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  • View in gallery

    University of Miami Rosenstiel School of Marine and Atmospheric Science (RSMAS) Surge Structure Atmosphere Interaction tank.

  • View in gallery

    Instrumentation used in the laboratory experiment at the SUSTAIN facility. (a) Sensor, sensor cable, and sensor driver module and active zone for the cesium-vapor magnetometer. (b) TW Connectivity 4630A low-noise triaxial accelerometer. (c) Senix ultrasonic distance measures.

  • View in gallery

    Schematic diagram of the laboratory experiment (Kluge et al. 2018). For each survey, red indicates the position of the master magnetometer, and green indicates the location of the slave magnetometer. The numbering indicates the positions of the magnetometer pair for each survey. Multiple surveys were conducted at each survey location. (a) The tank view of the side and top. (b) View of the tank from below with transparency to see the wave recorder.

  • View in gallery

    (a) Time series subset of magnetic signature of surface waves. The master (red) and slave (blue) signals. (b) The three ultrasonic distance measures are represented by red, blue, and black, which show the wave elevation. (c) The extended version of the magnetic time series shown in (a). (d) Wave measurements over the same time as the magnetic data shown in (c).

  • View in gallery

    Spectra calculated from the magnetic signature of surface waves. The master (red) and slave (blue). The dashed lines indicate 95% confidence intervals.

  • View in gallery

    Spectra of the master magnetometer data and the magnetic noise calculated from displacement of the accelerometer attached near the magnetometer filtered over the range of 0.2 to 1 Hz. The magnetometer data are shown in red, and the magnetic noise is shown in blue. The dashed lines indicate 95% confidence intervals of the spectrum.

  • View in gallery

    Time series of the magnetometer data after filtering out magnetic noise and normalization. The red line is the magnetic signature from the master magnetometer, and the blue line is the signal from the slave magnetometer. The green line shows the difference between the master and slave signals.

  • View in gallery

    The averaged magnetic signature amplitude at the tank bottom, near the air–water interface, at the tank top, and 2.5 m above the tank top for (a) saltwater and (b) freshwater and (c) when the tank was empty. The blue and red symbols indicate the averaged magnetic amplitude from all surveys conducted for that experiment type (saltwater, freshwater, or empty tank). The blue circles show the surveys averaged in locations with high signal strength. The red circle indicates positions with low signal strength. Signal strength is determined to be high if the quality is >2 and otherwise deemed low. More information regarding signal strength can be found in the geometrics manual (Geometrics 2015). The pink line shows the 95% confidence intervals of those averaged points. The blue curve represents the traditional theoretical curve (Weaver 1965; Lilley et al. 2004). The green line is the effect of magnetic permeability.

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Analysis of the Magnetic Signature of Surface Waves Measured in a Laboratory Experiment

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  • 1 aHalmos College of Arts and Sciences, Nova Southeastern University, Dania Beach, Florida
  • | 2 bRosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida
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Abstract

A magnetic signature is created by secondary magnetic field fluctuations caused by the phenomenon of seawater moving in Earth’s magnetic field. A laboratory experiment was conducted at the Surge Structure Atmosphere Interaction (SUSTAIN) facility to measure the magnetic signature of surface waves using a differential method: a pair of magnetometers, separated horizontally by one-half wavelength, were placed at several locations on the outer tank walls. This technique significantly reduced the extraneous magnetic distortions that were detected simultaneously by both sensors and additionally doubled the magnetic signal of surface waves. Accelerometer measurements and local gradients were used to identify magnetic noise produced from tank vibrations. Wave parameters of 4-m-long waves with a 0.56-Hz frequency and a 0.1-m amplitude were used in this experiment. Freshwater and saltwater experiments were completed to determine the magnetic difference generated by the difference in conductivity. Tests with an empty tank were conducted to identify the noise of the facility. When the magnetic signal was put through spectral analysis, it showed the primary peak at the wave frequency (0.56 Hz) and less pronounced higher-frequency harmonics, which are caused by the nonlinearity of shallow water surface waves. The magnetic noise induced by the wavemaker and related vibrations peaked around 0.3 Hz, which was removed using filtering techniques. These results indicate that the magnetic signature produced by surface waves was an order of magnitude larger than in traditional model predictions. The discrepancy may be due to the magnetic permeability difference between water and air that is not considered in the traditional model.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: J. A. Kluge, jk1083@nova.edu

