A RECONCILIATION OF MATHEMATICAL MODELS FOR SPONTANEOUS MINERALIZATION POTENTIALS¹

Abstract

Two methods for computing spontaneous mineralization potentials in the region external to the source body are reviewed. The first of these is a long‐established technique in which the causation is assumed to be a distribution of simple current source on the boundary of the mineralization. The second is a more recent technique which assumes a surface distribution of current dipole moment (double layer) along the boundary of the source body. The former technique is a special case of a more general spontaneous potential (SP) model in which the source is a density of current dipole moment (current polarization) distributed throughout the mineralization. As far as the potentials in the region external to the source body are concerned this current polarization can be simply related to an equivalent double layer source function, i.e. the potential discontinuity produced over the boundary of the mineralization by an equivalent double layer model. This simple relationship suggests an integral equation technique for the exact numerical solution of boundary value problems appropriate to the polarization model for spontaneous mineralization potentials. The technique is applied to exploring the justification of interpreting mineralization self‐potentials by the traditional approach.

The hydroelectric problem of porous rocks: inversion of the position of the water table from self-potential data

“…Using the definition of the unit normal vector to the step surface, n δ( z − h ) =∇ H ( z − h ), one then obtains through standard manipulations (e.g. Furness 1992, 1993; Sobolev 1989) The boundary condition for the electrical potential at the ground surface and the construction of the Green's function ensure that the last term in at the Earth's surface vanishes. After some algebraic manipulations, yields where the potential is defined to an additive constant of integration and where is a drop in the electric potential through the interface ∂Ω.…”

“…Using the definition of the unit normal vector to the step surface, nδ(z − h) = ∇ H (z − h), one then obtains through standard manipulations (e.g. Furness 1992Furness , 1993Sobolev 1989)…”

“…The most important SP anomalies (several hundreds of mV) are redox in nature and associated with ore deposits (e.g. Furness 1992, 1993) and contaminant plumes (Naudet et al 2003). Hydrothermal systems also generate strong SP anomalies associated with the vorticities of the convection pattern (e.g.…”

A new method of quantitative interpretation of SP anomalies produced by a polarized inclined sheet1

“…SP anomalies at the ground surface are usually interpreted in terms of the dipolar charge distribution of various and rather simple geometries collectively named 'polarization models' (Furness 1993). A thin rod, a polarized sphere, an inclined sheet and a polarized horizontal cylinder are the models most commonly employed and the interpretation procedures are usually treated in the space domain.…”

“…The equations describing this effect are numerically solved for regions inside and outside the ore body. Furness (1993) uses the term " double-layer model " and states that the " polarization model " can describe quite successfully the SP field due to the ore body and that the SP curves of both models may have essentially the same shape. We believe that the doublelayer model can help significantly in understanding the production mechanism of the mineralization SP anomalies, as well as in describing the behaviour of the SP curve in drill holes.…”