Static spontaneous potential. The maximum SP that would be recorded when the SP electrode passes from a position well inside a very thick, porous, permeable [[clean]] sand (or other reservoir rock) to a point well within a thick shale. The static spontaneous potential given by the sum of the components of the [[electrochemical potential]] is:

;#;
SSP = –K log<sub>10</sub> (a<sub>w</sub> / a<sub>mf</sub>) ,
;#;

where

 
{{:terms:p91f2.gif}}

and a<sub>w</sub> and a<sub>mf</sub> are the [[activity|activities]] of the [[formation water]] and [[mud filtrate]], respectively. Because of the inverse relationship between activity and equivalent resistivity in dilute solutions, this equation is approximated by

SSP = –K log<sub>10</sub> (R<sub>mfe</sub> / R<sub>we</sub>)

where R<sub>mfe</sub> and R<sub>we</sub> are the equivalent resistivities of mud filtrate and formation water, respectively. For NaCI solutions which are not too saline, R<sub>mfe</sub> = R<sub>mf</sub> and R<sub>we</sub> = R<sub>w</sub>; for more concentrated solutions, an activity correction should be made. Since the static SP in a sandstone is equal to the [[potential]] causing current (I) to flow in a mud column of resistance (R<sub>m</sub>), [[shale]] of resistance (R<sub>sh</sub>), and a sandstone of resistance (R<sub>ss</sub>), then

SSP = IR<sub>m</sub> + IR<sub>sh</sub> + IR<sub>ss</sub>

where the measured SP is IR<sub>m</sub>.