Unmanned Airborne Magnetic and VLF Investigations: Effective Geophysical Methodology for the Near Future
Lev Eppelbaum, Arie Mishne
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DOI: 10.4236/pos.2011.23012   PDF    HTML     7,972 Downloads   16,106 Views   Citations

Abstract

Airborne geophysical investigations are now recognized as a powerful tool for geological-geophysical mapping, mineral prospecting, environmental assessments, ecological monitoring, etc. Currently, however, there are two main drawbacks to effective application of these investigations: (a) the difficulty of conducting geophysical surveys at low altitudes, (b) heightened danger for the aircraft crew, especially in regions with a rugged topography. Unmanned or so-called Remote Operated Vehicles (ROV) surveys are not bound by these limitations. The new unmanned generation of small and maneuvering vehicles can fly at levels of a few (even one) meters above the Earth’s surface, and thus follow the relief, while simultaneously making geophysical measurements. In addition, ROV geophysical investigations have extremely low exploitation costs. Finally, measurements of geophysical fields at different observation levels can provide new, unique geological-geophysical information. This chapter discusses future geophysical integration into ROV of measurements of magnetic and VLF electromagnetic fields. The use of GPS with improved wide-band Kalman filtering will be able to provide exact geodetic coordinates. A novel interpreting system for complex environments is presented that includes non-conventional methods for localizing targets in noisy backgrounds, filtering temporary variations from magnetic and VLF fields, eliminating terrain relief influence, quantitative analysis of the observed anomalies and their integrated examination. This system can be successfully applied at various scales for analysis of geophysical data obtained by ROVs to search for useful minerals, geological mapping, the resolution of many environmental problems, and geophysical monitoring of dangerous geological phenomena.

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Eppelbaum, L. and Mishne, A. (2011) Unmanned Airborne Magnetic and VLF Investigations: Effective Geophysical Methodology for the Near Future. Positioning, 2, 112-133. doi: 10.4236/pos.2011.23012.

1. Introduction

The first airborne geophysical survey was carried out by Logachev in the former Soviet Union in 1936 [1]. He used an inductor magnetometer to measure the magnetic field from an aircraft. This first air-magnetometer had a sensitivity of about 100 nT. By contrast, current aeromagnetic surveys in conventional vehicles can provide an accuracy of 5 nT and higher [2]. Salem et al. [3] described an equivalent source approach that removes small environmental noise from the airborne measurements. Tezkan et al. [4] reported a recent pilot project that tested the feasibility of unmanned aircraft systems to carry out aeromagnetic surveys. Advances in reduced size and maneuverability of Remote Operated Vehicles (ROV) have led to an accuracy of 0.5 - 1 nT (and higher) in surveys at low altitudes. The main advantages of ROVs are the absence of an aircraft crew (GPS controlled unmanned surveys can be carried out even at very low altitudes and in risky conditions) and comparatively low expenditures for geophysical observation projects. In addition, most methods of geophysical field analysis require knowledge of the field distribution at different levels over the Earth’s surface. The ROV facilitates the collection of these data without having to use transformation methods. Finally, unmanned air geophysical surveys are extremely cheap (many tens of times less than conventional aircraft surveys).

A magnetic field is natural, and a Very Low Frequency (VLF) field can be considered to be quasi-natural [5] (given that perhaps several dozen VLF transmitters in the world radiate electromagnetic waves almost continuously). Combined aircraft magnetic/VLF measurements are potentially highly effective (e.g., [6-11]), but the highflying altitudes of conventional aircraft have limited the possibilities of using VLF. The ROV application can substantially reduce the distance between the airborne vehicle and the target while preserving the main advantages of conventional surveys. Thus the two main advantages of ROVs are their low cost and the fact that they are unmanned and hence do not put crew at risk.

ROV geophysical surveys at low altitudes can make important contributions to the search for minerals, geological mapping, various environmental (including archeological-geophysical) investigations, and military monitoring [4,12-17]. To increase the amount of data retrieved on such missions, new algorithms for the processing and interpretation of magnetic/VLF fields have been developed, especially for complex physical-geological conditions (mainly presented in [18]) including inclined magnetization (polarization), rugged terrain relief, unknown level of the normal field and a variety of anomalous sources.

