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4.6 Frequency-domain helicopter-borne electromagnetics 89 4.6 Frequency-domain helicopter- borne electromagnetics 4.6.1 Physical base All electromagnetic methods are based on Maxwell’s equations (here: frequency-domain formulation): ( ) q = E , B i = E × , 0 = B , J = H × ε ω (4.6.1) with H [A/m] magnetic and E [V/m] electric field intensity, B [Vs/m 2 ] magnetic induction, J [A/m 2 ] electric current density, ε [As/Vm] dielectric permittivity, q [As/m 3 ] electric charge density, ω = 2πf angular frequency, f [Hz] frequency, π 3.14, and i = (–1) 1/2 . The correspondent material equations are: H = B and E = J 0 μ σ (4.6.2) with σ [S/m] electric conductivity (the reciprocal of the resistivity ρ [Ωm]) and μ 0 = 4π 10 –7 Vs/Am free-space magnetic permeability assuming that displacement currents are negligible and the magnetic permeability in the subsurface is that of free space. Maxwell’s equations describe the typical phenomenon that a varying magnetic field causes a varying electric field and thus a current flow in a conductive medium. These varying currents cause varying magnetic fields, and so on. Combining Maxwell’s equations and the material equations and assuming a point source (e.g. magnetic dipole) located above the Earth’s surface (i.e. q = 0 inside the Earth) lead to the induction equation for a homogeneous or layered half-space ( ) F i + = z d F d 2 2 2 σ μ ω λ (4.6.3) where λ [1/m] is the wave-number and F = E or H. 4.6.2 Field techniques Modern frequency-domain helicopter-borne electromagnetic (HEM) systems utilise small transmitter and receiver coils having a diameter of about half a metre. The transmitter signal, the primary magnetic field, is generated by sinusoidal current flow through the transmitter coil at a discrete frequency. As the primary magnetic field is very close to a dipole field at some distance from the transmitter coil, it can be regarded as a field of a magnetic dipole sitting in the centre of the transmitter coil and having an axis perpendicular to the area of the coil. The oscillating primary magnetic field induces eddy currents in the subsurface. These currents, in turn, generate the secondary magnetic field which is dependent on the underground conductivity distribution. The secondary magnetic field is picked up by the receiver coil and related to the primary magnetic field expected at the centre of the receiver coil. As the secondary field is very small with respect to the primary field, the primary field is generally bucked out and the relative secondary field is measured in parts per million (ppm). Due to the induction process in the underground, there is a small phase shift between the primary and secondary field, i.e., the relative secondary magnetic field is a complex quantity having inphase (R) and quadrature (Q) components. The orientation of the transmitter coil is horizontal (VMD: vertical magnetic dipole) or vertical (HMD: horizontal magnetic dipole) and the receiver coil is oriented in a maximum coupled position, resulting in horizontal coplanar, vertical coplanar or vertical coaxial coil systems. Solving the induction equation with respect to a horizontal coplanar coil system leads to (Wait 1982) ( ) ( ) λ λ λ ρ λ ω λ d ) r ( J e ) z ( , , R r = iQ + R = Z 0 h 2 2 0 1 3 (4.6.4) with Z [ppm] secondary magnetic field, R 1 complex reflection factor containing the underground vertical resistivity distribution ρ(z) with z pointing vertically downwards, r [m] coil separation, h [m] sensor height, and J 0 Bessel functions of first kind and zero order.

Transcript of 089-098 - liag-hannover.de · a conductive medium. These varying currents cause varying magnetic...

