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deposits, the exploration boreholes may be sparsely spaced for two major reasons: (1) the attributed grades do not tend to vary significantly across the deposit; (2) the overall exploration costs must be minimized. However, since the geological contact between the ore and underlying waste unit fluctuates in a rather complex manner, one should not rely solely on the interpolation of the sparselyspaced borehole data, as the estimates would not reflect the actual variability in the surface. Therefore, it is imperative that the sparselyspaced borehole data be supplemented with appropriate geophysical information for more accurate resource estimations (Erten et al., 2015, 2013). Ground-penetrating radar (GPR) has widely been used to acquire a complementary dense data-set to better delineate the interface between two geological units (bauxite/ferricrete) (Francke and Nobes 2000; Francke and Parkinson 2000; Watts 1997). Due to the tropical weathering and leaching mechanisms that generate lateritetype deposits, the geological interface measured through GPR appears to be well correlated with the easting (X) and northing (Y) coordinates of the surface, which indicates the presence of a spatial trend (McLennan, Ortiz, and Deutch, 2006; Leuangthong, Lyall, and Deutsch, 2002). Geostatistical techniques are the main tools which are used to estimate the elevation of the interface at non-sampled locations, and there are different approaches used to account for the trend in a data-set. In this paper, we estimate the elevation of the geological interface through ordinary kriging (OK), universal kriging (UK), intrinsic random function of order k (RF-k) methods and compare the estimation performances. Geostatistical techniques are based on the theory of regionalized variables (RVs) and are used to estimate an attribute of interest at non-sampled locations (Goovaerts, 1997; Journel and Huijbregts, 1978). The idea behind the theory is that a RV z(u ),{ +1,...,n} is considered to be the realization of an ordertwo random function (RF) Z(u) and is assumed to have been generated according to a probability density function (Matheron, 1971; Olea, 1974). Due to this characteristic of the RV, there is a spatial correlation between the samples, which allows the prediction of Z*(u) at each non-sampled location u. The prediction of Z*(u) requires the covariance function C(h) of Z(u) to be known, and this statistical inference can practically be made from an available realization if the realization Accounting for a spatial trend in finescale ground-penetrating radar data: a comparative case study

Accounting for a spatial trend in fine-scale ground-penetrating radar data: a comparative case study