3-D synthetic near surface data set with frequency-domain electromagnetic induction data

Realistic three-dimensional exhaustive data set that mimics a near surface mining landfill deposit of waste fine-shaly sands. The data set is composed by petrophysical properties and frequency domain electromagnetic induction (FDEM) data and was created with the purpose of testing algorithms for near-surface modeling and characterization using electromagnetic data.

The set of petrophysical properties include porosity, water saturation, particle density and density. Each property corresponds to a single geostatistical realization. The three-dimensional model has a dimension of 150 by 200 by 4 meters (i.e., length, width, depth) with a cell size of 0.5 m by 0.5 m by 0.1 m, respectively (grid size of 300 x 400 x 40). The model grid has 4.8 million cells.
Porosity and particle density were modelled based on samples of fine-shaly sands collected at a mine tailing in Portugal for which we investigated porosity, specific weight and particle density. The results of these investigations were used to generate three-dimensional models of subsurface rock properties with unconditional stochastic sequential simulation (Deutsch & Journel, 1998).
Porosity was modelled with an omnidirectional spherical variogram model in the horizontal direction. The variogram model has a horizontal range of 10 m, a vertical range of 1 m and a nugget effect of 0.2 % of the total variance of the data. This variogram model describes the expected spatial distribution of this property in the mine tailing.

To ensure plausibility between rock properties, particle density and water saturation models were generated with stochastic sequential co-simulation (Deutsch & Journel, 1998) conditioned to the porosity model. For particle density we imposed an omnidirectional spherical variogram model in the horizontal direction with a range of 10 m, a vertical range of 1 m and a nugget effect of 0.2 % of the total variance of the data, and the correlation between porosity and particle density from the lab measurements. For water saturation we imposed an omnidirectional spherical variogram model in the horizontal direction with a range of 16 m, a vertical range of 2 m and a nugget effect of 0.1 (%). For the co-simulation we imposed a correlation between porosity and water content, borrowed from Bhanbhro et al. (2013) and Dumont et al. (2016).

The pore fluid was defined as consisting in 80% of water and 20% of leachate, having a density of 0.99114 g/cm3 at a temperature of 30ºC (Souza et al., 2014). The density was mathematically calculated from porosity and particle density models and the density of the pore fluid by using a simple volumetric average of the geological material densities and its relationship to porosity (Mavko et al., 2009),  d_b = (1 - Ø) d₀ Ø d_fl  , where d₀ is the density of the mineral grains, d_fl is the density of the pore fluids, and Ø is porosity.

The electrical conductivity (EC) was created based on the well-known empirical relationship of Archie’s law (Archie, 1942). We first calculate electrical conductivity using the following equation, R_t = a S_w^-n Ø^-m R_w  , where a is the tortuosity constant, assumed as 0.88, S_w is the water saturation, n is the saturation exponent, assumed as 2, Ø is the porosity, m is the cementation exponent, assumed as 1.37, and R_w is the electrical resistivity of the pore fluid, assumed as 0.25. From the lithology and range of porosity values of the mining landfill model, the values of a, n and m were defined from Keller (1987). The electrical resistivity of the pore fluid was defined based on its composition and density (Keller, 1987). The EC was calculated based on Archie´s second law (Archie, 1942), where conductivity of the partially saturated rock (c_t) is the inverse of its resistivity (R_t),  c_t = 1 / R_t   (Mavko et al., 2009).

Since the relationship between magnetic minerals and the magnetic properties of the rocks depends primarily of the composition and grain size of them (Butler, 2005), the magnetic susceptibility (MS) was modelled using the common range of magnetic susceptibility for unconsolidated sediments (Hudson et al., 1999) with unconditional stochastic sequential simulation (Deutsch & Journel, 1998), imposing an omnidirectional spherical variogram model in the horizontal direction with a range of 20 m, a vertical range of 4 m and a nugget effect of 0.1 % of the total variance.

From the resulting three-dimensional models of EC and MS, we retrieved nine equally spaced boreholes along the same yz profile. These borehole data might be used as experimental data for modelling workflows, including geophysical inversion.

FDEM data, both the in-phase (IP) and quadrature-phase (QP), were calculated using a 1-D forward model (Hanssens et al., 2019). The acquisition configuration replicates one of the most common sensors for FDEM near-surface surveys, namely the DUALEM-421S (DUALEM Inc., Milton, Canada). It considers two loop-loop coil orientations, a horizontal coplanar (HCP) and a perpendicular one (PRP), with the normal 3 offsets per coil orientation for this equipment, 1, 2 and 4 meters for HCP, and 1.1, 2.1 and 4.1 meters for PRP, plus an extra offset per coil orientation, 10 meters for HCP and 10.1 meters for PRP, ensuring a theoretical larger depth of investigation. The FDEM data were calculated defining the operating frequency of the sensor as 9000 Hz, with an elevation to the surface of 0.15 m.