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4.6 Frequency-domain helicopter-borne electromagnetics

4.6.1 Physical base

All electromagnetic methods are based on Maxwell’s equations (here: frequency-domain formulation):

( ) q=E,Bi=E×,0=B,J=H× ε∇ω∇∇∇ (4.6.1)

with H [A/m] magnetic and E [V/m] electric field intensity, B [Vs/m2] magnetic induction, J [A/m2] electric current density, ε [As/Vm] dielectric permittivity, q [As/m3] electric charge density, ω = 2πf angular frequency, f [Hz] frequency, π ≈ 3.14, and i = (–1)1/2. The correspondent material equations are:

H=BandE=J 0μσ (4.6.2)

with σ [S/m] electric conductivity (the reciprocal of the resistivity ρ [Ωm]) and µ0 = 4π 10–7 Vs/Am free-space magnetic permeability assuming that displacement currents are negligible and the magnetic permeability in the subsurface is that of free space. Maxwell’s equations describe the typical phenomenon that a varying magnetic field causes a varying electric field and thus a current flow in a conductive medium. These varying currents cause varying magnetic fields, and so on. Combining Maxwell’s equations and the material equations and assuming a point source (e.g. magnetic dipole) located above the Earth’s surface (i.e. q = 0 inside the Earth) lead to the induction equation for a homogeneous or layered half-space

( ) Fi+=zdFd 22

2

σμωλ (4.6.3)

where λ [1/m] is the wave-number and F = E or H.

4.6.2 Field techniques

Modern frequency-domain helicopter-borne electromagnetic (HEM) systems utilise small transmitter and receiver coils having a diameter of about half a metre. The transmitter signal, the primary magnetic field, is generated by sinusoidal current flow through the transmitter coil at a discrete frequency. As the primary magnetic field is very close to a dipole field at some distance from the transmitter coil, it can be regarded as a field of a magnetic dipole sitting in the centre of the transmitter coil and having an axis perpendicular to the area of the coil. The oscillating primary magnetic field induces eddy currents in the subsurface. These currents, in turn, generate the secondary magnetic field which is dependent on the underground conductivity distribution. The secondary magnetic field is picked up by the receiver coil and related to the primary magnetic field expected at the centre of the receiver coil. As the secondary field is very small with respect to the primary field, the primary field is generally bucked out and the relative secondary field is measured in parts per million (ppm). Due to the induction process in the underground, there is a small phase shift between the primary and secondary field, i.e., the relative secondary magnetic field is a complex quantity having inphase (R) and quadrature (Q) components. The orientation of the transmitter coil is horizontal (VMD: vertical magnetic dipole) or vertical (HMD: horizontal magnetic dipole) and the receiver coil is oriented in a maximum coupled position, resulting in horizontal coplanar, vertical coplanar or vertical coaxial coil systems. Solving the induction equation with respect to a horizontal coplanar coil system leads to (Wait 1982)

( ) ( ) λλλρλω λ∞

∫ d)r(Je)z(,,Rr=iQ+R=Z 0h22

01

3

(4.6.4)

with Z [ppm] secondary magnetic field, R1 complex reflection factor containing the underground vertical resistivity distribution ρ(z) with z pointing vertically downwards, r [m] coil separation, h [m] sensor height, and J0 Bessel functions of first kind and zero order.

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Fig. 4.6.1: BGR’s helicopter-borne geophysical system: Electromagnetic, magnetic, GPS and laser altimeter sensors are housed by a “bird”, a cigar-shaped 9 m long tube, which is kept at about 30–40 m above ground level. The EM system operates at five frequencies ranging from 0.38 to 130 kHz. The coil orientation is horizontal coplanar throughout. The gamma-ray spectrometer, radar and barometric altimeters as well as the navigation system are installed into the helicopter, a Sikorsky S-76B. The sampling rate is 10 Hz except for the spectrometer (1 Hz). That provides sampling distances of about 4 m and 40 m, respectively, taking an average flight velocity of about 140 km/h into account. The base station records the time varying parameters diurnal magnetic variations and air pressure history.

