Open AccessPotential representation by independent configurations on a multi‐electrode array
Author(s) -
Lehmann Holger
Publication year - 1995
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1995.tb01822.x
Subject(s) - electrode , inversion (geology) , set (abstract data type) , representation (politics) , inverse , electrode array , section (typography) , algorithm , computer science , mathematics , geometry , physics , geology , paleontology , quantum mechanics , structural basin , politics , political science , law , programming language , operating system
SUMMARY Multi‐electrode arrays are finding increasing attention in DC electrical probing. A new proof is presented showing that only L ( L ‐ 3)/2 linearly independent four‐electrode arrangements exist within a set of L electrodes. This basic set then serves to synthesize all other four‐electrode configurations. I introduce an experimentally stable basic set and show how any configuration, which has not been measured, can be obtained by a linear combination of at most six elements. This allows, for instance, the presentation of the data in terms of a Schlumberger pseudo‐section, without actually having measured all the required data. A particular measured data set is interpreted using simplified 2‐D inversion, and the resulting inverse model is compared with the corresponding pseudo‐section.