Abstract

A magnetic signature is created by secondary magnetic field fluctuations caused by the phenomenon of seawater moving in Earth’s magnetic field. A laboratory experiment was conducted at the Surge Structure Atmosphere Interaction (SUSTAIN) facility to measure the magnetic signature of surface waves using a differential method: a pair of magnetometers, separated horizontally by one-half wavelength, were placed at several locations on the outer tank walls. This technique significantly reduced the extraneous magnetic distortions that were detected simultaneously by both sensors and additionally doubled the magnetic signal of surface waves. Accelerometer measurements and local gradients were used to identify magnetic noise produced from tank vibrations. Wave parameters of 4-m-long waves with a 0.56-Hz frequency and a 0.1-m amplitude were used in this experiment. Freshwater and saltwater experiments were completed to determine the magnetic difference generated by the difference in conductivity. Tests with an empty tank were conducted to identify the noise of the facility. When the magnetic signal was put through spectral analysis, it showed the primary peak at the wave frequency (0.56 Hz) and less pronounced higher-frequency harmonics, which are caused by the nonlinearity of shallow water surface waves. The magnetic noise induced by the wavemaker and related vibrations peaked around 0.3 Hz, which was removed using filtering techniques. These results indicate that the magnetic signature produced by surface waves was an order of magnitude larger than in traditional model predictions. The discrepancy may be due to the magnetic permeability difference between water and air that is not considered in the traditional model.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: J. A. Kluge, jk1083@nova.edu

1. Introduction

Maxwell theory predicts that an electromagnetic signature should result from seawater moving in Earth’s magnetic field. In the 1950s, the electromagnetic field fluctuations resulting from the movement of seawater across Earth’s magnetic field caught the attention of physical oceanographers. This sparked research that led to the development of the theory of electromagnetic fields caused by ocean currents and surface and internal ocean waves based on Maxwell’s equations (Von Arx 1950; Longuet-Higgins et al. 1954; Crews and Futterman 1962; Maclure et al. 1964; Warburton and Caminiti 1964; Weaver 1965; Fraser 1966; Larsen 1973; Beal and Weaver 1970; Sanford 1971; Podney 1975; Ochadlick 1989; Watermann and Magunia 1997; Lilley et al. 2004).

Podney (1975) did an extensive theoretical summary of electromagnetic fields generated by surface and internal waves. This work was conducted in order to provide “sensible signals” for the, at the time, newly developed magnetic gradiometers. The author stated that these gradiometers provided unique datasets, which showed that “(1) magnetic field strength above the surface is proportional to seawater speed over the ocean… (2) field strength decreases exponentially above the sea surface… (3) magnetic field gradients can provide directional information on wave spectra.” In this work, the velocity profiles for internal and surface waves were derived and simplified using a series of assumptions. Similar to the velocity section, Podney simplified the magnetic signature of the internal and surface waves. Theoretical case studies in Podney (1975) for surface and internal waves evaluated the effect of different parameters on the magnetic signature.

Weaver (1965) used a more straightforward method to solve for the magnetic field above and below the ocean’s surface than previously conducted work (Von Arx 1950; Longuet-Higgins et al. 1954; Crews and Futterman 1962; Maclure et al. 1964; Warburton and Caminiti 1964). Weaver stressed the importance of swell, especially long-period swell, where the magnetic signal was significantly increased even in a “slight” sea state. Like Podney’s work, Weaver developed theoretical case studies to estimate the induced magnetic field per meter amplitude of surface waves as a function of altitude and depths at various wave periods. Weaver found that even for a “slight sea-state,” with 20 cm amplitude waves with a 20-s period could induce a magnetic signature of 0.2 nT 100 m below the sea surface and a 0.1-nT signature 50 m above the sea surface.

The work conducted by Lilley et al. (2004) studied the magnetic signature of ocean swell based off of Weaver (1965). In Lilley’s experiment, a free-floating magnetometer was released off the coast of southern Australia. Over several days the magnetometer was tracked via satellite and recorded measurements of the ocean swell. The authors found that the period of the waves was approximately 13 s and typically had a signature of 5-nT trough to peak, consistent with Weaver’s (1965) approximations.