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The penetration of the electromagnetic field into the Earth, for which the plane-wave skin depth p = (2ρ/ωμ0)

1/2 is an approximate measure, depends on both the system frequency used and the resistivity of the subsurface. Deep penetration is achieved using low frequencies. Figure 4.6.1 shows a sketch of a typical helicopter-borne geophysical system. In general, three geophysical methods are used simulta-neously: electromagnetics, magnetics, and radiometrics. 4.6.3 Data processing and resistivity

calculation

The receiver coils of a frequency-domain HEM system measure the induced voltages of the secondary magnetic fields at specific frequencies. These voltages have to be converted to relative values with respect to the primary fields at the receivers. These conversions are done using special calibration coils which produce definite signals in the measured HEM data. Based on these well-known calibration signals, the measured secondary field voltages are transformed to ppm values. As the secondary field is a complex quantity, a phase adjustment has to take place at the beginning of each survey flight, e.g., using the well-defined signals of the calibration coils. Calibration and phase adjustment are best performed above a highly resistive subsurface or in the air at high flight altitude. The secondary fields are strongly dependent on the sensor altitude, even for a homogeneous subsurface. Flight altitudes of several hundred meters (e.g. 350 m for a common HEM system) are sufficient to drop down the signal of the secondary field below the system noise level. This effect is not only used for accurate calibrations and phase adjustments but also for determining the zero levels of the HEM data. Remaining signals due to insufficiently bucked-out primary fields, coupling effects with the helicopter, or (thermal) system drift are generally detected at high flight altitude several times during a survey flight. These basic values measured at reference points are used to shift the HEM data with respects to their zero levels

(Valleau 2000). This procedure enables the elimination of a long-term, quasi-linear drift; short-term variations caused by, e.g., varying air temperatures due to alternating sensor elevations, however, cannot be determined successfully by this procedure. Therefore, additional reference points – also along the profiles at normal survey flight altitude – may be determined where the secondary fields are small but not negligible. At these locations, the estimated half-space parameters are used to calculate the expected secondary field values which then serve as local reference levels (Siemon 2006). A standard airborne survey consists of a number of parallel profile lines covering the entire survey area and several tie-lines which should be flown perpendicular to the profile lines. At the cross-over points, the HEM data from profile and tie-lines are compared and statistically analysed to correct the HEM line data for remaining strong zero-level errors. Due to the altitude dependency of the HEM data, the tie-line levelling and further HEM levelling procedures (e.g. Huang & Fraser 1999, Siemon 2006) are normally applied to parameters of a homogeneous half-space (apparent resistivity and apparent depth) which are less affected by variations of the sensor altitude. Noise from external sources (e.g. from radio transmitters or power lines) should be eliminated from the HEM data by appropriate filtering or interpolation procedures. Induction effects from buildings and other electrical installations or effects from strongly magnetised underground sources should not be erased from the data during the first step of data processing. These effects appear particularly on a low-frequency resistivity map as conductive or resistive features outlining the locations of man-made installations or strongly magnetised sources, respectively. If necessary, these effects can be cancelled out after a thorough inspection, and the data may be interpolated in case of small data gaps and smoothly varying resistivities. Generally, the (measured) secondary field data (R, Q) is inverted into resistivity using two principal models: the homogeneous half-space model and the layered half-space model (Fig. 4.6.2). While the homogeneous half-space inversion uses

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single frequency data, i.e., resistivities and depths are calculated individually for each of the frequencies used, the multi-layer (or one dimensional, 1-D) inversion is able to take the data of all frequencies available into account. As the dependency of the secondary field on the half-space resistivity is highly non-linear, the inversion is not straightforward and the apparent resistivities have to be derived by the use of look-up tables, curve fitting or iterative inversion procedures. The sensor altitude, which is measured in field surveys by laser or radar altimeters, may be affected by trees or buildings. That is the most crucial disadvantage for using the sensor altitude as an input parameter for the inversion. Therefore, only the components of the secondary field are used for the inversion based on a pseudo-layer half-space model (Fraser 1978) in order to calculate both the apparent resistivity

(or half-space resistivity) ρa, which is the inverse of the apparent conductivity, and the apparent distance Da of the sensor from the top of the conducting half-space. The apparent distance Da can be greater or smaller than the measured sensor altitude h. The difference of both, which is called apparent depth da = Da – h is positive in case of a resistive cover (including air) as it is the case in Figure 4.6.2; otherwise a conductive cover exists above a more resistive substratum. From the apparent resistivity and the apparent depth, the centroid depth (Fig. 4.6.2) z* = da + pa/2 with pa = 505.3 (ρa/f)

1/2, which is a measure of the mean penetration of the induced underground currents (Siemon 2001), can be derived. Each set of half-space parameters is obtained individually at each of the HEM frequencies and at each of the sampling points of a flight line.

