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 log₁₀ (a_w / a_mf) , ;#;

where

and a_w and a_mf are the 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 log₁₀ (R_mfe / R_we)

where R_mfe and R_we are the equivalent resistivities of mud filtrate and formation water, respectively. For NaCI solutions which are not too saline, R_mfe = R_mf and R_we = R_w; 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_m), shale of resistance (R_sh), and a sandstone of resistance (R_ss), then

SSP = IR_m + IR_sh + IR_ss

where the measured SP is IR_m.