Despite the progress in geophysical inertial navigation systems [19-21], etc., small ROVs flying at low altitudes are not sufficiently precise. The improved Kalman filtering with wide-band noise model presented here is designed to eliminate some of the obstacles to precise navigation.

2. Improved Kalman Filtering for Precise Vehicle Navigation

Kalman filtering (KF) is one of the most widely used methods for optimal estimation of random processes. The KF algorithm is the best linear real-time recursive filtering algorithm and is used to solve optimal filtration problems for non-stationary and multidimensional systems [22-24]. However, the conventional Kalman filter is limited by the fact that KF uses white noise and that the useful signal and noise are independent. However, these limitations are a mathematical idealization that gives an approximate description of real noise. In fact, the actual noise is marked by a property that ensures the correlation of its values within a small time interval; i.e. if we denote this noise by j, then

, (1)

where is a small value.

The first attempts to introduce wide-band noise into the KF model to solve navigation problems in geophysics were carried out by Eppelbaum et al. [25].

The basic idea behind the method consists of modeling physical wide-band noise in the form of a distributed delay of the mathematical noise, i.e.

, , (2)

where w is the white noise, = const > 0, and F is the deterministic function. If cov[w(t), w(s)] = (t – s), then cov[,] = 0 with s ³ and

(3)

with 0 £ s <, i.e. is the stationary wide-band noise.

In geophysical practice, forms of wideband noise can be expressed by autocovariance functions. Therefore, the problem involves modeling wideband noise in the form of (2), when the autocovariance function is given.

Let the wideband noise have the autocovariance function (1), i.e., the function is known. Then from Equation (3) it follows that for to be modeled in the form of Equation (2) must satisfy the equation [26]:

=, 0 £ s £. (4)

Equation (4) is a convolution equation. It can be solved by direct and inverse Fourier or Laplace transforms. Application of the abovementioned approach can thus enhance the precision of GPS navigation in ROVs.

3. Airborne Magnetic Data Analysis in Complex Environments

3.1. Elimination of Temporary Magnetic  Variations

The accuracy of a high-precision ROV magnetic survey should not exceed the value of 1 nT. At the same time, the presence of both natural (basalts, diabases, gabbro, etc.) and artificial (iron and iron-containing) objects that have high magnetization may cause secondary variation effects which can be seen above this value. Conventional procedures for eliminating temporary (primary) magnetic variations are based on the trivial additive expression (e.g., [27]):

, (5)

where t is the time, x, y are the spatial coordinates, DT (x, y, t) is the magnetic field recorded along a profile, is the sum of “useful” anomalies and is the sum of the noise component caused by temporary variations. This formula only allows for simple subtracttion of the noise component from the observed magnetic field and cannot be used to calculate the effect of seconddary variations.

Since the secondary variation effect depends linearly on the intensity of the primary variations [28], the typical model of magnetic observations may be described in the following way [29]:

(6)

where are the field variations in time, is the sum of the effects from the anomalous objects and geological inhomogeneities of the medium with regard to their dependence on the field variations.

Measurements at the points of the profile made at different times t (³2) make it possible to obtain a solvable set of algebraic equations so that the signal DT can be extracted with sufficient accuracy.

3.2. Calculation of Terrain Relief Influence and Estimation of Magnetization of the Medium

Another disturbance factor is the influence of inclined relief on the magnetic measurements (the illustration here is limited to the case where the ROV follows the relief forms). Interestingly, this disturbance can help estimate the average magnetization of the medium.

It is well known that in the case of direct magnetization, the field maxima correspond to ridges of the “magnetic” relief, while the minima correspond to its valleys [27,30]. At the same time, the terrain relief effect is generally two-fold and can be attributed to the effect of the form and physical properties of the topographic bodies making up the relief and secondly to the effect of the slope of the observation line (profile), which causes variations in the distance from the field recording point to the target of excitation [18]. The correlation technique below (see Equations (7)-(9)) eliminates the effect of the first component. The second effect can be eliminated by using special expressions during the quantitative interpretation of magnetic anomalies [18].

