Introduction to ground surface self-potential tomography

A new approach to self-potential (SP) data interpretation for the recognition of a buried causative SP source system is presented. The general model considered is characterized by the presence of primary electric sources or sinks, located within any complex resistivity structure with a flat air-earth boundary. First, using physical considerations of the nature of the electric potential generated by any arbitrary distribution of primary source charges and the related secondary induced charges over the buried resistivity discontinuity planes, a general formula is derived for the potential and the electric field component along any fixed direction on the ground surface. The total effect is written as a sum of elementary contributions, all of the same simple mathematical form. It is then demonstrated that the total electric power associated with the standing natural electric field component can be written in the space domain as a sum of cross-correlation integrals between the observed component of the total electric field and the component of the field due to each single constitutive elementary charge. By means of the cross-correlation bounding inequality, the concept of a scanning function is introduced as the key to the new interpretation procedure. In the space domain, the scanning function is the unit strength electric field component generated by an elementary positive charge. Next, the concept of charge occurrence probability is introduced as a suitable function for the tomographic imaging of the charge distribution geometry underground. This function is defined as the cross-correlation product of the total observed electric field component and the scanning function, divided by the square root of the product of the respective variances. Using this physical scheme, the tomographic procedure is described. It consists of scanning the section, through any SP survey profile, by the unit strength elementary charge, which is given a regular grid of space coordinates within the section, at each point of which the charge occurrence probability function is calculated. The complete set of calculated grid values can be used to draw contour lines in order to single out the zones of highest probability of concentrations of polarized, primary and secondary electric charges. An extension to the wavenumber domain and to three-dimensional tomography is also presented and discussed. A few simple synthetic examples are given to demonstrate the resolution power of the new SP inversion procedure.