Abstract
This chapter describes the physical environment where measurements will be made. It then presents the electromagnetic properties of the concerned media (electrical conductivity, magnetic permeability and dielectric permittivity) depending on the characteristics of seawater and subsoil rocks (facies, lithology). It then discusses the frequency and temporal aspects of the detection method depending on the propagation media and the background noise in the deep sea (several \( \mathrm{p}\mathrm{V}/\mathrm{m}/\sqrt{\mathrm{Hz}} \)). It defines in substance the skin effect, the energy attenuation, the investigation depth, the magnitude of the amplitudes of the fields accessible to measurement (about 1 \( \upmu \mathrm{V}/\mathrm{m}/\sqrt{\mathrm{Hz}} \) or, if normalized, about 10−12 V/A.m2), the signal-to-noise ratio and the modes and propagation/diffusion conditions in the presence or absence of oil. Then it proposes data acquisition systems to establish the intrinsic characteristics of the measuring instruments and especially the power of the transmitters and the receptor sensitivity. This chapter ends with a description of optimal conditions of detection and favorable field procedures.
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Notes
- 1.
An increase in accuracy (see note below) can only be effective if the quantity to be measured is well defined at each point where the determination is made.
- 2.
Minerals such as arsenides and sulphides have the two conductivity types, which do not make them good conductors.
- 3.
The conductivity of minerals is more complex to understand.
- 4.
Porous and permeable rocks have resistivities that may very significantly differ depending on the nature of the fluids contained therein. For example, sands containing oil or gas will have a much larger resistivity than those containing salt water. Moreover, if we consider that the resistivity is part of a more macroscopic concept (volume including the notions of stratum, bench, layer, etc.), the resistivity at a given temperature then depends on three basic factors, which are the lithologic character, the amount of present pore water and the mineralization of the latter.
- 5.
The hydrostatic pressure is given by the formula: p = hρg where h is the height of water, ρ is the volumic mass of water (1028 kg/m3) and g is the value of the acceleration of gravity (9.81 m/s2). Depending on the case, it is expressed in bars, Pa or psi. Whenever it sinks 10 m, the pressure increases a bar. At 4000 m deep, the pressure is equal to 40 MPa (5800 psi).
- 6.
- 7.
The first temperature measurements at sea and in deep water date from the end of the eighteenth century (1785–1788 campaigns of the Venus).
- 8.
- 9.
This factor is to link the shape of the pores and their degree of connection. For round grains (sand), m is equal to 1.4, while for the tabular grains (clay), the m value increases to 1.9. For fractured rocks, m can rise to 2.5.
- 10.
For oil and gas, the n values respectively are 2.08 and 1.162.
- 11.
They are also used in industry as an electrical insulator (e.g., in transformers).
- 12.
The deposit water contains salts and ions in solution (Cl−, Na+, Ca2+, Mg2+, K+), dispersed colloids and dissolved gases (N2, CO2 and CH4). The main characteristics of the deposit water come from their primary and secondary origin (Robert 1959).
- 13.
The Archie and Humble formulas, used for the exploitation of electric logs, admit higher values for exponents m and n (close to 2). This leads us to assign to the reservoirs resistivity values much lower than those observed on electrical logs (Serra 2004). The anisotropy of the geological layers is one of the reasons partly invoked to explain these differences. The factors m and n are described in detail in the technical literature, and more particularly the one concerned with logs.
- 14.
Research led in the context of underwater detection and published as monographs by the US Navy Underwater Sound Laboratory also relating the EM studies (Bannister 1980).
- 15.
Distance at which the amplitude of the wave is equal to 36.8 % of the amplitude Eo, ie \( {E}_{\mathrm{o}}={\mathrm{e}}^{-\frac{k}{\sqrt{2}}\ \updelta}={E}_{\mathrm{o}}/ e \) being the base of natural logarithms and corresponding to ln(e) = or to exp(1) = e. This number may be defined as: \( e=\mathrm{l}\underset{n\to\ \infty }{\mathrm{im}\ {e}_n}=2,718281.... \) with e n = 1/0! + 1/1! + 1/2! + .... + 1/n!
- 16.
In various nonmagnetic sedimentary grounds, μr varies from 1 to 1.00001, and can be then considered as a constant (≈1).
- 17.
Ampere/Maxwell’s law implicitly involves a duality between two types of current. At low frequencies, in the conductors, conduction currents are predominant, whereas in the higher frequencies (σ/ωε ≪ 1), i.e., those that are above the light spectra, the movement currents predominate. In DC, investigation depth and penetration depth are then equivalent (no skin effect) and among other things depend on the geometry of the acquisition device (the distance between the electrodes of the injection device particularly). These concepts were defined for the first time in 1938 (Evjen 1938) then supplemented by many authors (Guérin 2007).
- 18.
Unique field independent of the distance.
- 19.
The electric field is distributed according to the same law.
