Conversion between measures using Schlumberger and Wenner Soil resistivity

measured volume

the conversion between values measured using schlumberger , wenner methods possible in approximate way. in cases, both wenner , schlumberger methods electrode spacing between currents probe corresponds depth of soil investigation , measured apparent soil resistivity referred soil volume in figure.

the current tends flow near surface small probe spacing, whereas more current penetrates deeper soil large spacing. resistivity measured given current probe spacing represents, first approximation, apparent resistivity of soil depth equal spacing.

if apparent soil resistivity measured schlumberger method ρe (with corresponding electrode spacing , c) given, assuming soil resistivity refers volume in figure a=l/3 follows:

r

w


=



ρ

e



2
⋅
π
⋅

a

w








{\displaystyle r_{w}={\frac {\rho _{e}}{2\cdot \pi \cdot a_{w}}}\,}

with

a

w


=




a

s


+
2
c

3





{\displaystyle a_{w}={\frac {a_{s}+2c}{3}}\,}

where:

rw = equivalent wenner resistance (Ω)

aw = equivalent electrode spacing wenner method (m)

as = electrode spacing between voltages probe schlumberger method (m)

c = electrode spacing between voltages , currents probe schlumberger method (m)

if measured schlumberger resistance given, before calculating apparent soil resistivity following factor must calculated:

ρ

e


=

π




c
⋅
(
c
+

a

s


)


a

s





r

s





{\displaystyle \rho _{e}={\pi }{\frac {c\cdot (c+a_{s})}{a_{s}}}r_{s}\,}

the wenner method used method measuring soil resistivity electrical grounding (earthing) purposes. schlumberger method developed increase voltage signal earlier, less sensitive instruments, placing potential probes closer current probes.

the soil resistivity measurements affected existing nearby grounded electrodes. buried conductive objects in contact soil can invalidate readings made methods described if close enough alter test current flow pattern. particularly true large or long objects.