Constitutive relationships for electrochemical and thermoelectric cross-coupling coefficients are derived using ionic mobilities, applying a general derivative of chemical potential and employing the zero net current condition. The general derivative of chemical potential permits thermal variations which give rise to the thermoelectric effect. It also accounts for nonideal solution behavior. An equation describing electric field strength is similarly derived with the additional assumption of electrical neutrality in the fluid Planck approximation. The Planck approximation implies that self-potential (SP) is caused only by local sources and also that the electric field strength has only first order spatial variations. The derived relationships are applied to the NaCl-KCl concentration cell with predicted and measured voltages agreeing within 0.4 mV. The relationships are also applied to the Long Valley and Yellowstone geothermal systems. There is a high degree of correlation between predicted and measured SP response for both systems, giving supporting evidence for the validity of the approach. Predicted SP amplitude exceeds measured in both cases; this is a possible consequence of the Planck approximation. Electrochemical sources account for more than 90% of the predicted response in both cases while thermoelectric mechanisms account for the remaining 10%; electrokinetic effects are not considered. Predicted electrochemical and thermoelectric voltage coupling coefficients are comparable to values measured in the laboratory. The derived relationships are also applied to arbitrary distributions of temperature and fluid composition to investigate the geometric diversity of observed SP anomalies. Amplitudes predicted for hypothetical saline spring and hot spring environments are less than 40 mV. In contrast, hypothetical near surface steam zones generate very large amplitudes, over 2 V in one case. These results should be viewed with some caution due to the uncertain validity of the Planck approximation for these conditions. All amplitudes are controlled by electrochemical mechanisms. Polarities are controlled by the curvature of the concentration or thermal profile. Concave upward thermal profiles produce positive anomalies, for constant fluid concentrations, whereas concave upward concentration profiles produce negative anomalies. Concave downward concentration profiles are characterized by small negative closures bounding a larger, positive SP anomaly
