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We fitted the Weiner Process model to the apparent resistivities for each frequency/altitude combination to get a mean apparent resistivity over the sets of five replications.
The estimated posterior mean apparent resistivity μ(d) is shown as a solid black line and the raw data as coloured lines.
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The black line represents the modelled mean in apparent resistivity for the Weiner Process model detailed in Section "Approach 1 - Weiner process".
The quantitative interpretation of the VES curves is hampered by the well-known principle of equivalence, which means that different resistivity models can generate practically the same apparent resistivity curve.
An apparent resistivity is calculated from a resistance value and geometric factors that account for the electrode spacing configuration.
In spite of the large site-to-site variation in the synthetic site gain of nearly one order of magnitude (two orders of magnitude in terms of the static shift in the apparent resistivity), its estimation error by the mean apparent ssq site gains is as small as only a few percent.
Even in the absence of a site gain, the Berdichevsky average causes downward bias in the apparent resistivity as compared with those from the regional mean 1D conductivity profile ((sigma _{text {R}} z))) defined by Eqs.
The first approach involves fitting a single statistical model where the apparent resistivity for each frequency/altitude combination is given an overall mean modelled as a continuous time random walk (a Weiner Process, e.g. [14]) in distance, together with a random effect for replicate.
The electrical resistivity method though may be plagued with ambiguities and uncertainties in interpretation, provides an economical and reliable means to identify and delineate the subsurface characteristics/properties through the measurement of apparent resistivity (Batayneh 2009; Muchingami et al. 2012; Ebong et al. 2014; Okiongbo and Mebine 2015).
In Approach 1 we model the response as coming from an underlying mean process which we set as a Weiner Process to capture the variability in apparent resistivity along the transect.
When the vertical fracture intersects the borehole, which means that the distance from the fracture to the center of borehole is less than 0.1 m, the apparent resistivity is significantly small and a positive separation occurs between the deep and shallow resistivities.
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