrum of the signals with the Larmor frequency of 2330 Hz. Fig. 4(a) shows the whole observed dataset after signal processing. In addition, we applied a logarithmic data resampling (Behroozmand et al. 2012; Dalgaard et al. 2016) using 30 gates. As expected for a shallow water reservoir, the signal amplitude quickly decreases with increasing pulse moments. Further, the data shows long decays, indicating free water. We do not show the full dataset without PP except for the pulse moment of 9.3 A ms, which has been shown in Fig. 3, as NMR signals were submerged in the environmental noise, and the signals can hardly be distinguished with the high-noise levels. Figure 4. View largeDownload slide Results of the SNMR field experiment at the Taipingchi water reservoir site using PP fields. (a) displays the observed data, (b) shows the simulated data for the estimated model, given as black line in (d, e), and the deviation shown in (c) is between (a) and (b). (d) and (e) show the relaxation times and water contents of 10 block models obtained from independent inversion runs. All models fit the observed data equally well. (f) provides the ground-truth of the water reservoir from the literature. Figure 4. View largeDownload slide Results of the SNMR field experiment at the Taipingchi water reservoir site using PP fields. (a) displays the observed data, (b) shows the simulated data for the estimated model, given as black line in (d, e), and the deviation shown in (c) is between (a) and (b). (d) and (e) show the relaxation times and water contents of 10 block models obtained from independent inversion runs. All models fit the observed data equally well. (f) provides the ground-truth of the water reservoir from the literature. 2.5 Inverse modelling To verify our forward modelling kernel for PP, we carried out an inverse modelling to evaluate whether the estimated model matches the available ground-truth. We used MRSmatlab (Müller-Petke et al. 2016) to estimate a three-layer model (Figs 4d and e) of the mono-exponential relaxation time of each layer and water content. The bounds of the relaxation time and water content are 50–2000 ms and 0.05–2 m3 m−3 (i.e. 5–200 per cent), respectively. The block inversion implemented in MRSmatlab is based on a genetic algorithm (Akca et al. 2014). The data misfit (Fig. 4c) shows no remaining structure and the error weighted data fit with χ2 = 1.14 indicates that the data is well explained by the estimated model (Figs 4d and e). To display the model uncertainty, ten independent inversion runs are conducted and are plotted as grey lines. Each of the models fit the data equally well. The obtained relaxation times and water content models are in good agreement with the ground truth (Fig. 4f). The first layer represents the ice layer. As short decays cannot be detected with SNMR (Müller–Petke et al.2011), this layer is given a low water content. Note, even though the water content uncertainty is low, the uncertainty of the relaxation time can be high as no water and, therefore, no signals are detected. Next, the bottom of the ice layer and the top of the water reservoir are very well estimated to be at approximately 0.6 m below surface. The water content of the free water reservoir is well estimated at 100 per cent with an approximately 10 per cent uncertainty. Furthermore, the relaxation time of approximately 650 ms is well within what can be expected for free water. The lower boundary of the water reservoir is represented with high uncertainty. Considering an SNR of approximately 6 and a loop size of 2 m, this is not surprising. 3 DISCUSSION As the measurements presented in this paper were conducted under high environmental noise conditions, the SNMR signals taken with PP are clearly detected while, without PP, no SNMR signals are visible. According to our measurements the maximum measured SNMR amplitude of an SNR of 6 is achieved (for a pulse moment 9.3 A ms, calculated by divided the maximum signal amplitude with the noise estimate). In contrast, without PP the SNR is at least below 1, as no SNMR signals were reliably detected. Consequently, by using a small transmitter loop of 2 m, 10 turns and 120 A, an obvious signal boost at shallow depths is gained by using PP in SNMR measurements. The maximum signal boost was achieved by using a small 2 m square loop with 10 turns and a 120 A DC. The increase in SNR is controlled by the DC. Increasing the DC will result in further increasing the magnetization MBp and, consequently, the SNMR signal amplitude will be increased. There is a linear relationship between the current and signal amplitudes. The focus of the presented study and the developed device is near-surface investigations and underground tunnel applications. Thus, the demanded penetration depth is low and the loop sizes are generally limited by the tunnel diameter. Nevertheless, one could consider the performance of PP for deeper penetrations and with the use of larger loops. Even though detailed analyses of these questions are beyond the scope of this paper, PP will be a valuable technique only for shallow depths, probably down to approximately 10 m. According the law of Biot-Savart, the magnetic field in the centre of a circular loop reads as follows:   $$B(z) = \frac{{{\mu _0}I{r^2}}}{{2{z^3}}},$$ (4)with I as the DC, r as the loop radius and z as the quadratic sum of depth and loop radius. Thus, a 120 A DC with 10 turns and a 2 m loop size at a depth of 1 m achieves a magnetic field of 0.27 mT, while Bp/B0 is approximately 5(B0 = 54 720 nT) and MBp/M0 is the same as that of the implemented configuration. To build up a similar polarization field to a 10 m depth, a 20 m diameter 100 turn loop needs to be energized by a 120 A DC, while at a 30 m depth, a 60 m diameter 300 turn loop needs to be energized by a 120 A DC. The latter appears unrealistic because as the size of the loop increases, the resistance also increase, causing large voltages and increased power. In detail, the transmitter is now a 2 m square loop with 10 turns, with 0.1 Ω in total. For the same material used for 60 m square loops, the resistance would be 90 Ω with 300 turns. Therefore, the voltage and power are 10800 V and 1296 kW for a 120 A DC. To satisfy the power supply, a parameter of ‘10800 V’ is necessary, which will require a large number of the batteries. It is unfeasible to integrate such a large number of batteries into the PP system, even without considering the tremendous resistive heating and other issues. 4 CONCLUSIONS In this letter, we presented the detection of SNMR signals after PP using 2 m coils and provided evidence that PP helps to improve the SNR and, thus, the detectability of SNMR signals. We provide the theoretical considerations for forward modelling of PP signals and show the increases of sensitivity in shallow regions by comparing a 1-D kernel function to traditional AC pulses. Conducting field measurements at a water reservoir site under high-noise conditions, we evaluated our forward and inverse modelling algorithms and found the estimated model to agree well with the available ground-truth data. In the future, we expect considerable interest in the use of SNMR with PP as a method of obtaining information about the properties of subsurface aquifers in tunnels and mines, where noise is a critical issue. ACKNOWLEDGEMENTS This work was supported by the National Foundation of China (Grant Nos 41722405, 2011YQ03113, 20140204022GX and 41374075) and the German Research Council (DFG) (Grant MU 3318/4–1). The authors thank PhDs Yang Zhang and Kun Zhou for their help in instrument system development. REFERENCES Akca İ., Günther M., Müller-Petke M., Baokur A.T., Yaramanci U., 2014. Joint parameter estimation from magnetic resonance and vertical electric soundings using a multi-objective genetic algorithm, Geophys. Prospect. , 62, 364– 376. Google Scholar CrossRef Search ADS   Behroozmand A.A., Auken E., Fiandaca G., Christiansen A.V., Christensen N.B., 2012. Efficient full decay inversion of MRS data with a stretched-exponential approximation of the distribution, Geophys. J. Int. , 190( 2), 900– 912. https://doi.org/10.1111/j.1365-246X.2012.05558.x Google Scholar CrossRef Search ADS   Callaghan P.T., Eccles C.D., Seymour J.D., 1997. 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Geophysical Journal InternationalOxford University Press

Published: Feb 1, 2018

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