24 2 Introductory Remarks
the equation ∇
2
F=γ
2
F where F stands for magnetic field, electric field,
vector potentials and or scalar potential. γ is the propagation constant
(see Chap. 12). For γ = 0, i.e., for zero frequency, the Helmholtz equation
changes to a Laplace equation. So electromagnetic field is a non-Laplacian
field.
(4) A large number of non-Laplacian potentials exist and are being used by the
geophysicists. These potentials are known a s self-potentials and they are of
electrochemical and electrokinetic origin. Potentiometers used for measur-
ing Laplacian potentials can also mea sure these self-potentials. Important
members of this family are (i) liquid junction potential, (ii) membrane
potential, (iii) oxidation-reduction potential, and (iv) electrode potential
of electrochemical origin and (i) streaming potential, (ii) eletrofiltration
potential and (iii) thermal potentials of electrokinetic origin. A source
of energy is required to generate these potentials. In the case of direct
current field a battery or a g enerator is used to create the field. For self-
potentials, electrochemical cells are generated within the earth to sustain
the flow of current for a long time. These electrochemical cells originate
at the contact of the two different electrolytes o f different chemical activ-
ities or they may be at different oxidation-reduction environment. These
redox cells of oxidation-reduction origin sustain flow of current across an
ore body for many years In any thermodynamic system there is always
some free energy which can be easily converted into work. Some poten-
tials are generated when one form of energy is converted into another
form of energy. For example, mechanical energy is converted into electri-
cal energy for generation of streaming p otential in a fractured rock zone
inside a borehole. Due to maintenance of high pressure in a borehole, the
mud filtrate enters into the formations through fractures and generates
streaming potentials. For electrofiltration potentials, gr avitational energy
is converted into electrical energy. When fluid moves through a porous
medium under a gravity gradient, the potentials are developed and can
be measured. Thermal gradients in a geothermal area generate potentials
where thermal energy is converted to a n electrical energy. Geothermal
gradient cells are created. These potentials satisfy Nerst equation, Han-
derson’s equation and Oxidation-Reduction equations. They form a big
group of non-Laplacian potentials. Self-potentials as such is a major topic
in geophysics and fairly lengthy discussion is necessary to do any justice
to this topic.
2.2.10 Type J Classification
(i) Global field
(ii) Local field
Gravity field is a g lobal field, which is present in the entire universe. It includes
different stars, planets and satellites. Magnetic field of the earth and earth’s