THE SMOOTH SOUNDING GRAPH. A Manual for Field Work ... - BGR

1. Basic rules
4
The first chapter deals with the fundamentals of direct current resistivity
measurements. The attempt was made to give an elementary introduction
into what really happens within the earth during a measurement. The
physical process should be understood by the reader.
Each physical parameter will be checked with respect to its influence on
the measured data. This will be done by reducing mathematical formulae
to a minimum. A well-trained mathematician will sometimes have a bad
feeling seeing the rigorous way of using mathematical "tools". But this
manual is written for a field crew working with modern equipments on the
earth’s surface. Going on step by step in recording data they should follow
up in mind the subsurface process, i.e. they should know what they are
really doing.
One remark should be added: In the theoretical part of this chapter only
one very simple integral appears. The authors would be very glad if read-
ers could make any proposal to get rid of this integral in explaining the
necessary background of direct current resistivity sounding.
1.1. Ohm's Law
Geo-electrical measurements are carried out on the earth's surface. The
air space is assumed as an insulator and the earth's surface as a plane.
The underground is an electrical conductor. A direct current is running
from the surface through this conductive infinite half-space, limited above
by the plane earth's surface. Which laws are valid for this current flow
through the underground?
Regarding electrical currents we generally are accustomed to think of a
wire. A wire has a certain resistance which can be calculated from Ohm's
law. We regard (see Fig.1) a wire of the length a, measured in meters [m]
with a cross-section q, measured in [m 2 ]. Ohm's law then can be written
as
U
I
a
= R = ρ
(1)
q