An analytical approach [18] shows the possibility of obtaining the linear relation between the magnetic field and the height of observation to a typical element of rugged relief—a slope (an inclined ledge, or step). All the main relief forms can be approximated with the use of one or another combination of slopes (for each of these slopes, the correlation field can be constructed). Hence, as rough as it may be, there is a simple and effective method for eliminating the effect of magnetized rock relief. To apply this method, a correlation field is constructed between DT (total magnetic field) and h (height of observation) values. For typical cases the correlation field is used to determine the terrain correction:

, (7)

where DT is the magnetic field, and b and c are the factors of a linear equation computed using the least-square method (LSM).

It was shown that a b factor could be utilized to estimate the magnetization of the upper part of a geological section [18]:

, (8)

where I is the magnetization of the upper part of geological section, a is the acute angle between the slope face and horizon, R is the slope length across the strike.

Given that a and R are known from the field observations and coefficient b is calculated using the LSM, the I value is easy to determine. Consequently, magnetic lowaltitude measurements along the inclined slopes may be used for quick estimation of the magnetization of the target medium. Eppelbaum [31] concluded that integrated ROV horizontal and inclined observations can serve to obtain the parameters of the medium magnetization even over a flat relief.  

The corrected field DTcorr may be formulated as:

, (9)

where DTobser is the observed field.

Elimination of the topographic effect by the correlation technique allows practically complete smoothing out of the anomalies caused by the influence of uneven relief.

Along with the linear approximation of the relationship between the field and the height, approximations in the form of the square trinomial (parabolic equation) are appropriate here. This method can be used to improve the choice of the level for reducing the field to one plane. When computing a correlation field, the areas with the largest dispersion (compared to the averaging line), correspond to the profile intervals under which the disturbing bodies are situated. The presence of dispersion in itself is indicative of a hidden inhomogeneity in the section.

3.3. Initial Analysis of Magnetic Data

Visual analysis of magnetic anomalies is one of the most important steps in an investigation and all further stages may depend on the results of this initial decision-making. The standard principles of magnetic map analysis are presented in Table 1. However, for oblique magnetization (polarization), principles 3 - 7 are not applicable. The shape of the anomalies is complicated by the horizontal component effect. This is why in the northern hemisphere, anomalies become asymmetric when the body’s magnetization is parallel to the Earth’s field. Thus, anomaly maxima of sublatitudinal-oriented bodies are

Table 1. Common principles of magnetic map analysis (developed for vertical positive redundant magnetization) (after [18], with modifications).

shifted southward, whereas the minimum is located in the northern periphery of the anomaly. If the magnetization inclination with respect to the horizon is not large (in southern latitudes), the maximum is shifted more to the south, and the intensity of the minimum increases. Inflection points (maximum gradients) in the anomaly plots are displaced southward from the projections of lateral sides of the anomalous body on the plane. In the case of a depth-limited body, one of the minima (the southern one) may disappear along the maximum periphery. In the case of three-dimensional bodies of approximately isometric section, magnetic anomaly distortions occur not only due the inclination of the magnetization vector to the horizon plane, but also due to the difference in orientation of the horizontal magnetization projection with respect to the body’s axes [32]. Therefore, the analysis of graphs is not sufficient, and generally maps need to be analyzed as well.

3.4. Advanced Quantitative Interpretation of Magnetic Anomalies

One of the main interpretation problems is the quantitative determination of magnetic anomalies (inverse problem solution). The interpretation problem consists of a detailed description of the anomalous source using the measured magnetic field. However, the major principles of quantitative interpretation that were formalized for vertical magnetization do not work under conditions of oblique magnetization in low and central latitudes. Besides the influence of oblique magnetization, additional DT anomaly distortions occur due to rugged (inclined) relief and unknown level of the normal magnetic field.

This stage involves the application of rapid methods for quantitative interpretation of magnetic anomalies to construct an initial model of the geological section. Unlike certain conventional techniques [27,33-37], the methods presented below are applicable in conditions of rugged terrain topography and arbitrary magnetization of objects where the normal field level is unknown [18].