Fig. 4.6.2: HEM data inversion: I) homogeneous half-space model, II) layered half-space model (for a five-frequency data set).

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The model parameters of the 1-D inversion (cf. Fig. 4.6.2) are the resistivities ρ and thicknesses t of the model layers (the thickness of the underlying half-space is assumed to be infinite). There are several procedures for the inversion of HEM data available (e.g. Qian et al. 1997, Fluche & Sengpiel 1997, Beard & Nyquist 1998, Ahl 2003, Huang & Fraser 2003) which are often adapted from algorithms developed for ground EM data. We use the Marquardt-Levenberg inversion procedure which searches the smoothest model fitting the data (Sengpiel & Siemon 1998, 2000). Due to huge number of inversion models to be calculated in an airborne survey, it is necessary to generate the starting model required for the Marquardt inversion automatically. The standard model contains as many layers as frequencies used plus a highly resistive cover layer (Fig. 4.6.3).

Fig. 4.6.3: Derivation of the starting model: The layer resistivities ρ are set equal to the apparent resistivities ρa, the layer boundaries are chosen as the logarithmic mean of each two neighbouring centroid depth values z*. The thickness of the top layer is derived from the apparent depth da of the highest frequency used for the inversion as long as it is greater than a minimum depth value (e.g. 1 m). Otherwise the minimum depth value is used.

The inversion procedure is stopped when a given threshold is reached. This threshold is defined as the differential fit of the modelled data to the measured HEM data. We normally use a 10 % threshold; i.e., the inversion stops when the enhancement of the fit is less than 10 %.

4.6.4 What can you expect as results?

The HEM results are generally presented as maps and vertical resistivity sections (VRS). The maps display, e.g., the half-space parameters apparent resistivity and centroid depth or the resistivities derived from the 1-D inversion results for certain model layers or at several depth or elevation levels. An example is shown in Figure 4.6.4. The VRS – also based on the 1-D inversion results – are produced along the survey lines. The vertical sections are constructed by placing the resistivity models for every sounding point along a survey profile next to each other using the topographic relief as base line in metre above mean sea level (m asl). The altitude of the HEM bird, the misfit of the inversion, and the HEM data are plotted above the resistivity models (Fig. 4.6.5). The helicopter-borne survey between the estuaries of the Elbe and Weser rivers was surveyed in 2000/2001 (Siemon et al. 2004) and 2004 (Siemon et al. 2005) in order to map glacial melt-water channels and saltwater intrusions. The morphology of the survey area is described by wet marshlands just above sea level and smooth sand ridges called “Geest” with elevations of ten to thirty metres above sea level. Figure 4.6.4 displays the apparent resistivity at a frequency of 8.6 kHz. The central area between the marshlands to the west and north is characterised by elevated apparent resistivity values (ρa > 65 Ωm, orange/red) associated with freshwater saturated sands. Several linear, conductive features (ρa = 10–65 Ωm, light blue/green/yellow) can be ascribed to channels incised by glacial melt-water during Pleistocene glacial regression epochs. The most prominent one is the SSW–NNE striking Bremerhaven-Cuxhaven channel. These channels were subsequently filled with coarse sands and gravels in the bottom and mostly silt and clayish materials in the upper parts forming ideal freshwater aquifers that are often well protected against pollution. The maximum total thickness of the channel fillings is in the order of 300 m (Kuster & Meyer 1979) with several ten metres

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Fig. 4.6.4: Example for an apparent resistivity map of a coastal area in NW Germany. The survey was flown in three parts: the dashed lines mark the margins of the Cuxhaven, Bremerhaven, and Hadeln survey areas. The solid black line shows the location of profile 218.1 (see Fig. 4.6.5) and the solid light blue lines display the Quaternary base (after Kuster & Meyer 1995).