In the paper presented here, we follow Weaver’s (1965) approach to estimate the magnetic signature produced by surface waves. Furthermore, the magnetic permeability of water and air is slightly different; the air is paramagnetic forming internal induced magnetic fields in the direction of the applied magnetic field (Pendry et al. 2006). Water is diamagnetic, which forms induced magnetic fields in the direction opposite to that of the applied magnetic field (Miessler and Tarr 2010). Notably, the traditional models neglect the dissimilarity of water and air with regards to magnetic permeability.

A series of laboratory experiments has been conducted (Kluge et al. 2018) at the Surge Structure Atmosphere Interaction (SUSTAIN) facility. This paper presents extended analysis of the experimental results. Section 2 explains the air–sea interaction facility and the methods of the tests conducted for the magnetic signature of surface waves. Section 3 looks at the theoretical considerations of this work. In section 4, traditional magnetic models are compared to the laboratory results. In section 5, we formulate the main conclusions of this study.

2. Laboratory experiment

The University of Miami’s SUSTAIN facility (Fig. 1) was used to conduct the experiments. The SUSTAIN facility houses a 22-m-long, 6-m-wide, and 2-m-high wave tank. Simple sinusoidal waves with a set frequency and amplitude, which propagated down the length of the tank, were produced for this experiment. The wave parameters allowed for easier comparison to analytical models that were then compared to the laboratory results. Moreover, an artificial beach opposite the wavemaker suppressed wave reflection. Furthermore, the SUSTAIN facility contains natural seawater that is pumped directly from Biscayne Bay. During all surveys in our experiments, the water level was at 0.75 m, and the wavemaker produced waves with an amplitude of 0.1 m, a wavelength of 4 m, and at a frequency of 0.56 Hz. The surveys were conducted using saltwater, freshwater, and with an empty tank. The salt and freshwater surveys were used to determine how the difference in conductivity affected the fluctuations in the magnetic field generated by the surface waves. Surveys conducted with the empty tank were conducted to measure the facility’s baseline magnetic noise.

Fig. 1.
Fig. 1.

University of Miami Rosenstiel School of Marine and Atmospheric Science (RSMAS) Surge Structure Atmosphere Interaction tank.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0041.1

This experiment included the following instrumentation: two Geometrics G824-A cesium total field magnetometers (Fig. 2a), a TE 4630A triaxial accelerometer (Fig. 2b) attached near each magnetometer to measure local vibrations, and three Senix Ultrasonic Distances Measurers (Fig. 2c) located centrally on top of the tank.

Fig. 2.
Fig. 2.

Instrumentation used in the laboratory experiment at the SUSTAIN facility. (a) Sensor, sensor cable, and sensor driver module and active zone for the cesium-vapor magnetometer. (b) TW Connectivity 4630A low-noise triaxial accelerometer. (c) Senix ultrasonic distance measures.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0041.1

The Geometrics G-824 magnetometer utilizes an optically pumped cesium-vapor atomic magnetic resonance system that serves as the frequency control element in an oscillator circuit. “When this frequency is accurately measured, it provides an exact measurement of the earth’s total magnetic field (better than 1 part in 108)” (Geometrics 2015). The need to optimize the sensor orientation to obtain precise measurements is eliminated by the sensor’s optical package use of a split-beam design. The active zone permits the sensors to measure the total magnetic field without the need for precise sensor orientation (Geometrics 2015). Additionally, the sensor records signal level, which depends on the placement and orientation of sensors around the tank.

A TE connectivity 4630A accelerometer was positioned adjacent to each magnetometer to record possible tank movement from passing waves. In the relatively high magnetic gradients in the SUSTAIN facility, the tank displacement could lead to magnetic noise contamination of the magnetic signal if not accounted for. The 4630A triaxial accelerometer has available ranges from ±2 to ±500 g and is low noise.

Three Senix Ultrasonic Distance Measurers (UDM) arranged in a triangle formation act as the wave recorder for the experiment. The UDM produces an acoustic ping that travels to the water’s surface and reflects to the sensor, which measures the distance from the water’s surface. The sensor measures the amount of time that it takes for the ping to return and calculates the distance to the water’s surface.