In conditions of oblique magnetization, the “reduction to pole” calculation of “pseudogravimetric” anomalies [38] is often used. However, this procedure is only suitable when all the anomalous bodies in the area under study are magnetized parallel to the geomagnetic field, and simultaneously when the bodies have subvertical dipping. The magnetic fields can only be recalculated correctly when these restrictions are adhered to; this yields graphs that are symmetrical, and further interpretation using conventional methods can be carried out. Similar approaches based on the transformation of the observed magnetic field (for instance, analytic signal [39]), have the same limitations.

The methodology developed for complex environments [18] employs further modifications of the characteristic point method, the tangent method and the areal method, and utilizes the most commonly applied geometric models such as thin inclined bed (TIB), horizontal circular cylinder (HCC) and thick bed (TB) (a comprihensive explanation of these methods is given in [18]). These three geometric models, with different modifications, may be used for approximation and the corresponding quantitative interpretation of anomalies generated by various geological and environmental objects.

The procedures for interpreting anomalies generating the abovementioned models are presented in Tables 2-4.

The modern interpreting system developed for magnetic field analysis [18,40,41] includes the following components (besides the conventional ones): 1) Elimination of the secondary effect of time variations, 2) Calculation of the terrain relief influence and estimation of magnetization of the medium, 3) Application of an information-heuristic approach to geophysical field quailtative interpretation, 4) Inverse problem solution for complex environments (inclined relief, oblique magnetization and unknown level of the normal magnetic field), 5) 3-D modeling of magnetic (and gravity, if necessary) field. In the last 6) stage all kinds of information obtained in the previous stages (1-5) and conventional steps are integrated, and a final physical-geological model is developed.

The first stage of a ROV magnetic survey must include a priori investigation (generalization) of all available

Table 2. Formulae for quantitative interpretation of magnetic anomalies over anomalous bodies approximated by thin seam and a horizontal circular cylinder using the improved characteristic point method (after [18], with modifications).

magnetic properties of the targets and the surrounding medium. Figure 1 depicts a typical flow chart for aeromagnetic field analysis.

The following parameters are taken from the anomaly plot in the characteristic point method (Figure 2): d1 = difference of semiamplitude point abscissae, d2 = difference of extremum abscissae, d5 = difference of inflection point abscissae.

In the tangent method four tangents are employed: two horizontal lines with respect to the anomaly extrema and two inclined lines passing through the points of the bend on the leftand right-hand branches of the anomaly plot. The following terms are taken from the plot (Figure 2): d3 = difference in abscissae of the points of intersection

Table 3. Formulae for quantitative interpretation of magnetic anomalies over anomalous bodies approximated by thin seam and horizontal circular cylinder using the improved tangent method (after [18], with modifications).

Table 4. Formulae for quantitative interpretation of magnetic anomalies over anomalous bodies approximated by a thin bed and horizontal circular cylinder using the improved characteristic areal method [42].

of an inclined tangent with horizontal tangents on one branch; d4 = the same on the other branch (d3 is selected from the plot branch with conjugated extrema), d6 = interval between d3 and d4, d8 = difference in abscissae between point of intersection of left inclined tangent with lower horizontal tangent and inflection point on left branch (d6 and d8 are used for the model of thick bed only). A detailed description of magnetic field examination of a thick bed model is given in [18].

The areal method is based on calculation of separate areas limited by the anomalous curve, horizontal line and two vertical lines crossing some singular points at the anomalous curve.

When anomalies are observed on an inclined profile, the obtained parameters characterize a fictitious body. The transition from fictitious body parameters to those of

Figure 1. A generalized flow chart for airborne magnetic field analysis.

the real body is done by applying the following expressions (the subscript “r” stands for a parameter of the real body):

, (10)

where h is the depth of the body upper edge occurrence (or HCC center), xo is the shifting of the anomaly maximum from the projection of the center of the disturbing body to the Earth’s surface (caused by oblique magnetization), and wo is the angle of the terrain relief inclination (wo > 0 when the inclination is toward the positive direction of the x-axis).

Figure 3 illustrates the application of these methods— improved tangents and characteristic points (Figure 3(a)) and characteristic areal method (Figure 3(b))—for the airborne magnetic field analysis in the Big Somalit (southern slope of the Greater Caucasus).

Conflicts of Interest

The authors declare no conflicts of interest.

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