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Fig. 4.6.5: Example for a vertical resistivity section (VRS): From top to bottom, the inphase and out-of-phase (quadrature) values of the HEM data [ppm] at five frequencies (f1–f5), the 1-D resistivity models [Ωm] using the topographic relief [m asl] as base line, and the misfit of the inversion q [%] are displayed. The altitude of the HEM sensor is plotted above the resistivity models.

thick clay layers at their top, referred to as cover or lid clays which are covered by about 30–60 m thick Pleistocene sediments. The conductive response of the lid clays indicates the existence of buried melt-water channels. Very low apparent resistivities are associated with saltwater (ρa < 1 Ωm, dark blue) and saltwater saturated sediments (ρa < 10 Ωm, blue). The resistivity section in Figure 4.6.5 shows the results of the 1-D inversion of five-frequency HEM data collected along survey line 218.1. This line runs WNW–ESE and is approximately half way between the cities of Cuxhaven and Bremerhaven (cf. Fig. 4.6.4). From top to bottom, Figure 4.6.5 displays the inphase (R) and quadrature (Q) HEM data, the resistivity section, and the relative misfit of the 1-D inversion. The dotted line above the resistivity models indicates the HEM sensor elevation in metres above mean

sea level [m asl]. The ground elevation is obtained as the difference between the sensor elevation and the radar/laser altitude of the bird above ground level. Between profile-km 12 and 15, a pair of melt-water channels (buried valleys) has been identified due to the conductive properties of the lid clays (pilot area Cuxhavener Rinne Chap. 5.5). It can also be noted that the penetration depth of the HEM system is reduced within these melt-water channels because of the lid clays, i.e., the induced eddy currents may not have reached the bottom of the buried valley. The occurrence and the lateral extent of the buried valleys have reliably been located by the HEM system (see Fig. 4.6.5) as was confirmed by comparison with existing boreholes and ground geophysics (Gabriel et al. 2003).

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4.6.5 Resolution/depth penetration

HEM measurements are suitable for high-resolution surveys as the line separation can be arbitrarily chosen and the point distance along line is about 4 m. Taking the HEM footprint which depends on the sensor altitude (Beamish 2003) into account, line separations less than 50 m are only meaningful if the sensor altitude is very low (h << 30 m). For standard survey conditions with sensor altitudes of about of 30 – 50 m, single conductors closer than about 50 m are not resolvable. On the other hand the along-line data is over sampled providing information about the noise on the data that can easily be reduced by applying low-pass filters. Due to the skin-effect (high frequency currents are flowing on top of a perfect conductor) the plane-wave skin depth of the HEM fields increase with decreasing frequency and increasing underground resistivity. Therefore, the apparent resistivities derived from high-frequency HEM data describe the shallower parts of the conducting subsurface and the low-frequency ones the deeper parts. The starting models for the 1-D inversion take care of the maximum exploration depth because the deepest layer boundary is derived from the centroid depth belonging to the lowest frequency. Model simulations showed that the deepest layer boundary of the starting model can be chosen as deep as 1.5 × z*max. Typical maximum exploration depth values (fmin = 0.38 kHz) range from about 10 m (sea water) over 50 m (clay) and 150 m (freshwater saturated sand) to more than 200 m (dry sand or bedrock). 4.6.6 Restrictions, uncertainties, error

sources and pitfalls

Helicopter-borne electromagnetics is a very useful method for surveying large areas in order to support hydrogeological investigations. Due to the dependency of the geophysical parameter electrical conductivity on both the mineralization of the groundwater and the clay content, information on water quality and aquifer characteristics, respectively, can be derived from HEM data. The results, however, are sometimes ambiguous: A clayey low permeable layer in a freshwater environment and a brackish, sandy