Two Geometric G-824A cesium magnetometers, two 4630A accelerometers, and three UDMs were used for each survey. The magnetometer pairs were spaced one panel of the tank apart (about the distance of one-half wavelength) on the outside of the tank wall above the tank ceiling panels (Fig. 3a, position 7) or on 2.5-m-high tripods (Fig. 3a, position 2). Surveys were carried out below, at the mean water level (Fig. 3a, position 1), and on top of the tank as displayed in Figs. 3a and 3b. Surveys taken below the tank (Fig. 3b, positions 9 and 10) were done to measure the signature below the surface of the water. The magnetic signature at the air–sea interface was measured by surveys conducted on the side of the tank, where the water’s surface moved above and below the magnetometers as the wave traveled down the tank. The surveys on the top of the tank were used to measure the magnetic signature above the surface of the water. Each location, below, on the side, and on top of the tank, was surveyed multiple times for freshwater, saltwater, and when the tank was empty. Multiple surveys allowed for a higher degree of confidence in the results.

Fig. 3.
Fig. 3.

Schematic diagram of the laboratory experiment (Kluge et al. 2018). For each survey, red indicates the position of the master magnetometer, and green indicates the location of the slave magnetometer. The numbering indicates the positions of the magnetometer pair for each survey. Multiple surveys were conducted at each survey location. (a) The tank view of the side and top. (b) View of the tank from below with transparency to see the wave recorder.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0041.1

The master and slave, named for how the sensors interact while paired (Geometerics 2015), magnetometer pair was synchronized in time with the accelerometer and wave sensor for each survey. As shown in Figs. 4a and 4c, the total magnetic signal for both sensors was centered by removing the mean magnetic total field value from each sensor. Likewise, the UDM values were centered (mean value removed) to for comparison to the magnetic time series (Figs. 4b,d).

Fig. 4.
Fig. 4.

(a) Time series subset of magnetic signature of surface waves. The master (red) and slave (blue) signals. (b) The three ultrasonic distance measures are represented by red, blue, and black, which show the wave elevation. (c) The extended version of the magnetic time series shown in (a). (d) Wave measurements over the same time as the magnetic data shown in (c).

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0041.1

The spectra were then calculated from the master and slave magnetometers to identify our expected wave frequency (0.56 Hz) and other possible sources of noise. These spectra are shown in Fig. 5, calculated from the data shown in Fig. 4c (matching wave profile shown in Fig. 4d), which contains the three peaks consistently found in all surveys and the 95% confidence intervals. The most significant peak at 0.56 Hz correlates to the wave frequency generated by the propagation of the surface waves. The two other peaks recorded at approximately 0.3 and 1.2 Hz are ascribed to the facility noise and a secondary harmonic of the 0.56-Hz wave peak, respectively.

Fig. 5.
Fig. 5.

Spectra calculated from the magnetic signature of surface waves. The master (red) and slave (blue). The dashed lines indicate 95% confidence intervals.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0041.1

The accelerometer data for each survey were double integrated to obtain displacement in the X, Y, and Z directions. The movement was then multiplied by the local gradients at the sensor’s location, which produced the magnetic noise due to vibrations in the X, Y, and Z directions. The local magnetic gradients for each survey location shown in Table 1 were required to remove noise potentially present due to tank vibration movements. The gradients were measured by moving a total field magnetometer a designated distance in the X, Y, and Z directions. The change of total magnetic field was attributed to the gradients in the X, Y, and Z directions. The gradients were evaluated by matching the peak at the frequency of the tank vibration with the corresponding peak measured by the magnetometer at the survey location.

Table 1

Magnetic gradients from different locations on the SUSTAIN tank where magnetometers were placed during the surveys. These gradients were used to correct the magnetometer signal due to the gradients at the test facility. ΔBL is the gradient of Earth’s magnetic field in the X, Y, and Z directions, along the tank, across the tank, and vertically, respectively. The numbers and letters in the table represent the panels where the panels “closer” in Fig. 3a are column A and the numbers represent the number of rows in that column. For example, in Fig. 3b, position 9 are labeled B5 and B6 in this table. The asterisk indicates that the sensors were 2.45 m above the top of the tank, which is approximately 3.8 m above the water level.