- 20.
See Chap. 5.
- 21.
See Chap. 4.
- 22.
Phenomenon not yet exploited. In seismic exploration, in the 1960s, a similar technique was proposed to directly assess the thicknesses of the sedimentary layers.
- 23.
See also Kraichman (1976).
- 24.
Theory of images modified in a infinite conducting half space.
- 25.
Polar coordinates (r, θ) reported in Cartesian coordinates.
- 26.
For dialing (1, 2, 3, 4, 5) see diagram (see Fig. 3.19a ).
Fig. 3.19 
In the presence of a water reservoir, waves and energy are directly transmitted (σe ≈ σs). No wave is refracted and reflected. There is no upgoing wave; the transmission is complete
- 27.
An overview of this process is presented in the thesis of L. Loseth (2007).
- 28.
We call Green’s function, denoted G, the elementary solution of a linear differential equation or a partial derivative equation with constant coefficients. In electromagnetism, the solution is obtained using a single source (pulse or Dirac delta or δ). The general solution corresponding to the actual source is then equivalent to the superposition of impulse responses, that is to say, corresponding to the Green functions. These functions may take varied forms as, for example, analytic functions when the solution of the homogeneous differential equation is known, or an infinite series of orthogonal functions then satisfying the boundary conditions when the solution of the equation is unknown.
- 29.
Vector that indicates the direction and the sense of propagation of an electromagnetic wave. The modulus of the Poynting vector (P ≈ E∧H) corresponds to a flux, power per area unit (Skilling 1942).
- 30.
The potential vector is a mathematical tool that allows us, by introducing additional functions, to simplify the calculation procedures for the evaluation of magnetic and electric fields. For example, the fields are calculated from the potentials (specified sources), solutions of the Helmholtz equation.
- 31.
The Lorenz gauge decouples differential equations on the vector and scalar potential and then gives rise to a general solution using Green’s functions.
- 32.
Other authors have developed solutions in an infinite medium (Chave and Cox 1982).
- 33.
When the study of one of its parameters by either method produces the same result, the function is called ergodic.
- 34.
Generally these latter correspond to epiphenomena restricted in time.
- 35.
In marine exploration this could be the case above basaltic horizons or salt domes, diapirs, gas hydrates, etc. In the 1970s, very low frequency devices were proposed (Duroux 1974).
- 36.
See Chap. 4, devoted to instrumentation.
- 37.
Not to be confused with electrometer calibration, which is done on the surface ship before immersion (cf. Sect. 6.7).
- 38.
Accuracy is evaluating the absence of errors e (e = measured value – actual value). When the latter are present, the equation becomes Q e = f (P) + e, e = Q – Q e
There are two kinds of errors: time-independent (static) errors and time-dependent (dynamic) errors, which respectively are in the form e S = g(Q), e = g(Q, t)
The coherent noise is, for example, a case of dynamic error. However, there are random variations related to the environment that can only be treated by statistical methods. The arithmetic average of a finite number N of measurements is then:
$$ \overline{Q}=\frac{1}{N}{\displaystyle \sum_{i = 1}^N{Q}_i} $$The errors affecting the accuracy mainly come from the sensors, the processing and the location of the instruments (T/R). Errors can also be classified into systematic, random or accidental errors and mathematically defined. More simply, an absolute error is defined as the difference between the measurement and the true value, and a relative error as the ratio of the absolute error to the true or measured value.
- 39.
The anodes only debit when there is a loss of electrical insulation; steel is then in contact with seawater (Sainson 2007).
- 40.
Campaign led by the LETI (Commissariat for Atomic Energy) in the Mediterranean in July 1991.
- 41.
Additional measurements simultaneously realized on land.
- 42.
The means of propulsion of the ship, the shaft and propeller especially, produce (by their more or less regular rotation in sea water) alternating currents that are variable on the fundamental frequencies and their harmonics (hash of the lines of force static → modulation of the currents → BF variable fields).
- 43.
After determining the characteristic frequencies (captures and measures), electromagnetic signatures are obtained by modeling (solving Maxwell’s equations).
- 44.
Effect demonstrated for the first time in 1879 by British scientists of the Post Office Telegraph Services (Mathias et al. 1924) and seriously studied from the late 1950s (Parkinson 1959, 1962; Coquelle and Mosnier 1969; Filloux 1967; Cox and Filloux 1974; Larsen 1975; Le Mouel and Menvielle 1976; Mosnier 1977).
- 45.
EM seabed logging has not been considered practically in its principle without the help of sophisticated methods of interpretation, particularly those involving data inversion methods that have emerged in practice in the last decade. Without the latter, which require the provision of additional external information (including seismic data), the measures could not take all their senses.
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Sainson, S. (2017). Metrology and Environment. In: Electromagnetic Seabed Logging. Springer, Cham. https://doi.org/10.1007/978-3-319-45355-2_3
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