aquifer are associated with similar conductivities. Therefore, additional information, e.g., from drillings, is necessary for a sound hydrogeological interpretation of the HEM data. In addition to the geogenic contribution to the secondary fields measured over densely populated areas, there is often an anthropogenic contribution from buildings and electrical installations etc. Generally, these have little influence on the HEM data and the data can be corrected using the standard data processing tools. In some cases, e.g., large buildings with a high metal content, the anthropogenic components in the HEM data are no longer negligible. This can be seen particularly in the lower frequency data because the geogenic contribution to the secondary fields is comparatively smaller than at higher frequencies, i.e., although the anthropogenic source is situated at or close to the surface, the effect is projected to greater depths. Anthropogenic sources cause lower resistivities and associated depths pretending conductors like clay layers which do not exist. Low resistivities and low depths often correlate with towns or streets, particularly for the lower frequency data. Stitching the 1-D resistivity models together to construct a vertical resistivity section, the conducting layers appear to descend on either side of the anthropogenic source. Thus such three-dimensional effects cannot be interpreted adequately by the layered half-space model used. Such anthropogenic influences can be detected in HEM data due to their typical shape or by correlation with magnetic data. A topographic map of the survey area, an analysis of the video film or an on-site inspection can help identify such sources. As the HEM sensor is a moving object, its position is not constant with respect to the Earth’s surface, i.e., pitch and roll effects, which affect both the EM data and the altitude data, may occur. Generally, these effects are negligible, but strong bird movements due to heavy winds or abrupt helicopter manoeuvres may cause remarkable effects. Therefore, the HEM data has to be interpreted carefully at places where the bird altitude changes strongly, e.g., when crossing a power line, or the line path is winding.

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The 1-D inversion uses a number of layers that is close the number of frequencies used, i.e. the number of input parameters (data) is close to the number of output parameters (model) leading to slightly overconstrained or underdetermined equation systems. This ill-posed inversion problem is solved using a regularisation that provides smoother models the more model layers are used. Consequently, as many conductors may be resolved as possible, but on the other hand the model parameters, particularly the layer boundaries, may be weakly determined. 4.6.7 Discussion and recommendations

Diverse case studies (Eberle & Siemon 2006) demonstrate that multi–frequency airborne EM is an easy, fast and cost-effective tool to identify buried valleys and to delineate their lateral extent under various geological and climatic conditions. Indicative geological markers are either conductive cover layers or conductive fills in resistive bedrock or incisions in conductive host filled with resistive materials. Internal layering of the fills will be reflected within the depth of investigation of the HEM system used. The 1-D inversion is standard tool for modelling HEM data and proves to be fairly successful in reflecting buried valleys though they are at least two-dimensional features. Multi-dimensional modelling, e.g., Avdeev et al. (1998), Chernyavskiy & Zhdanov (2002), Newmann & Alumbaugh (1995), Sasaki (2001), Xiong & Tripp (1995), or Zhang (2003) might be required in cases where peripheral zones of buried valleys need more detailed investigation. Helicopter-borne electromagnetic measurements are suitable for high-resolution surveys as long as the targets are seated not far deeper than 100 m. In that case, ground-based or airborne time-domain measurements are more suitable. 4.6.8 References

Ahl A (2003): Automatic 1D inversion of multifrequency airborne electromagnetic data with artificial neural networks: discussion and case study. – Geophysical Prospecting 51: 89–97.

Avdeev DB, Kuvshinov AV, Pankratov OV, Newman GA (1998): Three-dimensional frequency-domain modelling of airborne electromagnetic responses. – Exploration Geophysics 29: 111–119.

Beamish D (2003): Airborne EM footprints. – Geophysical Prospecting 51: 49–60.