Table 1

The noise spectra for X, Y, and Z were then calculated and summed to determine the total spectral contribution from all three components of vibrations. Figure 6 shows the magnetic noise due to vibrations compared to the magnetometer data. Signals were bandpass filtered over the range of 0.2–2 Hz to suppress unrelated low-frequency trends below 0.2 Hz and high-frequency noises above 2 Hz. When the filter was applied, it became apparent that the main peak of the magnetic noise was approximately one-half of the primary wave peak.

Fig. 6.
Fig. 6.

Spectra of the master magnetometer data and the magnetic noise calculated from displacement of the accelerometer attached near the magnetometer filtered over the range of 0.2 to 1 Hz. The magnetometer data are shown in red, and the magnetic noise is shown in blue. The dashed lines indicate 95% confidence intervals of the spectrum.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0041.1

After the magnetic noise due to vibrations from the wavemaker was suppressed, the signals from the master and slave magnetometers at some survey locations on the tank showed differing amplitudes. We assume the different amplitudes are caused by the magnetic gradients around the tank distorting the magnetic field differently at each survey location. We normalized the amplitudes using the standard deviation of the master and slave magnetometer outputs and the ratio of the measured magnetic total field (Bm) at the survey location and Earth’s total magnetic field in Miami (B0). The normalization method determined which sensor, master, or slave, Bm most closely matched B0 and then fit the magnetic amplitudes to that sensor’s output. The amplitudes of the master and slave were then multiplied by B0/Bm, bringing the amplitude to a level that would be expected in the tank with no distortions from the infrastructure. The justification for this is that a wave would have the same magnetic signature at the two close locations of the master and slave magnetometers. Subsequently, the difference between the two magnetometer signals was calculated. This differential technique reduced the external noise that both magnetometers detected simultaneously.

An example of the magnetic amplitudes from the master and slave magnetometer after suppressing the noise of the wavemaker, normalization, and then applying the differential can be seen in Fig. 7. The differential is twice the amplitude of the master and slave magnetometer signals due to the magnetometer signals being in the opposite phase.

Fig. 7.
Fig. 7.

Time series of the magnetometer data after filtering out magnetic noise and normalization. The red line is the magnetic signature from the master magnetometer, and the blue line is the signal from the slave magnetometer. The green line shows the difference between the master and slave signals.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0041.1

3. Theoretical considerations

Various primary factors drive the electromagnetic theory in the ocean, including the total magnetic field, magnetic field line dip angle, and conductivity (Beal and Weaver 1970; Podney 1975; Lilley et al. 2004). However, some parameters, such as magnetic permeability and susceptibility, are not utilized in the traditional modeling approach. The magnetic field in the air and water are defined below:
Ba=B0(1+χa),
Bw=B0(1+χw),
where B0 is the magnetic field in the free space, Ba is the magnetic field in the air, and Bw is the magnetic field in the water. Additionally, χa and χw (χa = 0.36 × 10−6, χw = −9.05 × 10−6) are the volume magnetic susceptibilities of the air and water, respectively. The difference of the magnetic field between the air and water,
ΔB=BaBw=Ba(χaχw)/(1+χa)=9.41×106Ba.
When the total magnetic field of Earth in the Miami location is used in the equation above, we get Ba = 43 926.2 nT and ΔB = 0.41 nT. This change in the magnetic field across the interface is what we expect to see and have labeled the “magnetic permeability effect.” The magnetic permeability effect will be used when looking at localized magnetic amplitudes across the tank.

4. Discussion

The magnetic signal recorded from the magnetometers was filtered using a bandpass filter that had a range of 0.4 to 1.2 Hz, leaving the wave frequency (0.56 Hz) intact but removing the prominent peak of tank vibrations at 0.3 Hz. After filtering, the tank vibrations were substantially reduced. The differential method was then applied to reduce the external distortions from outside the facility that the sensors would see simultaneously. The differential signal was then used to calculate the magnetic amplitude from each survey at the corresponding location on the tank. The amplitudes from matching locations and experiments (freshwater, saltwater, or when the tank was empty) were then averaged to produce a single point for each experiment type.

