Abstract
Charge distributions were modeled in a three‐dimensional domain, 10 km on each side, by placing point charges in a 200 × 200 × 100 m grid. Charge locations were based on electric field soundings and the one‐dimensional approximation to Gauss's law. The model calculates the electric field due to all the point charges and their corresponding image charges using Coulomb's law. Vertical electric fields from the model are not significantly different from the observed fields and are also nearly identical to fields resulting from infinitely extensive charge layers. These findings show that Gauss's law in one dimension is a valid method for approximating the charge density of finite layers. The model vertical electric fields are almost equivalent for charge regions that are reduced in x and y dimensions from 10 km to 6 km. Thus, extending charge layers for as little as 3 km on either side of the sounding location sufficiently reproduces the entire field when typical, observed charge densities are used. For a vertical path 1 km from the edge of the 10 × 10 km model domain, the calculated vertical electric field is reduced by less than 10% from its value through the center of the domain. This finding means that the observed electric field profile can be far from the center of the charge layers and still allow a good approximation of the their charge densities and depths. Relatively large changes (factor of about 5) in charge density over relatively short (less than about 2 km) horizontal distances are needed to produce observed magnitudes of horizontal electric fields.
Published Version
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