Beard LP, Nyquist JE (1998): Simultaneous inversion of airborne electromagnetic data for resistivity and magnetic permeability. – Geophysics 63: 1556–1564.

Chernyavskiy A, Zhdanov MS, (2002): Fast 3-D inversion of helicopter-borne electromagnetic data using spectral Lanczos decomposition method. – Proceedings of 2002 CEMI Annual Meeting, 339–382.

Eberle DG, Siemon B (2006): Identification of buried valley using the BGR helicopter-borne geophysical system. – Near Surface Geophy-sics (accepted to be published in April 2006).

Fluche B, Sengpiel K-P (1997): Grundlagen und Anwendungen der Hubschrauber-Geophysik. – In: Beblo, M. (ed) Umweltgeophysik, Ernst und Sohn, Berlin, pp 363–393.

Fraser DC (1978): Resistivity mapping with an airborne multicoil electromagnetic system. – Geophysics 43: 144–172.

Gabriel G, Kirsch R, Siemon B, Wiederhold H. (2003): Geophysical investigation of Pleistocene valleys in Northern Germany. – Journal of Applied Geophysics 53: 159–180.

Huang H, Fraser DC (1999): Airborne resistivity data levelling. – Geophysics 64: 378–385.

Huang H, Fraser DC (2003): Inversion of helicopter electromagnetic data to a magnetic conductive layered earth. – Geophysics 68: 1211–1223.

Kuster H, Meyer KD (1979): Glaziäre Rinnen im mittleren und nordöstlichen Niedersachsen. – Eiszeitalter und Gegenwart 29: 135–156.

Kuster H, Meyer KD (1995): Karte der Lage der Quartärbasis in Niedersachsen und Bremen 1:500000. – Niedersächsisches Landesamt für Bodenforschung, Hannover.

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Newmann GA, Alumbaugh DL (1995): Frequency-domain modelling of airborne electromagnetic responses using staggered finite differences. – Geophysical Prospecting 43: 1021–1041.

Qian W, Gamey TJ, Holladay JS, Lewis R, Abernathy D (1997): Inversion of airborne electromagnetic data using an Occam technique to resolve a variable number of multiple layers. – Proceedings from the High-Resolution Geophysics Workshop, Laboratory of Advanced Subsurface Imaging (LASI), Univ. of Arizona, Tucson, CD-ROM.

Sasaki Y (2001): Full 3D inversion of electromagnetic data on PC. – Journal of Applied Geophysics 46: 45–54.

Sengpiel K-P, Siemon B (1998): Examples of 1-D inversion of multifrequency AEM data from 3-D resistivity distributions. – Exploration Geophysics 29: 133–141.

Sengpiel K-P, Siemon B (2000): Advanced inversion methods for airborne electromagnetic exploration. – Geophysics 65: 1983–1992.

Siemon B (2001): Improved and new resistivity-depth profiles for helicopter electromagnetic data. – Journal of Applied Geophysics 46: 65–76.

Siemon B (2006): HEM data processing and interpretation at BGR. – Extended Abstracts Book, AEM Workshop Hannover 2006: Airborne EM – Recent Activities and Future Goals: 45–49.

Siemon B, Eberle DG, Binot F (2004): Helicopter-borne electromagnetic investigation of coastal aquifers in North-West Germany. – Zeitschrift für Geologische Wissenschaften 32: 385–395.

Siemon B, Rehli H-J, Voß W, Pielawa J (2005): Ergebnisse der Hubschraubergeophysik im Bereich der Hadelner Marsch 2004, Technischer Bericht. – BGR–Report, Hannover.

Valleau N (2000): HEM data processing – a practical overview. – Exploration Geophysics 31: 584–594.

Wait JR (1982): Geo-electromagnetism. – Academic Press, New York.

Xiong Z, Tripp AC (1995): Electromagnetic scattering of large structures in layered earth using integral equations. – Radio Science 30: 921–929.

Zhang Z, (2003): 3D resistivity mapping of airborne EM data. – Geophysics 68: 1896–1905.