Figure 8 shows the averaged magnetic amplitude, from the multitude of surveys conducted at each location for the three experiments, in saltwater, freshwater, and when the tank was empty. The amplitude of the magnetic signature of surface waves was averaged within all surveys conducted at the same location. Confidence intervals were calculated using t values and degrees of freedom (Mackowiak et al. 1992). While the blue curve displays the traditional model’s expected values (0.015 and 0 nT for seawater and freshwater, respectively), the green line is the exponential fit of the measurements in the air (where measurements were less scattered) constrained by the theoretical value of magnetic induction at the air–water interface because of the difference in magnetic permeability (ΔB = 0.41 nT) according to Eq. (3). A similar curve was mirrored into the water layer.

Fig. 8.
Fig. 8.

The averaged magnetic signature amplitude at the tank bottom, near the air–water interface, at the tank top, and 2.5 m above the tank top for (a) saltwater and (b) freshwater and (c) when the tank was empty. The blue and red symbols indicate the averaged magnetic amplitude from all surveys conducted for that experiment type (saltwater, freshwater, or empty tank). The blue circles show the surveys averaged in locations with high signal strength. The red circle indicates positions with low signal strength. Signal strength is determined to be high if the quality is >2 and otherwise deemed low. More information regarding signal strength can be found in the geometrics manual (Geometrics 2015). The pink line shows the 95% confidence intervals of those averaged points. The blue curve represents the traditional theoretical curve (Weaver 1965; Lilley et al. 2004). The green line is the effect of magnetic permeability.

Citation: Journal of Atmospheric and Oceanic Technology 39, 5; 10.1175/JTECH-D-21-0041.1

According to Figs. 8a and 8b, the magnetic amplitude of surface waves was dominated by the effect of the magnetic permeability at the air–water interface and in the air. However, magnetic measurements near the bottom of the tank were higher than expected. One plausible explanation is that convergence/divergence of water occurs near the bottom of the tank in response to surface waves, producing large velocity gradients, which are not taken into consideration in the traditional model.

To study the difference in wave amplitude and frequency in the tank, we have conducted a number of experiments at a 20% higher wave amplitude, a 14% reduced water level, and a 29% reduction in the wave frequency (0.4 Hz versus the original 0.56 Hz). The measurements were taken from sensors located below the tank, attached to the glass wall. These additional measurements went through the same procedure as the original dataset and gave similar results (0.1425 nT versus the original 0.1419 nT) that were within the confidence intervals of the 0.56 Hz dataset. The 0.4-Hz data were corrected for the distance between the magnetometers no longer equal to half of a wavelength.

5. Conclusions

In summary, a laboratory experiment was conducted at the SUSTAIN facilities air–sea interaction tank with freshwater and seawater, as well as when the tank was empty. The seawater and freshwater measurements were not conducted to verify the traditional models but aimed to study the magnetic refraction caused by differences in magnetic permeability/susceptibility at the air–water interface. When referencing the analytical model [Eq. (3)], we found that magnetic refraction at the air–water interface due to the difference in magnetic permeability between the air and water results in a magnetic induction signal of approximately 0.41 nT based on the magnetic field in Miami. When comparing the laboratory results from our experiment to the analytical model, our laboratory results found a range of 0.25 to 0.38 nT at the air–water interface from the freshwater and seawater experiments. The disparity in these results may come from the magnetic noise still intact after removing the prominent magnetic distortion frequency. This study shows that if the traditional models were updated to include magnetic refraction at the air–water interface, it would help predict the magnetic signature of shallow water surface waves more accurately.

Acknowledgments.

We thank John Holmes, George Valdes, and Brian Glover (NSWC), William Avera (NRL-Stennis), and Brad Nelson (Aeromagnetic Solutions Inc.) for essential discussions pertaining to the laboratory experiment. We would also like to thank Bjorn Ryden from TE Connectivity for loaning us the accelerometers used in the experiments. This research was funded by the Naval Air Warfare Center Aircraft Division under Agreement N00421-15-0003 and the Office of Naval Research under Agreements N00014-18-1-2835 and N00014-21-1-4007. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Naval Air Warfare Center Aircraft Division, the Office of Naval Research, or the U.S. Government.

Data availability statement.

The data are available upon request from the first author (jk1083@nova.edu).

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